diff --git "a/annotations.json" "b/annotations.json"
--- "a/annotations.json"
+++ "b/annotations.json"
@@ -1,125094 +1,3 @@
-[
-  {
-    "id": 0,
-    "problem_id": 0,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/0.jpg"
-  },
-  {
-    "id": 1,
-    "problem_id": 1,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1.jpg"
-  },
-  {
-    "id": 2,
-    "problem_id": 2,
-    "problem": "line G J, line H G, line K J, line H K, line G J, line H G, line K J, line H K\nFind the measure of \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2.jpg"
-  },
-  {
-    "id": 3,
-    "problem_id": 3,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3.jpg"
-  },
-  {
-    "id": 4,
-    "problem_id": 4,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4.jpg"
-  },
-  {
-    "id": 5,
-    "problem_id": 5,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5.jpg"
-  },
-  {
-    "id": 6,
-    "problem_id": 6,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6.jpg"
-  },
-  {
-    "id": 7,
-    "problem_id": 7,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7.jpg"
-  },
-  {
-    "id": 8,
-    "problem_id": 8,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8.jpg"
-  },
-  {
-    "id": 9,
-    "problem_id": 9,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9.jpg"
-  },
-  {
-    "id": 10,
-    "problem_id": 10,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10.jpg"
-  },
-  {
-    "id": 11,
-    "problem_id": 11,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11.jpg"
-  },
-  {
-    "id": 12,
-    "problem_id": 12,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/12.jpg"
-  },
-  {
-    "id": 13,
-    "problem_id": 13,
-    "problem": "line Z Y, line Z X, line Y N X, line Z N, line Z Y, line Z X, line Y N X, line Z N\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/13.jpg"
-  },
-  {
-    "id": 14,
-    "problem_id": 14,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/14.jpg"
-  },
-  {
-    "id": 15,
-    "problem_id": 15,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/15.jpg"
-  },
-  {
-    "id": 16,
-    "problem_id": 16,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/16.jpg"
-  },
-  {
-    "id": 17,
-    "problem_id": 17,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/17.jpg"
-  },
-  {
-    "id": 18,
-    "problem_id": 18,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/18.jpg"
-  },
-  {
-    "id": 19,
-    "problem_id": 19,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/19.jpg"
-  },
-  {
-    "id": 20,
-    "problem_id": 20,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/20.jpg"
-  },
-  {
-    "id": 21,
-    "problem_id": 21,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/21.jpg"
-  },
-  {
-    "id": 22,
-    "problem_id": 22,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/22.jpg"
-  },
-  {
-    "id": 23,
-    "problem_id": 23,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/23.jpg"
-  },
-  {
-    "id": 24,
-    "problem_id": 24,
-    "problem": "line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C, line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/24.jpg"
-  },
-  {
-    "id": 25,
-    "problem_id": 25,
-    "problem": "line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C, line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/25.jpg"
-  },
-  {
-    "id": 26,
-    "problem_id": 26,
-    "problem": "line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C, line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/26.jpg"
-  },
-  {
-    "id": 27,
-    "problem_id": 27,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/27.jpg"
-  },
-  {
-    "id": 28,
-    "problem_id": 28,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/28.jpg"
-  },
-  {
-    "id": 29,
-    "problem_id": 29,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/29.jpg"
-  },
-  {
-    "id": 30,
-    "problem_id": 30,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/30.jpg"
-  },
-  {
-    "id": 31,
-    "problem_id": 31,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/31.jpg"
-  },
-  {
-    "id": 32,
-    "problem_id": 32,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/32.jpg"
-  },
-  {
-    "id": 33,
-    "problem_id": 33,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/33.jpg"
-  },
-  {
-    "id": 34,
-    "problem_id": 34,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/34.jpg"
-  },
-  {
-    "id": 35,
-    "problem_id": 35,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/35.jpg"
-  },
-  {
-    "id": 36,
-    "problem_id": 36,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/36.jpg"
-  },
-  {
-    "id": 37,
-    "problem_id": 37,
-    "problem": "line S P Q, line T P, line P R, \\odot P lieson T S R Q, line S P Q, line T P, line P R, \\odot P lieson T S R Q\nSolve for m \\widehat RQT in \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/37.jpg"
-  },
-  {
-    "id": 38,
-    "problem_id": 38,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/38.jpg"
-  },
-  {
-    "id": 39,
-    "problem_id": 39,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/39.jpg"
-  },
-  {
-    "id": 40,
-    "problem_id": 40,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/40.jpg"
-  },
-  {
-    "id": 41,
-    "problem_id": 41,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/41.jpg"
-  },
-  {
-    "id": 43,
-    "problem_id": 42,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the value of variable q in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/42.jpg"
-  },
-  {
-    "id": 44,
-    "problem_id": 43,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the value of variable q in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/43.jpg"
-  },
-  {
-    "id": 45,
-    "problem_id": 44,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/44.jpg"
-  },
-  {
-    "id": 46,
-    "problem_id": 45,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/45.jpg"
-  },
-  {
-    "id": 47,
-    "problem_id": 46,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/46.jpg"
-  },
-  {
-    "id": 48,
-    "problem_id": 47,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/47.jpg"
-  },
-  {
-    "id": 49,
-    "problem_id": 48,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/48.jpg"
-  },
-  {
-    "id": 50,
-    "problem_id": 49,
-    "problem": "line A C, line B C D, line C E, line A C, line B C D, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/49.jpg"
-  },
-  {
-    "id": 51,
-    "problem_id": 50,
-    "problem": "line A C, line B C D, line C E, line A C, line B C D, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/50.jpg"
-  },
-  {
-    "id": 52,
-    "problem_id": 51,
-    "problem": "line A C, line B C D, line C E, line A C, line B C D, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/51.jpg"
-  },
-  {
-    "id": 53,
-    "problem_id": 52,
-    "problem": "line K A M, line L M, line N M, line K L, line L A N, line K N, line K A M, line L M, line N M, line K L, line L A N, line K N\nQuadrilateral KLMN is a kite. What is m \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/52.jpg"
-  },
-  {
-    "id": 54,
-    "problem_id": 53,
-    "problem": "line A B C, line D B, line D C, line A B C, line D B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/53.jpg"
-  },
-  {
-    "id": 55,
-    "problem_id": 54,
-    "problem": "line A B C, line D B, line D C, line A B C, line D B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/54.jpg"
-  },
-  {
-    "id": 56,
-    "problem_id": 55,
-    "problem": "line A B C, line D B, line D C, line A B C, line D B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/55.jpg"
-  },
-  {
-    "id": 57,
-    "problem_id": 56,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If CF = 4x+1 and DF = x+13, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/56.jpg"
-  },
-  {
-    "id": 58,
-    "problem_id": 57,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If CF = 4x+1 and DF = x+13, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/57.jpg"
-  },
-  {
-    "id": 59,
-    "problem_id": 58,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/58.jpg"
-  },
-  {
-    "id": 60,
-    "problem_id": 59,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/59.jpg"
-  },
-  {
-    "id": 61,
-    "problem_id": 60,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/60.jpg"
-  },
-  {
-    "id": 62,
-    "problem_id": 61,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/61.jpg"
-  },
-  {
-    "id": 63,
-    "problem_id": 62,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/62.jpg"
-  },
-  {
-    "id": 64,
-    "problem_id": 63,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/63.jpg"
-  },
-  {
-    "id": 65,
-    "problem_id": 64,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/64.jpg"
-  },
-  {
-    "id": 66,
-    "problem_id": 65,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/65.jpg"
-  },
-  {
-    "id": 67,
-    "problem_id": 66,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/66.jpg"
-  },
-  {
-    "id": 68,
-    "problem_id": 67,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/67.jpg"
-  },
-  {
-    "id": 69,
-    "problem_id": 68,
-    "problem": "line A C F H, line E F G, line B C D, line A C F H, line E F G, line B C D\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/68.jpg"
-  },
-  {
-    "id": 70,
-    "problem_id": 69,
-    "problem": "line D B A, line A C, line B C, line D C, line D B A, line A C, line B C, line D C\nIf x = 14, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/69.jpg"
-  },
-  {
-    "id": 71,
-    "problem_id": 70,
-    "problem": "line S R, line T R, line T S, line S R, line T R, line T S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/70.jpg"
-  },
-  {
-    "id": 72,
-    "problem_id": 71,
-    "problem": "line S R, line T R, line T S, line S R, line T R, line T S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/71.jpg"
-  },
-  {
-    "id": 73,
-    "problem_id": 72,
-    "problem": "line S R, line T R, line T S, line S R, line T R, line T S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/72.jpg"
-  },
-  {
-    "id": 74,
-    "problem_id": 73,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/73.jpg"
-  },
-  {
-    "id": 75,
-    "problem_id": 74,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/74.jpg"
-  },
-  {
-    "id": 76,
-    "problem_id": 75,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/75.jpg"
-  },
-  {
-    "id": 77,
-    "problem_id": 76,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/76.jpg"
-  },
-  {
-    "id": 78,
-    "problem_id": 77,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/77.jpg"
-  },
-  {
-    "id": 79,
-    "problem_id": 78,
-    "problem": "line C B A, line D C, line D B, line C B A, line D C, line D B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/78.jpg"
-  },
-  {
-    "id": 80,
-    "problem_id": 79,
-    "problem": "line C B A, line D C, line D B, line C B A, line D C, line D B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/79.jpg"
-  },
-  {
-    "id": 81,
-    "problem_id": 80,
-    "problem": "line I E Y B D H, line G X Y Z K, line F A B C J, line I E Y B D H, line G X Y Z K, line F A B C J\nFind m \\angle CBY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/80.jpg"
-  },
-  {
-    "id": 82,
-    "problem_id": 81,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/81.jpg"
-  },
-  {
-    "id": 83,
-    "problem_id": 82,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/82.jpg"
-  },
-  {
-    "id": 85,
-    "problem_id": 83,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/83.jpg"
-  },
-  {
-    "id": 86,
-    "problem_id": 84,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/84.jpg"
-  },
-  {
-    "id": 87,
-    "problem_id": 85,
-    "problem": "line B C, line B D, line A C, line B A, line D C, line B C, line B D, line A C, line B A, line D C\nFind the value of a that would make the quadrilateral a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/85.jpg"
-  },
-  {
-    "id": 88,
-    "problem_id": 86,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle JKL of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/86.jpg"
-  },
-  {
-    "id": 89,
-    "problem_id": 87,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle JKL of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/87.jpg"
-  },
-  {
-    "id": 90,
-    "problem_id": 88,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle JKL of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/88.jpg"
-  },
-  {
-    "id": 92,
-    "problem_id": 89,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/89.jpg"
-  },
-  {
-    "id": 93,
-    "problem_id": 90,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/90.jpg"
-  },
-  {
-    "id": 94,
-    "problem_id": 91,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/91.jpg"
-  },
-  {
-    "id": 95,
-    "problem_id": 92,
-    "problem": "line A B, line C A D, line D E F, line C G F, \\odot B lieson A E G, line A B, line C A D, line D E F, line C G F, \\odot B lieson A E G\nFind the area of the circle. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/92.jpg"
-  },
-  {
-    "id": 96,
-    "problem_id": 93,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/93.jpg"
-  },
-  {
-    "id": 97,
-    "problem_id": 94,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/94.jpg"
-  },
-  {
-    "id": 98,
-    "problem_id": 95,
-    "problem": "line A D, line D E, line B E, line A B, line A C E, line B C D, line A D, line D E, line B E, line A B, line A C E, line B C D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/95.jpg"
-  },
-  {
-    "id": 99,
-    "problem_id": 96,
-    "problem": "line A D, line D E, line B E, line A B, line A C E, line B C D, line A D, line D E, line B E, line A B, line A C E, line B C D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/96.jpg"
-  },
-  {
-    "id": 100,
-    "problem_id": 97,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/97.jpg"
-  },
-  {
-    "id": 101,
-    "problem_id": 98,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/98.jpg"
-  },
-  {
-    "id": 102,
-    "problem_id": 99,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/99.jpg"
-  },
-  {
-    "id": 103,
-    "problem_id": 100,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/100.jpg"
-  },
-  {
-    "id": 104,
-    "problem_id": 101,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/101.jpg"
-  },
-  {
-    "id": 105,
-    "problem_id": 102,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/102.jpg"
-  },
-  {
-    "id": 106,
-    "problem_id": 103,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/103.jpg"
-  },
-  {
-    "id": 107,
-    "problem_id": 104,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/104.jpg"
-  },
-  {
-    "id": 108,
-    "problem_id": 105,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/105.jpg"
-  },
-  {
-    "id": 109,
-    "problem_id": 106,
-    "problem": "line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C, line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C\nFind the area of the regular polygon. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/106.jpg"
-  },
-  {
-    "id": 110,
-    "problem_id": 107,
-    "problem": "line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C, line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C\nFind the area of the regular polygon. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/107.jpg"
-  },
-  {
-    "id": 111,
-    "problem_id": 108,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/108.jpg"
-  },
-  {
-    "id": 112,
-    "problem_id": 109,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/109.jpg"
-  },
-  {
-    "id": 113,
-    "problem_id": 110,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/110.jpg"
-  },
-  {
-    "id": 114,
-    "problem_id": 111,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/111.jpg"
-  },
-  {
-    "id": 115,
-    "problem_id": 112,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/112.jpg"
-  },
-  {
-    "id": 116,
-    "problem_id": 113,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/113.jpg"
-  },
-  {
-    "id": 117,
-    "problem_id": 114,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/114.jpg"
-  },
-  {
-    "id": 118,
-    "problem_id": 115,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/115.jpg"
-  },
-  {
-    "id": 119,
-    "problem_id": 116,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/116.jpg"
-  },
-  {
-    "id": 120,
-    "problem_id": 117,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/117.jpg"
-  },
-  {
-    "id": 121,
-    "problem_id": 118,
-    "problem": "line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/118.jpg"
-  },
-  {
-    "id": 122,
-    "problem_id": 119,
-    "problem": "line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/119.jpg"
-  },
-  {
-    "id": 123,
-    "problem_id": 120,
-    "problem": "line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/120.jpg"
-  },
-  {
-    "id": 124,
-    "problem_id": 121,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/121.jpg"
-  },
-  {
-    "id": 125,
-    "problem_id": 122,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/122.jpg"
-  },
-  {
-    "id": 126,
-    "problem_id": 123,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/123.jpg"
-  },
-  {
-    "id": 127,
-    "problem_id": 124,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/124.jpg"
-  },
-  {
-    "id": 128,
-    "problem_id": 125,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/125.jpg"
-  },
-  {
-    "id": 129,
-    "problem_id": 126,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat BAD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/126.jpg"
-  },
-  {
-    "id": 130,
-    "problem_id": 127,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/127.jpg"
-  },
-  {
-    "id": 131,
-    "problem_id": 128,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/128.jpg"
-  },
-  {
-    "id": 132,
-    "problem_id": 129,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/129.jpg"
-  },
-  {
-    "id": 133,
-    "problem_id": 130,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/130.jpg"
-  },
-  {
-    "id": 134,
-    "problem_id": 131,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/131.jpg"
-  },
-  {
-    "id": 135,
-    "problem_id": 132,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/132.jpg"
-  },
-  {
-    "id": 136,
-    "problem_id": 133,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/133.jpg"
-  },
-  {
-    "id": 137,
-    "problem_id": 134,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/134.jpg"
-  },
-  {
-    "id": 138,
-    "problem_id": 135,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/135.jpg"
-  },
-  {
-    "id": 139,
-    "problem_id": 136,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/136.jpg"
-  },
-  {
-    "id": 140,
-    "problem_id": 137,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/137.jpg"
-  },
-  {
-    "id": 141,
-    "problem_id": 138,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/138.jpg"
-  },
-  {
-    "id": 142,
-    "problem_id": 139,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/139.jpg"
-  },
-  {
-    "id": 143,
-    "problem_id": 140,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/140.jpg"
-  },
-  {
-    "id": 144,
-    "problem_id": 141,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/141.jpg"
-  },
-  {
-    "id": 145,
-    "problem_id": 142,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/142.jpg"
-  },
-  {
-    "id": 146,
-    "problem_id": 143,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/143.jpg"
-  },
-  {
-    "id": 147,
-    "problem_id": 144,
-    "problem": "line A C D, line B C, line B A, line B D, line A C D, line B C, line B A, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/144.jpg"
-  },
-  {
-    "id": 148,
-    "problem_id": 145,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/145.jpg"
-  },
-  {
-    "id": 149,
-    "problem_id": 146,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/146.jpg"
-  },
-  {
-    "id": 150,
-    "problem_id": 147,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/147.jpg"
-  },
-  {
-    "id": 151,
-    "problem_id": 148,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/148.jpg"
-  },
-  {
-    "id": 152,
-    "problem_id": 149,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/149.jpg"
-  },
-  {
-    "id": 153,
-    "problem_id": 150,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/150.jpg"
-  },
-  {
-    "id": 154,
-    "problem_id": 151,
-    "problem": "line A B, line C B, line D B, line A D C, line A B, line C B, line D B, line A D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/151.jpg"
-  },
-  {
-    "id": 155,
-    "problem_id": 152,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nFind the measure of \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/152.jpg"
-  },
-  {
-    "id": 156,
-    "problem_id": 153,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/153.jpg"
-  },
-  {
-    "id": 157,
-    "problem_id": 154,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/154.jpg"
-  },
-  {
-    "id": 158,
-    "problem_id": 155,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/155.jpg"
-  },
-  {
-    "id": 159,
-    "problem_id": 156,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/156.jpg"
-  },
-  {
-    "id": 160,
-    "problem_id": 157,
-    "problem": "line A D, line A B C, line C E, line D E, line B D, line A D, line A B C, line C E, line D E, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/157.jpg"
-  },
-  {
-    "id": 161,
-    "problem_id": 158,
-    "problem": "line A D, line A B C, line C E, line D E, line B D, line A D, line A B C, line C E, line D E, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/158.jpg"
-  },
-  {
-    "id": 162,
-    "problem_id": 159,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/159.jpg"
-  },
-  {
-    "id": 163,
-    "problem_id": 160,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/160.jpg"
-  },
-  {
-    "id": 164,
-    "problem_id": 161,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/161.jpg"
-  },
-  {
-    "id": 165,
-    "problem_id": 162,
-    "problem": "line E D, line D C, line A B C, line E B, line E A, line E D, line D C, line A B C, line E B, line E A\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/162.jpg"
-  },
-  {
-    "id": 166,
-    "problem_id": 163,
-    "problem": "line E D, line D C, line A B C, line E B, line E A, line E D, line D C, line A B C, line E B, line E A\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/163.jpg"
-  },
-  {
-    "id": 167,
-    "problem_id": 164,
-    "problem": "line E D, line D C, line A B C, line E B, line E A, line E D, line D C, line A B C, line E B, line E A\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/164.jpg"
-  },
-  {
-    "id": 168,
-    "problem_id": 165,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/165.jpg"
-  },
-  {
-    "id": 169,
-    "problem_id": 166,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/166.jpg"
-  },
-  {
-    "id": 170,
-    "problem_id": 167,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/167.jpg"
-  },
-  {
-    "id": 171,
-    "problem_id": 168,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/168.jpg"
-  },
-  {
-    "id": 172,
-    "problem_id": 169,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/169.jpg"
-  },
-  {
-    "id": 173,
-    "problem_id": 170,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/170.jpg"
-  },
-  {
-    "id": 174,
-    "problem_id": 171,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/171.jpg"
-  },
-  {
-    "id": 175,
-    "problem_id": 172,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/172.jpg"
-  },
-  {
-    "id": 176,
-    "problem_id": 173,
-    "problem": "line D E F, line H G F, line D J G, line E J H, \\odot A lieson D H G E, line D E F, line H G F, line D J G, line E J H, \\odot A lieson D H G E\nFind m \\widehat DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/173.jpg"
-  },
-  {
-    "id": 177,
-    "problem_id": 174,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/174.jpg"
-  },
-  {
-    "id": 178,
-    "problem_id": 175,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/175.jpg"
-  },
-  {
-    "id": 179,
-    "problem_id": 176,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/176.jpg"
-  },
-  {
-    "id": 180,
-    "problem_id": 177,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/177.jpg"
-  },
-  {
-    "id": 181,
-    "problem_id": 178,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/178.jpg"
-  },
-  {
-    "id": 182,
-    "problem_id": 179,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/179.jpg"
-  },
-  {
-    "id": 183,
-    "problem_id": 180,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/180.jpg"
-  },
-  {
-    "id": 184,
-    "problem_id": 181,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/181.jpg"
-  },
-  {
-    "id": 185,
-    "problem_id": 182,
-    "problem": "line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R, line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R\nPolygon BCDE \\cong polygon RSTU. Find z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/182.jpg"
-  },
-  {
-    "id": 187,
-    "problem_id": 183,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/183.jpg"
-  },
-  {
-    "id": 188,
-    "problem_id": 184,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/184.jpg"
-  },
-  {
-    "id": 189,
-    "problem_id": 185,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/185.jpg"
-  },
-  {
-    "id": 190,
-    "problem_id": 186,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/186.jpg"
-  },
-  {
-    "id": 191,
-    "problem_id": 187,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/187.jpg"
-  },
-  {
-    "id": 192,
-    "problem_id": 188,
-    "problem": "line A B C D, line A B C D\nFind the length of DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/188.jpg"
-  },
-  {
-    "id": 193,
-    "problem_id": 189,
-    "problem": "line A B C D, line A B C D\nFind the length of DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/189.jpg"
-  },
-  {
-    "id": 194,
-    "problem_id": 190,
-    "problem": "line A B C D, line A B C D\nFind the length of DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/190.jpg"
-  },
-  {
-    "id": 195,
-    "problem_id": 191,
-    "problem": "line A B, line D E, line B C, line E F, line A D, line C F, line A B, line D E, line B C, line E F, line A D, line C F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/191.jpg"
-  },
-  {
-    "id": 196,
-    "problem_id": 192,
-    "problem": "line A B, line D E, line B C, line E F, line A D, line C F, line A B, line D E, line B C, line E F, line A D, line C F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/192.jpg"
-  },
-  {
-    "id": 197,
-    "problem_id": 193,
-    "problem": "line A B, line D E, line B C, line E F, line A D, line C F, line A B, line D E, line B C, line E F, line A D, line C F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/193.jpg"
-  },
-  {
-    "id": 198,
-    "problem_id": 194,
-    "problem": "line D B A, line D C, line B C, line D B A, line D C, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/194.jpg"
-  },
-  {
-    "id": 199,
-    "problem_id": 195,
-    "problem": "line D B A, line D C, line B C, line D B A, line D C, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/195.jpg"
-  },
-  {
-    "id": 200,
-    "problem_id": 196,
-    "problem": "line D B A, line D C, line B C, line D B A, line D C, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/196.jpg"
-  },
-  {
-    "id": 201,
-    "problem_id": 197,
-    "problem": "line S T, line S R, line T R, line S T, line S R, line T R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/197.jpg"
-  },
-  {
-    "id": 202,
-    "problem_id": 198,
-    "problem": "line S T, line S R, line T R, line S T, line S R, line T R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/198.jpg"
-  },
-  {
-    "id": 203,
-    "problem_id": 199,
-    "problem": "line S T, line S R, line T R, line S T, line S R, line T R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/199.jpg"
-  },
-  {
-    "id": 204,
-    "problem_id": 200,
-    "problem": "line S T, line S R, line T R, line S T, line S R, line T R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/200.jpg"
-  },
-  {
-    "id": 205,
-    "problem_id": 201,
-    "problem": "line A C B, line B F, line F H, line G H, line D G, line A D, line C E, line A C B, line B F, line F H, line G H, line D G, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/201.jpg"
-  },
-  {
-    "id": 206,
-    "problem_id": 202,
-    "problem": "line A C B, line B F, line F H, line G H, line D G, line A D, line C E, line A C B, line B F, line F H, line G H, line D G, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/202.jpg"
-  },
-  {
-    "id": 207,
-    "problem_id": 203,
-    "problem": "line A C B, line B F, line F H, line G H, line D G, line A D, line C E, line A C B, line B F, line F H, line G H, line D G, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/203.jpg"
-  },
-  {
-    "id": 208,
-    "problem_id": 204,
-    "problem": "line A C B, line B F, line F H, line G H, line D G, line A D, line C E, line A C B, line B F, line F H, line G H, line D G, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/204.jpg"
-  },
-  {
-    "id": 209,
-    "problem_id": 205,
-    "problem": "line A C B, line B F, line F H, line G H, line D G, line A D, line C E, line A C B, line B F, line F H, line G H, line D G, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/205.jpg"
-  },
-  {
-    "id": 210,
-    "problem_id": 206,
-    "problem": "line B A, line A D F, line F E, line B D E, \\odot C lieson B F E A, line B A, line A D F, line F E, line B D E, \\odot C lieson B F E A\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/206.jpg"
-  },
-  {
-    "id": 211,
-    "problem_id": 207,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/207.jpg"
-  },
-  {
-    "id": 212,
-    "problem_id": 208,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/208.jpg"
-  },
-  {
-    "id": 213,
-    "problem_id": 209,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/209.jpg"
-  },
-  {
-    "id": 214,
-    "problem_id": 210,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/210.jpg"
-  },
-  {
-    "id": 215,
-    "problem_id": 211,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/211.jpg"
-  },
-  {
-    "id": 216,
-    "problem_id": 212,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/212.jpg"
-  },
-  {
-    "id": 217,
-    "problem_id": 213,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/213.jpg"
-  },
-  {
-    "id": 218,
-    "problem_id": 214,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/214.jpg"
-  },
-  {
-    "id": 219,
-    "problem_id": 215,
-    "problem": "line Y B, line Y X, line B X, line Y B, line Y X, line B X\nSolve for m \\angle YBX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/215.jpg"
-  },
-  {
-    "id": 221,
-    "problem_id": 216,
-    "problem": "line Y B, line Y X, line B X, line Y B, line Y X, line B X\nSolve for m \\angle YBX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/216.jpg"
-  },
-  {
-    "id": 222,
-    "problem_id": 217,
-    "problem": "line Y B, line Y X, line B X, line Y B, line Y X, line B X\nSolve for m \\angle YBX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/217.jpg"
-  },
-  {
-    "id": 223,
-    "problem_id": 218,
-    "problem": "line P Q, line P R, line Q R, line P Q, line P R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/218.jpg"
-  },
-  {
-    "id": 224,
-    "problem_id": 219,
-    "problem": "line P Q, line P R, line Q R, line P Q, line P R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/219.jpg"
-  },
-  {
-    "id": 225,
-    "problem_id": 220,
-    "problem": "line P Q, line P R, line Q R, line P Q, line P R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/220.jpg"
-  },
-  {
-    "id": 226,
-    "problem_id": 221,
-    "problem": "line P Q, line P R, line Q R, line P Q, line P R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/221.jpg"
-  },
-  {
-    "id": 227,
-    "problem_id": 222,
-    "problem": "line P Q, line P R, line Q R, line P Q, line P R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/222.jpg"
-  },
-  {
-    "id": 228,
-    "problem_id": 223,
-    "problem": "line H F B A, line r lieson D B C, line s lieson E F G, line H F B A, line r lieson D B C, line s lieson E F G\nFind the value of x that makes line r \\parallel line s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/223.jpg"
-  },
-  {
-    "id": 229,
-    "problem_id": 224,
-    "problem": "line H F B A, line r lieson D B C, line s lieson E F G, line H F B A, line r lieson D B C, line s lieson E F G\nFind the value of x that makes line r \\parallel line s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/224.jpg"
-  },
-  {
-    "id": 230,
-    "problem_id": 225,
-    "problem": "line A Q, line Q B, \\odot Q lieson A B, line A Q, line Q B, \\odot Q lieson A B\nFind m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/225.jpg"
-  },
-  {
-    "id": 231,
-    "problem_id": 226,
-    "problem": "line A Q, line Q B, \\odot Q lieson A B, line A Q, line Q B, \\odot Q lieson A B\nFind m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/226.jpg"
-  },
-  {
-    "id": 232,
-    "problem_id": 227,
-    "problem": "line A Q, line Q B, \\odot Q lieson A B, line A Q, line Q B, \\odot Q lieson A B\nFind m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/227.jpg"
-  },
-  {
-    "id": 233,
-    "problem_id": 228,
-    "problem": "line A Q, line Q B, \\odot Q lieson A B, line A Q, line Q B, \\odot Q lieson A B\nFind m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/228.jpg"
-  },
-  {
-    "id": 234,
-    "problem_id": 229,
-    "problem": "line C D, \\odot D lieson C A B, line C D, \\odot D lieson C A B\nFind the perimeter of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/229.jpg"
-  },
-  {
-    "id": 235,
-    "problem_id": 230,
-    "problem": "line C D, \\odot D lieson C A B, line C D, \\odot D lieson C A B\nFind the perimeter of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/230.jpg"
-  },
-  {
-    "id": 236,
-    "problem_id": 231,
-    "problem": "line C D, \\odot D lieson C A B, line C D, \\odot D lieson C A B\nFind the perimeter of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/231.jpg"
-  },
-  {
-    "id": 237,
-    "problem_id": 232,
-    "problem": "line C D, \\odot D lieson C A B, line C D, \\odot D lieson C A B\nFind the perimeter of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/232.jpg"
-  },
-  {
-    "id": 238,
-    "problem_id": 233,
-    "problem": "line E J H, line G H, line F G, line F J, line F E, line E J H, line G H, line F G, line F J, line F E\nWhat is the area of trapezoid EFGH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/233.jpg"
-  },
-  {
-    "id": 239,
-    "problem_id": 234,
-    "problem": "line E J H, line G H, line F G, line F J, line F E, line E J H, line G H, line F G, line F J, line F E\nWhat is the area of trapezoid EFGH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/234.jpg"
-  },
-  {
-    "id": 240,
-    "problem_id": 235,
-    "problem": "line E J H, line G H, line F G, line F J, line F E, line E J H, line G H, line F G, line F J, line F E\nWhat is the area of trapezoid EFGH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/235.jpg"
-  },
-  {
-    "id": 241,
-    "problem_id": 236,
-    "problem": "line E J H, line G H, line F G, line F J, line F E, line E J H, line G H, line F G, line F J, line F E\nWhat is the area of trapezoid EFGH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/236.jpg"
-  },
-  {
-    "id": 242,
-    "problem_id": 237,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/237.jpg"
-  },
-  {
-    "id": 243,
-    "problem_id": 238,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/238.jpg"
-  },
-  {
-    "id": 244,
-    "problem_id": 239,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/239.jpg"
-  },
-  {
-    "id": 245,
-    "problem_id": 240,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/240.jpg"
-  },
-  {
-    "id": 246,
-    "problem_id": 241,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/241.jpg"
-  },
-  {
-    "id": 247,
-    "problem_id": 242,
-    "problem": "line A M L B, line C J B, \\odot D lieson N M L J, line A M L B, line C J B, \\odot D lieson N M L J\nFind m \\widehat JLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/242.jpg"
-  },
-  {
-    "id": 248,
-    "problem_id": 243,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/243.jpg"
-  },
-  {
-    "id": 249,
-    "problem_id": 244,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/244.jpg"
-  },
-  {
-    "id": 250,
-    "problem_id": 245,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/245.jpg"
-  },
-  {
-    "id": 251,
-    "problem_id": 246,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/246.jpg"
-  },
-  {
-    "id": 252,
-    "problem_id": 247,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/247.jpg"
-  },
-  {
-    "id": 253,
-    "problem_id": 248,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/248.jpg"
-  },
-  {
-    "id": 254,
-    "problem_id": 249,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/249.jpg"
-  },
-  {
-    "id": 255,
-    "problem_id": 250,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/250.jpg"
-  },
-  {
-    "id": 256,
-    "problem_id": 251,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/251.jpg"
-  },
-  {
-    "id": 257,
-    "problem_id": 252,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/252.jpg"
-  },
-  {
-    "id": 258,
-    "problem_id": 253,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/253.jpg"
-  },
-  {
-    "id": 259,
-    "problem_id": 254,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/254.jpg"
-  },
-  {
-    "id": 260,
-    "problem_id": 255,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/255.jpg"
-  },
-  {
-    "id": 261,
-    "problem_id": 256,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/256.jpg"
-  },
-  {
-    "id": 262,
-    "problem_id": 257,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/257.jpg"
-  },
-  {
-    "id": 263,
-    "problem_id": 258,
-    "problem": "line C A, \\odot C lieson A, line C A, \\odot C lieson A\nWhat is the circumference?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/258.jpg"
-  },
-  {
-    "id": 264,
-    "problem_id": 259,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/259.jpg"
-  },
-  {
-    "id": 265,
-    "problem_id": 260,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/260.jpg"
-  },
-  {
-    "id": 266,
-    "problem_id": 261,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/261.jpg"
-  },
-  {
-    "id": 267,
-    "problem_id": 262,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\n\\triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/262.jpg"
-  },
-  {
-    "id": 268,
-    "problem_id": 263,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\n\\triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/263.jpg"
-  },
-  {
-    "id": 269,
-    "problem_id": 264,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\n\\triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/264.jpg"
-  },
-  {
-    "id": 270,
-    "problem_id": 265,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\n\\triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/265.jpg"
-  },
-  {
-    "id": 271,
-    "problem_id": 266,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\n\\triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/266.jpg"
-  },
-  {
-    "id": 272,
-    "problem_id": 267,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/267.jpg"
-  },
-  {
-    "id": 273,
-    "problem_id": 268,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/268.jpg"
-  },
-  {
-    "id": 274,
-    "problem_id": 269,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/269.jpg"
-  },
-  {
-    "id": 275,
-    "problem_id": 270,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/270.jpg"
-  },
-  {
-    "id": 276,
-    "problem_id": 271,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/271.jpg"
-  },
-  {
-    "id": 277,
-    "problem_id": 272,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/272.jpg"
-  },
-  {
-    "id": 278,
-    "problem_id": 273,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/273.jpg"
-  },
-  {
-    "id": 279,
-    "problem_id": 274,
-    "problem": "line D A, line A B, line B C, line D C, line D A, line A B, line B C, line D C\nIf ABCD is a kite. Find m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/274.jpg"
-  },
-  {
-    "id": 280,
-    "problem_id": 275,
-    "problem": "line D A, line A B, line B C, line D C, line D A, line A B, line B C, line D C\nIf ABCD is a kite. Find m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/275.jpg"
-  },
-  {
-    "id": 281,
-    "problem_id": 276,
-    "problem": "line B C E G H, line M L K J I, line A C L N, line D E K O, line F G J P, line B C E G H, line M L K J I, line A C L N, line D E K O, line F G J P\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/276.jpg"
-  },
-  {
-    "id": 282,
-    "problem_id": 277,
-    "problem": "line B C E G H, line M L K J I, line A C L N, line D E K O, line F G J P, line B C E G H, line M L K J I, line A C L N, line D E K O, line F G J P\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/277.jpg"
-  },
-  {
-    "id": 283,
-    "problem_id": 278,
-    "problem": "line A D, line C D, line A C, line A B, line A D, line C D, line A C, line A B\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/278.jpg"
-  },
-  {
-    "id": 284,
-    "problem_id": 279,
-    "problem": "line B A, line C D, \\odot E lieson C B A D, line B A, line C D, \\odot E lieson C B A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/279.jpg"
-  },
-  {
-    "id": 285,
-    "problem_id": 280,
-    "problem": "line B A, line C D, \\odot E lieson C B A D, line B A, line C D, \\odot E lieson C B A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/280.jpg"
-  },
-  {
-    "id": 286,
-    "problem_id": 281,
-    "problem": "line B A, line C D, \\odot E lieson C B A D, line B A, line C D, \\odot E lieson C B A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/281.jpg"
-  },
-  {
-    "id": 287,
-    "problem_id": 282,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle QRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/282.jpg"
-  },
-  {
-    "id": 288,
-    "problem_id": 283,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle QRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/283.jpg"
-  },
-  {
-    "id": 289,
-    "problem_id": 284,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle QRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/284.jpg"
-  },
-  {
-    "id": 290,
-    "problem_id": 285,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle QRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/285.jpg"
-  },
-  {
-    "id": 291,
-    "problem_id": 286,
-    "problem": "line A R T, line W T S, line R W, line R S, line A R T, line W T S, line R W, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/286.jpg"
-  },
-  {
-    "id": 292,
-    "problem_id": 287,
-    "problem": "line A R T, line W T S, line R W, line R S, line A R T, line W T S, line R W, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/287.jpg"
-  },
-  {
-    "id": 293,
-    "problem_id": 288,
-    "problem": "line A R T, line W T S, line R W, line R S, line A R T, line W T S, line R W, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/288.jpg"
-  },
-  {
-    "id": 294,
-    "problem_id": 289,
-    "problem": "line A R T, line W T S, line R W, line R S, line A R T, line W T S, line R W, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/289.jpg"
-  },
-  {
-    "id": 295,
-    "problem_id": 290,
-    "problem": "line A R T, line W T S, line R W, line R S, line A R T, line W T S, line R W, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/290.jpg"
-  },
-  {
-    "id": 296,
-    "problem_id": 291,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/291.jpg"
-  },
-  {
-    "id": 297,
-    "problem_id": 292,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/292.jpg"
-  },
-  {
-    "id": 298,
-    "problem_id": 293,
-    "problem": "line A B, line B C, line D C, line A D, \\odot E lieson A D C B, line A B, line B C, line D C, line A D, \\odot E lieson A D C B\nA square is inscribed in a circle. What is the area of the circle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/293.jpg"
-  },
-  {
-    "id": 299,
-    "problem_id": 294,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of LK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/294.jpg"
-  },
-  {
-    "id": 300,
-    "problem_id": 295,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of LK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/295.jpg"
-  },
-  {
-    "id": 301,
-    "problem_id": 296,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of LK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/296.jpg"
-  },
-  {
-    "id": 302,
-    "problem_id": 297,
-    "problem": "line P M, line N M, line P N, line P M, line N M, line P N\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/297.jpg"
-  },
-  {
-    "id": 303,
-    "problem_id": 298,
-    "problem": "line P M, line N M, line P N, line P M, line N M, line P N\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/298.jpg"
-  },
-  {
-    "id": 304,
-    "problem_id": 299,
-    "problem": "line P M, line N M, line P N, line P M, line N M, line P N\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/299.jpg"
-  },
-  {
-    "id": 305,
-    "problem_id": 300,
-    "problem": "line P M, line N M, line P N, line P M, line N M, line P N\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/300.jpg"
-  },
-  {
-    "id": 306,
-    "problem_id": 301,
-    "problem": "line A G, line A H, \\odot B lieson A H G, line A G, line A H, \\odot B lieson A H G\nFind the measure of \\widehat GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/301.jpg"
-  },
-  {
-    "id": 307,
-    "problem_id": 302,
-    "problem": "line A C E, line A B D, line A F, \\odot G lieson B F D, \\odot H lieson C E F, line A C E, line A B D, line A F, \\odot G lieson B F D, \\odot H lieson C E F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/302.jpg"
-  },
-  {
-    "id": 308,
-    "problem_id": 303,
-    "problem": "line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D, line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D\nFind the area of the shaded region. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/303.jpg"
-  },
-  {
-    "id": 309,
-    "problem_id": 304,
-    "problem": "line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D, line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D\nFind the area of the shaded region. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/304.jpg"
-  },
-  {
-    "id": 310,
-    "problem_id": 305,
-    "problem": "line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D, line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D\nFind the area of the shaded region. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/305.jpg"
-  },
-  {
-    "id": 311,
-    "problem_id": 306,
-    "problem": "line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D, line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D\nFind the area of the shaded region. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/306.jpg"
-  },
-  {
-    "id": 312,
-    "problem_id": 307,
-    "problem": "line A B C, line D C, line E D, line E A, line E B, line A B C, line D C, line E D, line E A, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/307.jpg"
-  },
-  {
-    "id": 313,
-    "problem_id": 308,
-    "problem": "line A B C, line D C, line E D, line E A, line E B, line A B C, line D C, line E D, line E A, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/308.jpg"
-  },
-  {
-    "id": 314,
-    "problem_id": 309,
-    "problem": "line A B C, line D C, line E D, line E A, line E B, line A B C, line D C, line E D, line E A, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/309.jpg"
-  },
-  {
-    "id": 315,
-    "problem_id": 310,
-    "problem": "line A B, line B C, line D C, line E D, line F E, line F A, line A B, line B C, line D C, line E D, line F E, line F A\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/310.jpg"
-  },
-  {
-    "id": 316,
-    "problem_id": 311,
-    "problem": "line A B, line B C, line D C, line E D, line F E, line F A, line A B, line B C, line D C, line E D, line F E, line F A\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/311.jpg"
-  },
-  {
-    "id": 317,
-    "problem_id": 312,
-    "problem": "line J S B, line J P C, line A M J, line M S, line S P, line J S B, line J P C, line A M J, line M S, line S P\nFind SP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/312.jpg"
-  },
-  {
-    "id": 318,
-    "problem_id": 313,
-    "problem": "line J S B, line J P C, line A M J, line M S, line S P, line J S B, line J P C, line A M J, line M S, line S P\nFind SP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/313.jpg"
-  },
-  {
-    "id": 319,
-    "problem_id": 314,
-    "problem": "line J S B, line J P C, line A M J, line M S, line S P, line J S B, line J P C, line A M J, line M S, line S P\nFind SP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/314.jpg"
-  },
-  {
-    "id": 320,
-    "problem_id": 315,
-    "problem": "line J S B, line J P C, line A M J, line M S, line S P, line J S B, line J P C, line A M J, line M S, line S P\nFind SP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/315.jpg"
-  },
-  {
-    "id": 321,
-    "problem_id": 316,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/316.jpg"
-  },
-  {
-    "id": 322,
-    "problem_id": 317,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/317.jpg"
-  },
-  {
-    "id": 323,
-    "problem_id": 318,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/318.jpg"
-  },
-  {
-    "id": 324,
-    "problem_id": 319,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/319.jpg"
-  },
-  {
-    "id": 326,
-    "problem_id": 320,
-    "problem": "line C D E F, line B D H, line A E G, line C D E F, line B D H, line A E G\nm \\angle 4 = 101. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/320.jpg"
-  },
-  {
-    "id": 327,
-    "problem_id": 321,
-    "problem": "line B V X, line X Z, line X Y A, line Z W C, \\odot D lieson V Z X, line B V X, line X Z, line X Y A, line Z W C, \\odot D lieson V Z X\nWhat is m \\widehat XV?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/321.jpg"
-  },
-  {
-    "id": 328,
-    "problem_id": 322,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/322.jpg"
-  },
-  {
-    "id": 329,
-    "problem_id": 323,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/323.jpg"
-  },
-  {
-    "id": 330,
-    "problem_id": 324,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/324.jpg"
-  },
-  {
-    "id": 331,
-    "problem_id": 325,
-    "problem": "line C B, line B D, line A C, line C D, line A B, line C B, line B D, line A C, line C D, line A B\nFind the measure of \\angle 1 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/325.jpg"
-  },
-  {
-    "id": 332,
-    "problem_id": 326,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/326.jpg"
-  },
-  {
-    "id": 333,
-    "problem_id": 327,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/327.jpg"
-  },
-  {
-    "id": 334,
-    "problem_id": 328,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/328.jpg"
-  },
-  {
-    "id": 335,
-    "problem_id": 329,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/329.jpg"
-  },
-  {
-    "id": 336,
-    "problem_id": 330,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/330.jpg"
-  },
-  {
-    "id": 337,
-    "problem_id": 331,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/331.jpg"
-  },
-  {
-    "id": 338,
-    "problem_id": 332,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/332.jpg"
-  },
-  {
-    "id": 339,
-    "problem_id": 333,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/333.jpg"
-  },
-  {
-    "id": 340,
-    "problem_id": 334,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/334.jpg"
-  },
-  {
-    "id": 341,
-    "problem_id": 335,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/335.jpg"
-  },
-  {
-    "id": 342,
-    "problem_id": 336,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/336.jpg"
-  },
-  {
-    "id": 343,
-    "problem_id": 337,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/337.jpg"
-  },
-  {
-    "id": 344,
-    "problem_id": 338,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/338.jpg"
-  },
-  {
-    "id": 345,
-    "problem_id": 339,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/339.jpg"
-  },
-  {
-    "id": 346,
-    "problem_id": 340,
-    "problem": "line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E, line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/340.jpg"
-  },
-  {
-    "id": 347,
-    "problem_id": 341,
-    "problem": "line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E, line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/341.jpg"
-  },
-  {
-    "id": 348,
-    "problem_id": 342,
-    "problem": "line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E, line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/342.jpg"
-  },
-  {
-    "id": 349,
-    "problem_id": 343,
-    "problem": "line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E, line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/343.jpg"
-  },
-  {
-    "id": 350,
-    "problem_id": 344,
-    "problem": "line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E, line B C, line D C, line E D, line A E, line A B, line F D, \\odot F lieson A B C D E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/344.jpg"
-  },
-  {
-    "id": 352,
-    "problem_id": 345,
-    "problem": "line A E, line A B, line B D, line A F D, line E D, \\odot F lieson A E D B, line A E, line A B, line B D, line A F D, line E D, \\odot F lieson A E D B\nTriangles ABD and ADE are inscribed in \\odot F with AB = BD. Find the measure of \\angle 4 if m \\angle 1 = 12x-8 and m \\angle 2 = 3x+8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/345.jpg"
-  },
-  {
-    "id": 353,
-    "problem_id": 346,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/346.jpg"
-  },
-  {
-    "id": 354,
-    "problem_id": 347,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/347.jpg"
-  },
-  {
-    "id": 355,
-    "problem_id": 348,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/348.jpg"
-  },
-  {
-    "id": 356,
-    "problem_id": 349,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/349.jpg"
-  },
-  {
-    "id": 357,
-    "problem_id": 350,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/350.jpg"
-  },
-  {
-    "id": 358,
-    "problem_id": 351,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/351.jpg"
-  },
-  {
-    "id": 359,
-    "problem_id": 352,
-    "problem": "line E F G, line E F G\nFind the measurement of EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/352.jpg"
-  },
-  {
-    "id": 360,
-    "problem_id": 353,
-    "problem": "line A B, line E B, line A C E, line D A, line D C B, line A B, line E B, line A C E, line D A, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/353.jpg"
-  },
-  {
-    "id": 361,
-    "problem_id": 354,
-    "problem": "line A B, line B C, \\odot D lieson A C B, line A B, line B C, \\odot D lieson A C B\nFind m \\widehat AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/354.jpg"
-  },
-  {
-    "id": 362,
-    "problem_id": 355,
-    "problem": "line A B, line B C, \\odot D lieson A C B, line A B, line B C, \\odot D lieson A C B\nFind m \\widehat AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/355.jpg"
-  },
-  {
-    "id": 363,
-    "problem_id": 356,
-    "problem": "line C A, line C D B, line A B, line A D, line C A, line C D B, line A B, line A D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/356.jpg"
-  },
-  {
-    "id": 364,
-    "problem_id": 357,
-    "problem": "line C A, line C D B, line A B, line A D, line C A, line C D B, line A B, line A D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/357.jpg"
-  },
-  {
-    "id": 365,
-    "problem_id": 358,
-    "problem": "line C A, line C D B, line A B, line A D, line C A, line C D B, line A B, line A D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/358.jpg"
-  },
-  {
-    "id": 366,
-    "problem_id": 359,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/359.jpg"
-  },
-  {
-    "id": 367,
-    "problem_id": 360,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/360.jpg"
-  },
-  {
-    "id": 368,
-    "problem_id": 361,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/361.jpg"
-  },
-  {
-    "id": 369,
-    "problem_id": 362,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/362.jpg"
-  },
-  {
-    "id": 370,
-    "problem_id": 363,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/363.jpg"
-  },
-  {
-    "id": 371,
-    "problem_id": 364,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/364.jpg"
-  },
-  {
-    "id": 372,
-    "problem_id": 365,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/365.jpg"
-  },
-  {
-    "id": 373,
-    "problem_id": 366,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/366.jpg"
-  },
-  {
-    "id": 374,
-    "problem_id": 367,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/367.jpg"
-  },
-  {
-    "id": 375,
-    "problem_id": 368,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/368.jpg"
-  },
-  {
-    "id": 376,
-    "problem_id": 369,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/369.jpg"
-  },
-  {
-    "id": 377,
-    "problem_id": 370,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/370.jpg"
-  },
-  {
-    "id": 378,
-    "problem_id": 371,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/371.jpg"
-  },
-  {
-    "id": 379,
-    "problem_id": 372,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/372.jpg"
-  },
-  {
-    "id": 380,
-    "problem_id": 373,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/373.jpg"
-  },
-  {
-    "id": 381,
-    "problem_id": 374,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/374.jpg"
-  },
-  {
-    "id": 382,
-    "problem_id": 375,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/375.jpg"
-  },
-  {
-    "id": 383,
-    "problem_id": 376,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/376.jpg"
-  },
-  {
-    "id": 384,
-    "problem_id": 377,
-    "problem": "line A E C, line B F C, line A D B, line G C, line B G, line A G, line D G, line E G, line G F, line A E C, line B F C, line A D B, line G C, line B G, line A G, line D G, line E G, line G F\nThe perpendicular bisectors of \\triangle ABC meet at point G. Find GC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/377.jpg"
-  },
-  {
-    "id": 385,
-    "problem_id": 378,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/378.jpg"
-  },
-  {
-    "id": 386,
-    "problem_id": 379,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/379.jpg"
-  },
-  {
-    "id": 387,
-    "problem_id": 380,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/380.jpg"
-  },
-  {
-    "id": 388,
-    "problem_id": 381,
-    "problem": "line B C, line A F, line E F, line D E, line C D, line B A, line B C, line A F, line E F, line D E, line C D, line B A\nWhat is the value of x in polygon ABCDEF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/381.jpg"
-  },
-  {
-    "id": 389,
-    "problem_id": 382,
-    "problem": "line B C, line A F, line E F, line D E, line C D, line B A, line B C, line A F, line E F, line D E, line C D, line B A\nWhat is the value of x in polygon ABCDEF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/382.jpg"
-  },
-  {
-    "id": 390,
-    "problem_id": 383,
-    "problem": "line B C, line A F, line E F, line D E, line C D, line B A, line B C, line A F, line E F, line D E, line C D, line B A\nWhat is the value of x in polygon ABCDEF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/383.jpg"
-  },
-  {
-    "id": 391,
-    "problem_id": 384,
-    "problem": "line A C D, line E D, line E C, line B C, line A B, line A C D, line E D, line E C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/384.jpg"
-  },
-  {
-    "id": 392,
-    "problem_id": 385,
-    "problem": "line A C D, line E D, line E C, line B C, line A B, line A C D, line E D, line E C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/385.jpg"
-  },
-  {
-    "id": 393,
-    "problem_id": 386,
-    "problem": "line A C D, line E D, line E C, line B C, line A B, line A C D, line E D, line E C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/386.jpg"
-  },
-  {
-    "id": 394,
-    "problem_id": 387,
-    "problem": "line Y B, line Y X, line B X, line Y B, line Y X, line B X\nSolve for m \\angle BYX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/387.jpg"
-  },
-  {
-    "id": 395,
-    "problem_id": 388,
-    "problem": "line Y B, line Y X, line B X, line Y B, line Y X, line B X\nSolve for m \\angle BYX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/388.jpg"
-  },
-  {
-    "id": 396,
-    "problem_id": 389,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/389.jpg"
-  },
-  {
-    "id": 397,
-    "problem_id": 390,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/390.jpg"
-  },
-  {
-    "id": 398,
-    "problem_id": 391,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/391.jpg"
-  },
-  {
-    "id": 399,
-    "problem_id": 392,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/392.jpg"
-  },
-  {
-    "id": 400,
-    "problem_id": 393,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/393.jpg"
-  },
-  {
-    "id": 401,
-    "problem_id": 394,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/394.jpg"
-  },
-  {
-    "id": 402,
-    "problem_id": 395,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/395.jpg"
-  },
-  {
-    "id": 403,
-    "problem_id": 396,
-    "problem": "line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J, line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J\nFor the pair of similar figures, the area of the blue figure is 1050 cm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/396.jpg"
-  },
-  {
-    "id": 404,
-    "problem_id": 397,
-    "problem": "line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J, line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J\nFor the pair of similar figures, the area of the blue figure is 1050 cm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/397.jpg"
-  },
-  {
-    "id": 405,
-    "problem_id": 398,
-    "problem": "line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J, line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J\nFor the pair of similar figures, the area of the blue figure is 1050 cm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/398.jpg"
-  },
-  {
-    "id": 406,
-    "problem_id": 399,
-    "problem": "line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J, line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J\nFor the pair of similar figures, the area of the blue figure is 1050 cm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/399.jpg"
-  },
-  {
-    "id": 407,
-    "problem_id": 400,
-    "problem": "line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J, line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J\nFor the pair of similar figures, the area of the blue figure is 1050 cm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/400.jpg"
-  },
-  {
-    "id": 408,
-    "problem_id": 401,
-    "problem": "line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J, line E D, line E A, line A B, line C B, line D C, line G H, line I H, line J I, line F G, line F J\nFor the pair of similar figures, the area of the blue figure is 1050 cm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/401.jpg"
-  },
-  {
-    "id": 409,
-    "problem_id": 402,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/402.jpg"
-  },
-  {
-    "id": 410,
-    "problem_id": 403,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/403.jpg"
-  },
-  {
-    "id": 411,
-    "problem_id": 404,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/404.jpg"
-  },
-  {
-    "id": 412,
-    "problem_id": 405,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/405.jpg"
-  },
-  {
-    "id": 413,
-    "problem_id": 406,
-    "problem": "line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y, line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y\nQuadrilateral WXYZ is inscribed in \\odot V. Find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/406.jpg"
-  },
-  {
-    "id": 414,
-    "problem_id": 407,
-    "problem": "line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y, line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y\nQuadrilateral WXYZ is inscribed in \\odot V. Find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/407.jpg"
-  },
-  {
-    "id": 415,
-    "problem_id": 408,
-    "problem": "line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y, line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y\nQuadrilateral WXYZ is inscribed in \\odot V. Find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/408.jpg"
-  },
-  {
-    "id": 416,
-    "problem_id": 409,
-    "problem": "line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y, line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y\nQuadrilateral WXYZ is inscribed in \\odot V. Find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/409.jpg"
-  },
-  {
-    "id": 417,
-    "problem_id": 410,
-    "problem": "line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y, line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y\nQuadrilateral WXYZ is inscribed in \\odot V. Find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/410.jpg"
-  },
-  {
-    "id": 418,
-    "problem_id": 411,
-    "problem": "line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y, line W X, line Y X, line Z Y, line Z W, \\odot V lieson Z W X Y\nQuadrilateral WXYZ is inscribed in \\odot V. Find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/411.jpg"
-  },
-  {
-    "id": 419,
-    "problem_id": 412,
-    "problem": "line D C, line A B, line B C, line A D, line D C, line A B, line B C, line A D\nWhat is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/412.jpg"
-  },
-  {
-    "id": 420,
-    "problem_id": 413,
-    "problem": "line D C, line A B, line B C, line A D, line D C, line A B, line B C, line A D\nWhat is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/413.jpg"
-  },
-  {
-    "id": 422,
-    "problem_id": 414,
-    "problem": "line C F, line A C E, line D C, line B C, line C F, line A C E, line D C, line B C\nSuppose \\angle 4 and \\angle 5 form a linear pair. If m \\angle 1 = 2x, m \\angle 2 = 3x-20, and m \\angle 3 = x-4, what is m \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/414.jpg"
-  },
-  {
-    "id": 423,
-    "problem_id": 415,
-    "problem": "line C F, line A C E, line D C, line B C, line C F, line A C E, line D C, line B C\nSuppose \\angle 4 and \\angle 5 form a linear pair. If m \\angle 1 = 2x, m \\angle 2 = 3x-20, and m \\angle 3 = x-4, what is m \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/415.jpg"
-  },
-  {
-    "id": 424,
-    "problem_id": 416,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable b in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/416.jpg"
-  },
-  {
-    "id": 425,
-    "problem_id": 417,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable b in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/417.jpg"
-  },
-  {
-    "id": 426,
-    "problem_id": 418,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable b in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/418.jpg"
-  },
-  {
-    "id": 427,
-    "problem_id": 419,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable b in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/419.jpg"
-  },
-  {
-    "id": 428,
-    "problem_id": 420,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/420.jpg"
-  },
-  {
-    "id": 429,
-    "problem_id": 421,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/421.jpg"
-  },
-  {
-    "id": 430,
-    "problem_id": 422,
-    "problem": "line B C E, line E D, line A C D, line A B, line B C E, line E D, line A C D, line A B\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/422.jpg"
-  },
-  {
-    "id": 431,
-    "problem_id": 423,
-    "problem": "line B C E, line E D, line A C D, line A B, line B C E, line E D, line A C D, line A B\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/423.jpg"
-  },
-  {
-    "id": 432,
-    "problem_id": 424,
-    "problem": "line B C E, line E D, line A C D, line A B, line B C E, line E D, line A C D, line A B\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/424.jpg"
-  },
-  {
-    "id": 433,
-    "problem_id": 425,
-    "problem": "line B C E, line E D, line A C D, line A B, line B C E, line E D, line A C D, line A B\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/425.jpg"
-  },
-  {
-    "id": 434,
-    "problem_id": 426,
-    "problem": "line X Y, line X Z, line Y Z, line X Y, line X Z, line Y Z\nSolve for the measurement of \\angle XZY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/426.jpg"
-  },
-  {
-    "id": 435,
-    "problem_id": 427,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/427.jpg"
-  },
-  {
-    "id": 436,
-    "problem_id": 428,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/428.jpg"
-  },
-  {
-    "id": 437,
-    "problem_id": 429,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is perimeter of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/429.jpg"
-  },
-  {
-    "id": 438,
-    "problem_id": 430,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is perimeter of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/430.jpg"
-  },
-  {
-    "id": 439,
-    "problem_id": 431,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is perimeter of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/431.jpg"
-  },
-  {
-    "id": 440,
-    "problem_id": 432,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is perimeter of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/432.jpg"
-  },
-  {
-    "id": 441,
-    "problem_id": 433,
-    "problem": "line A B, line A D C, line C B, line D B, line A B, line A D C, line C B, line D B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/433.jpg"
-  },
-  {
-    "id": 443,
-    "problem_id": 434,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/434.jpg"
-  },
-  {
-    "id": 444,
-    "problem_id": 435,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/435.jpg"
-  },
-  {
-    "id": 445,
-    "problem_id": 436,
-    "problem": "line A B, line C A, line C B, line D B, \\odot D lieson C A B, line A B, line C A, line C B, line D B, \\odot D lieson C A B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/436.jpg"
-  },
-  {
-    "id": 446,
-    "problem_id": 437,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 4 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/437.jpg"
-  },
-  {
-    "id": 448,
-    "problem_id": 438,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 4 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/438.jpg"
-  },
-  {
-    "id": 449,
-    "problem_id": 439,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 4 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/439.jpg"
-  },
-  {
-    "id": 450,
-    "problem_id": 440,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 4 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/440.jpg"
-  },
-  {
-    "id": 451,
-    "problem_id": 441,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 4 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/441.jpg"
-  },
-  {
-    "id": 452,
-    "problem_id": 442,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 1 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/442.jpg"
-  },
-  {
-    "id": 453,
-    "problem_id": 443,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 1 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/443.jpg"
-  },
-  {
-    "id": 454,
-    "problem_id": 444,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 1 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/444.jpg"
-  },
-  {
-    "id": 455,
-    "problem_id": 445,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 1 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/445.jpg"
-  },
-  {
-    "id": 456,
-    "problem_id": 446,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle BAD of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/446.jpg"
-  },
-  {
-    "id": 457,
-    "problem_id": 447,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle BAD of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/447.jpg"
-  },
-  {
-    "id": 458,
-    "problem_id": 448,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle BAD of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/448.jpg"
-  },
-  {
-    "id": 459,
-    "problem_id": 449,
-    "problem": "line A C, line A B, line B C D, line A D, line A C, line A B, line B C D, line A D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/449.jpg"
-  },
-  {
-    "id": 460,
-    "problem_id": 450,
-    "problem": "line A C, line A B, line B C D, line A D, line A C, line A B, line B C D, line A D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/450.jpg"
-  },
-  {
-    "id": 461,
-    "problem_id": 451,
-    "problem": "line A C, line A B, line B C D, line A D, line A C, line A B, line B C D, line A D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/451.jpg"
-  },
-  {
-    "id": 462,
-    "problem_id": 452,
-    "problem": "line B A, line B C, line A D C, \\odot A lieson D B, line B A, line B C, line A D C, \\odot A lieson D B\nThe segment is tangent to the circle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/452.jpg"
-  },
-  {
-    "id": 463,
-    "problem_id": 453,
-    "problem": "line A D I, line B F H, line G F E, line C D E, line A D I, line B F H, line G F E, line C D E\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/453.jpg"
-  },
-  {
-    "id": 464,
-    "problem_id": 454,
-    "problem": "line A D I, line B F H, line G F E, line C D E, line A D I, line B F H, line G F E, line C D E\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/454.jpg"
-  },
-  {
-    "id": 465,
-    "problem_id": 455,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find GR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/455.jpg"
-  },
-  {
-    "id": 466,
-    "problem_id": 456,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find GR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/456.jpg"
-  },
-  {
-    "id": 467,
-    "problem_id": 457,
-    "problem": "line Q S, line R S, \\odot S lieson Q R, line Q S, line R S, \\odot S lieson Q R\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/457.jpg"
-  },
-  {
-    "id": 468,
-    "problem_id": 458,
-    "problem": "line Q S, line R S, \\odot S lieson Q R, line Q S, line R S, \\odot S lieson Q R\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/458.jpg"
-  },
-  {
-    "id": 469,
-    "problem_id": 459,
-    "problem": "line Q S, line R S, \\odot S lieson Q R, line Q S, line R S, \\odot S lieson Q R\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/459.jpg"
-  },
-  {
-    "id": 470,
-    "problem_id": 460,
-    "problem": "line Q S, line R S, \\odot S lieson Q R, line Q S, line R S, \\odot S lieson Q R\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/460.jpg"
-  },
-  {
-    "id": 471,
-    "problem_id": 461,
-    "problem": "line Q S, line R S, \\odot S lieson Q R, line Q S, line R S, \\odot S lieson Q R\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/461.jpg"
-  },
-  {
-    "id": 472,
-    "problem_id": 462,
-    "problem": "line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J, line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/462.jpg"
-  },
-  {
-    "id": 473,
-    "problem_id": 463,
-    "problem": "line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J, line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/463.jpg"
-  },
-  {
-    "id": 474,
-    "problem_id": 464,
-    "problem": "line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J, line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/464.jpg"
-  },
-  {
-    "id": 476,
-    "problem_id": 465,
-    "problem": "line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J, line C D E F, line P M I E B, line K L M N, line A D H L O, line G H I J\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/465.jpg"
-  },
-  {
-    "id": 477,
-    "problem_id": 466,
-    "problem": "line t lieson D E F G, line u lieson H I J K, line s lieson A C E I M, line r lieson B C F J L, line t lieson D E F G, line u lieson H I J K, line s lieson A C E I M, line r lieson B C F J L\nm \\angle 5 = 72 and m \\angle 9 = 102. Find the measure of \\angle 16.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/466.jpg"
-  },
-  {
-    "id": 478,
-    "problem_id": 467,
-    "problem": "line C E D, line A D, line B E A, \\odot A lieson C D B, line C E D, line A D, line B E A, \\odot A lieson C D B\nIn \\odot A, CD = 10. Solve for the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/467.jpg"
-  },
-  {
-    "id": 479,
-    "problem_id": 468,
-    "problem": "line A R, line B R, \\odot R lieson A B, line A R, line B R, \\odot R lieson A B\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/468.jpg"
-  },
-  {
-    "id": 480,
-    "problem_id": 469,
-    "problem": "line A R, line B R, \\odot R lieson A B, line A R, line B R, \\odot R lieson A B\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/469.jpg"
-  },
-  {
-    "id": 481,
-    "problem_id": 470,
-    "problem": "line A B C, line E D C, \\odot F lieson E A B D, line A B C, line E D C, \\odot F lieson E A B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/470.jpg"
-  },
-  {
-    "id": 482,
-    "problem_id": 471,
-    "problem": "line A J C, line F G C, line E H C, line E F A, line E G, line A G, line G J, line H G, line A J C, line F G C, line E H C, line E F A, line E G, line A G, line G J, line H G\nThe angle bisectors of \\triangle AEC meet at point G. Find GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/471.jpg"
-  },
-  {
-    "id": 483,
-    "problem_id": 472,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/472.jpg"
-  },
-  {
-    "id": 484,
-    "problem_id": 473,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/473.jpg"
-  },
-  {
-    "id": 485,
-    "problem_id": 474,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/474.jpg"
-  },
-  {
-    "id": 486,
-    "problem_id": 475,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/475.jpg"
-  },
-  {
-    "id": 487,
-    "problem_id": 476,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/476.jpg"
-  },
-  {
-    "id": 488,
-    "problem_id": 477,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/477.jpg"
-  },
-  {
-    "id": 489,
-    "problem_id": 478,
-    "problem": "line C B, line A D B, line A C, line C D, line C B, line A D B, line A C, line C D\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/478.jpg"
-  },
-  {
-    "id": 490,
-    "problem_id": 479,
-    "problem": "line C B, line A D B, line A C, line C D, line C B, line A D B, line A C, line C D\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/479.jpg"
-  },
-  {
-    "id": 491,
-    "problem_id": 480,
-    "problem": "line C B, line A D B, line A C, line C D, line C B, line A D B, line A C, line C D\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/480.jpg"
-  },
-  {
-    "id": 492,
-    "problem_id": 481,
-    "problem": "line M K P, line M L N, line P N, line K L, line M K P, line M L N, line P N, line K L\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/481.jpg"
-  },
-  {
-    "id": 493,
-    "problem_id": 482,
-    "problem": "line A B D, line C D, line C B, line A B D, line C D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/482.jpg"
-  },
-  {
-    "id": 494,
-    "problem_id": 483,
-    "problem": "line E A G, line D A F, line G F, line E F, line E D, line D G, line E A G, line D A F, line G F, line E F, line E D, line D G\nQuadrilateral DEFG is a kite. Find m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/483.jpg"
-  },
-  {
-    "id": 495,
-    "problem_id": 484,
-    "problem": "line E A G, line D A F, line G F, line E F, line E D, line D G, line E A G, line D A F, line G F, line E F, line E D, line D G\nQuadrilateral DEFG is a kite. Find m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/484.jpg"
-  },
-  {
-    "id": 496,
-    "problem_id": 485,
-    "problem": "line A C D, line A B, line B D, line C B, line A C D, line A B, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/485.jpg"
-  },
-  {
-    "id": 497,
-    "problem_id": 486,
-    "problem": "line A C D, line A B, line B D, line C B, line A C D, line A B, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/486.jpg"
-  },
-  {
-    "id": 498,
-    "problem_id": 487,
-    "problem": "line A C D, line A B, line B D, line C B, line A C D, line A B, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/487.jpg"
-  },
-  {
-    "id": 499,
-    "problem_id": 488,
-    "problem": "line A C D, line A B, line B D, line C B, line A C D, line A B, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/488.jpg"
-  },
-  {
-    "id": 500,
-    "problem_id": 489,
-    "problem": "line A C D, line A B, line B D, line C B, line A C D, line A B, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/489.jpg"
-  },
-  {
-    "id": 501,
-    "problem_id": 490,
-    "problem": "line A C D, line A B, line B D, line C B, line A C D, line A B, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/490.jpg"
-  },
-  {
-    "id": 502,
-    "problem_id": 491,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/491.jpg"
-  },
-  {
-    "id": 503,
-    "problem_id": 492,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/492.jpg"
-  },
-  {
-    "id": 504,
-    "problem_id": 493,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/493.jpg"
-  },
-  {
-    "id": 505,
-    "problem_id": 494,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/494.jpg"
-  },
-  {
-    "id": 506,
-    "problem_id": 495,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/495.jpg"
-  },
-  {
-    "id": 507,
-    "problem_id": 496,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/496.jpg"
-  },
-  {
-    "id": 508,
-    "problem_id": 497,
-    "problem": "line S T, line R A S, \\odot A lieson S T R, line S T, line R A S, \\odot A lieson S T R\nSolve for the measure of \\widehat RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/497.jpg"
-  },
-  {
-    "id": 509,
-    "problem_id": 498,
-    "problem": "line S T, line R A S, \\odot A lieson S T R, line S T, line R A S, \\odot A lieson S T R\nSolve for the measure of \\widehat RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/498.jpg"
-  },
-  {
-    "id": 510,
-    "problem_id": 499,
-    "problem": "line P C S, line C Q, line R C, \\odot C lieson P Q S R, line P C S, line C Q, line R C, \\odot C lieson P Q S R\nWhat is the measure of \\widehat RS in \\odot C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/499.jpg"
-  },
-  {
-    "id": 511,
-    "problem_id": 500,
-    "problem": "line P C S, line C Q, line R C, \\odot C lieson P Q S R, line P C S, line C Q, line R C, \\odot C lieson P Q S R\nWhat is the measure of \\widehat RS in \\odot C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/500.jpg"
-  },
-  {
-    "id": 512,
-    "problem_id": 501,
-    "problem": "line M L, line J K, line J M, line K L, line M L, line J K, line J M, line K L\nJKLM is a parallelogram. Find LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/501.jpg"
-  },
-  {
-    "id": 513,
-    "problem_id": 502,
-    "problem": "line M L, line J K, line J M, line K L, line M L, line J K, line J M, line K L\nJKLM is a parallelogram. Find LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/502.jpg"
-  },
-  {
-    "id": 514,
-    "problem_id": 503,
-    "problem": "line K M A, line K N, \\odot B lieson M K, line K M A, line K N, \\odot B lieson M K\nFind m \\angle MKN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/503.jpg"
-  },
-  {
-    "id": 515,
-    "problem_id": 504,
-    "problem": "line K M A, line K N, \\odot B lieson M K, line K M A, line K N, \\odot B lieson M K\nFind m \\angle MKN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/504.jpg"
-  },
-  {
-    "id": 516,
-    "problem_id": 505,
-    "problem": "line S R, line Q N R, line P Q, line P M S, line M N, line S R, line Q N R, line P Q, line P M S, line M N\nFind the length of the midsegment MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/505.jpg"
-  },
-  {
-    "id": 517,
-    "problem_id": 506,
-    "problem": "line S R, line Q N R, line P Q, line P M S, line M N, line S R, line Q N R, line P Q, line P M S, line M N\nFind the length of the midsegment MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/506.jpg"
-  },
-  {
-    "id": 518,
-    "problem_id": 507,
-    "problem": "line A B, line A D, line D E B, line A E C, line B C, line D C, line A B, line A D, line D E B, line A E C, line B C, line D C\nParallelogram ABCD is shown. AC is 40 and BD is \\frac{3}{5} AC. BD bisects AC. What value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/507.jpg"
-  },
-  {
-    "id": 519,
-    "problem_id": 508,
-    "problem": "line A B, line A D, line D E B, line A E C, line B C, line D C, line A B, line A D, line D E B, line A E C, line B C, line D C\nParallelogram ABCD is shown. AC is 40 and BD is \\frac{3}{5} AC. BD bisects AC. What value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/508.jpg"
-  },
-  {
-    "id": 521,
-    "problem_id": 509,
-    "problem": "line A D, line D C, line B C, line A B, line A C, line A D, line D C, line B C, line A B, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/509.jpg"
-  },
-  {
-    "id": 522,
-    "problem_id": 510,
-    "problem": "line A D, line D C, line B C, line A B, line A C, line A D, line D C, line B C, line A B, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/510.jpg"
-  },
-  {
-    "id": 523,
-    "problem_id": 511,
-    "problem": "line A D, line D C, line B C, line A B, line A C, line A D, line D C, line B C, line A B, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/511.jpg"
-  },
-  {
-    "id": 524,
-    "problem_id": 512,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/512.jpg"
-  },
-  {
-    "id": 525,
-    "problem_id": 513,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/513.jpg"
-  },
-  {
-    "id": 526,
-    "problem_id": 514,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/514.jpg"
-  },
-  {
-    "id": 527,
-    "problem_id": 515,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/515.jpg"
-  },
-  {
-    "id": 528,
-    "problem_id": 516,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/516.jpg"
-  },
-  {
-    "id": 529,
-    "problem_id": 517,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/517.jpg"
-  },
-  {
-    "id": 530,
-    "problem_id": 518,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/518.jpg"
-  },
-  {
-    "id": 531,
-    "problem_id": 519,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/519.jpg"
-  },
-  {
-    "id": 532,
-    "problem_id": 520,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/520.jpg"
-  },
-  {
-    "id": 533,
-    "problem_id": 521,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/521.jpg"
-  },
-  {
-    "id": 534,
-    "problem_id": 522,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/522.jpg"
-  },
-  {
-    "id": 535,
-    "problem_id": 523,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/523.jpg"
-  },
-  {
-    "id": 536,
-    "problem_id": 524,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/524.jpg"
-  },
-  {
-    "id": 537,
-    "problem_id": 525,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/525.jpg"
-  },
-  {
-    "id": 538,
-    "problem_id": 526,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/526.jpg"
-  },
-  {
-    "id": 539,
-    "problem_id": 527,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/527.jpg"
-  },
-  {
-    "id": 540,
-    "problem_id": 528,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/528.jpg"
-  },
-  {
-    "id": 541,
-    "problem_id": 529,
-    "problem": "line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D\nWhat is the measure of \\angle 2 in the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/529.jpg"
-  },
-  {
-    "id": 542,
-    "problem_id": 530,
-    "problem": "line B C, line D C, line A D, line A B, line A E C, line B E D, line B C, line D C, line A D, line A B, line A E C, line B E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/530.jpg"
-  },
-  {
-    "id": 543,
-    "problem_id": 531,
-    "problem": "line B C, line D C, line A D, line A B, line A E C, line B E D, line B C, line D C, line A D, line A B, line A E C, line B E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/531.jpg"
-  },
-  {
-    "id": 544,
-    "problem_id": 532,
-    "problem": "line B C, line D C, line A D, line A B, line A E C, line B E D, line B C, line D C, line A D, line A B, line A E C, line B E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/532.jpg"
-  },
-  {
-    "id": 545,
-    "problem_id": 533,
-    "problem": "line B C, line D C, line A D, line A B, line A E C, line B E D, line B C, line D C, line A D, line A B, line A E C, line B E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/533.jpg"
-  },
-  {
-    "id": 546,
-    "problem_id": 534,
-    "problem": "line B C, line D C, line A D, line A B, line A E C, line B E D, line B C, line D C, line A D, line A B, line A E C, line B E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/534.jpg"
-  },
-  {
-    "id": 547,
-    "problem_id": 535,
-    "problem": "line B C, line D C, line A D, line A B, line A E C, line B E D, line B C, line D C, line A D, line A B, line A E C, line B E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/535.jpg"
-  },
-  {
-    "id": 548,
-    "problem_id": 536,
-    "problem": "line E C A, line B C D, line A D, line B E, line E C A, line B C D, line A D, line B E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/536.jpg"
-  },
-  {
-    "id": 549,
-    "problem_id": 537,
-    "problem": "line E C A, line B C D, line A D, line B E, line E C A, line B C D, line A D, line B E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/537.jpg"
-  },
-  {
-    "id": 550,
-    "problem_id": 538,
-    "problem": "line A Q C, line B S A, line B R C, line S P C, line B P Q, line A P R, line A Q C, line B S A, line B R C, line S P C, line B P Q, line A P R\nP is the centroid of \\triangle ABC. If PB = 6, find QP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/538.jpg"
-  },
-  {
-    "id": 551,
-    "problem_id": 539,
-    "problem": "line G F, line D E F, line H E, line C H G, line C D, line G F, line D E F, line H E, line C H G, line C D\nRefer to trapezoid CDFG with median HE. Let YZ be the median of HEFG. Find YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/539.jpg"
-  },
-  {
-    "id": 552,
-    "problem_id": 540,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find the scale factor of ABCDE to PQRST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/540.jpg"
-  },
-  {
-    "id": 553,
-    "problem_id": 541,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find the scale factor of ABCDE to PQRST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/541.jpg"
-  },
-  {
-    "id": 554,
-    "problem_id": 542,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find the scale factor of ABCDE to PQRST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/542.jpg"
-  },
-  {
-    "id": 555,
-    "problem_id": 543,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find the scale factor of ABCDE to PQRST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/543.jpg"
-  },
-  {
-    "id": 556,
-    "problem_id": 544,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find the scale factor of ABCDE to PQRST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/544.jpg"
-  },
-  {
-    "id": 557,
-    "problem_id": 545,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/545.jpg"
-  },
-  {
-    "id": 558,
-    "problem_id": 546,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/546.jpg"
-  },
-  {
-    "id": 559,
-    "problem_id": 547,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/547.jpg"
-  },
-  {
-    "id": 560,
-    "problem_id": 548,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/548.jpg"
-  },
-  {
-    "id": 561,
-    "problem_id": 549,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/549.jpg"
-  },
-  {
-    "id": 562,
-    "problem_id": 550,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/550.jpg"
-  },
-  {
-    "id": 563,
-    "problem_id": 551,
-    "problem": "line S R, line X W, line P Q, line Q R, line T V, line S P, line V W, line X T, line S R, line X W, line P Q, line Q R, line T V, line S P, line V W, line X T\nPQRS \\sim TVWX. Find the perimeter of TVWX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/551.jpg"
-  },
-  {
-    "id": 564,
-    "problem_id": 552,
-    "problem": "line B A, line A C, line C G, line E F G, line B E, line D F, line B A, line A C, line C G, line E F G, line B E, line D F\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/552.jpg"
-  },
-  {
-    "id": 565,
-    "problem_id": 553,
-    "problem": "line B A, line A C, line C G, line E F G, line B E, line D F, line B A, line A C, line C G, line E F G, line B E, line D F\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/553.jpg"
-  },
-  {
-    "id": 566,
-    "problem_id": 554,
-    "problem": "line B A, line A C, line C G, line E F G, line B E, line D F, line B A, line A C, line C G, line E F G, line B E, line D F\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/554.jpg"
-  },
-  {
-    "id": 567,
-    "problem_id": 555,
-    "problem": "line A C D, line B D, line A B, line C B, line A C D, line B D, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/555.jpg"
-  },
-  {
-    "id": 568,
-    "problem_id": 556,
-    "problem": "line A C D, line B D, line A B, line C B, line A C D, line B D, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/556.jpg"
-  },
-  {
-    "id": 569,
-    "problem_id": 557,
-    "problem": "line A C D, line B D, line A B, line C B, line A C D, line B D, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/557.jpg"
-  },
-  {
-    "id": 570,
-    "problem_id": 558,
-    "problem": "line A C D, line B D, line A B, line C B, line A C D, line B D, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/558.jpg"
-  },
-  {
-    "id": 571,
-    "problem_id": 559,
-    "problem": "line A C D, line B D, line A B, line C B, line A C D, line B D, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/559.jpg"
-  },
-  {
-    "id": 572,
-    "problem_id": 560,
-    "problem": "line A C D, line B D, line A B, line C B, line A C D, line B D, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/560.jpg"
-  },
-  {
-    "id": 573,
-    "problem_id": 561,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/561.jpg"
-  },
-  {
-    "id": 574,
-    "problem_id": 562,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/562.jpg"
-  },
-  {
-    "id": 575,
-    "problem_id": 563,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/563.jpg"
-  },
-  {
-    "id": 576,
-    "problem_id": 564,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/564.jpg"
-  },
-  {
-    "id": 577,
-    "problem_id": 565,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/565.jpg"
-  },
-  {
-    "id": 578,
-    "problem_id": 566,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle KLN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/566.jpg"
-  },
-  {
-    "id": 579,
-    "problem_id": 567,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle KLN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/567.jpg"
-  },
-  {
-    "id": 580,
-    "problem_id": 568,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle KLN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/568.jpg"
-  },
-  {
-    "id": 581,
-    "problem_id": 569,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle KLN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/569.jpg"
-  },
-  {
-    "id": 582,
-    "problem_id": 570,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is c?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/570.jpg"
-  },
-  {
-    "id": 583,
-    "problem_id": 571,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is c?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/571.jpg"
-  },
-  {
-    "id": 584,
-    "problem_id": 572,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is c?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/572.jpg"
-  },
-  {
-    "id": 585,
-    "problem_id": 573,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is c?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/573.jpg"
-  },
-  {
-    "id": 586,
-    "problem_id": 574,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find the perimeter of PQRST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/574.jpg"
-  },
-  {
-    "id": 587,
-    "problem_id": 575,
-    "problem": "line p lieson E F H, line q lieson B C D, line r lieson A C F G, line p lieson E F H, line q lieson B C D, line r lieson A C F G\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/575.jpg"
-  },
-  {
-    "id": 588,
-    "problem_id": 576,
-    "problem": "line p lieson E F H, line q lieson B C D, line r lieson A C F G, line p lieson E F H, line q lieson B C D, line r lieson A C F G\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/576.jpg"
-  },
-  {
-    "id": 589,
-    "problem_id": 577,
-    "problem": "line J H, line G L H, line F G, line F J, line K L, line G K, line K H, \\odot K lieson F J H G, line J H, line G L H, line F G, line F J, line K L, line G K, line K H, \\odot K lieson F J H G\nSquare FGHJ is inscribed in \\odot K. Find the measure of \\angle GKL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/577.jpg"
-  },
-  {
-    "id": 590,
-    "problem_id": 578,
-    "problem": "line J H, line G L H, line F G, line F J, line K L, line G K, line K H, \\odot K lieson F J H G, line J H, line G L H, line F G, line F J, line K L, line G K, line K H, \\odot K lieson F J H G\nSquare FGHJ is inscribed in \\odot K. Find the measure of \\angle GKL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/578.jpg"
-  },
-  {
-    "id": 591,
-    "problem_id": 579,
-    "problem": "line K J, line J M, line J L, \\odot A lieson K L, \\odot B lieson L M, line K J, line J M, line J L, \\odot A lieson K L, \\odot B lieson L M\nAssume the segments that appear to be tangent are tangent. Find JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/579.jpg"
-  },
-  {
-    "id": 592,
-    "problem_id": 580,
-    "problem": "line K J, line J M, line J L, \\odot A lieson K L, \\odot B lieson L M, line K J, line J M, line J L, \\odot A lieson K L, \\odot B lieson L M\nAssume the segments that appear to be tangent are tangent. Find JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/580.jpg"
-  },
-  {
-    "id": 593,
-    "problem_id": 581,
-    "problem": "line C D, line B C, line C A, line C D, line B C, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/581.jpg"
-  },
-  {
-    "id": 594,
-    "problem_id": 582,
-    "problem": "line C D, line B C, line C A, line C D, line B C, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/582.jpg"
-  },
-  {
-    "id": 595,
-    "problem_id": 583,
-    "problem": "line S P, line W Z, line S R, line Y Z, line Q P, line W X, line R Q, line X Y, line S P, line W Z, line S R, line Y Z, line Q P, line W X, line R Q, line X Y\nWXYZ \\cong PQRS. Find the length of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/583.jpg"
-  },
-  {
-    "id": 596,
-    "problem_id": 584,
-    "problem": "line S P, line W Z, line S R, line Y Z, line Q P, line W X, line R Q, line X Y, line S P, line W Z, line S R, line Y Z, line Q P, line W X, line R Q, line X Y\nWXYZ \\cong PQRS. Find the length of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/584.jpg"
-  },
-  {
-    "id": 597,
-    "problem_id": 585,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/585.jpg"
-  },
-  {
-    "id": 599,
-    "problem_id": 586,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/586.jpg"
-  },
-  {
-    "id": 600,
-    "problem_id": 587,
-    "problem": "line E F G, line E F G\nIf FG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/587.jpg"
-  },
-  {
-    "id": 601,
-    "problem_id": 588,
-    "problem": "line E F G, line E F G\nIf FG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/588.jpg"
-  },
-  {
-    "id": 602,
-    "problem_id": 589,
-    "problem": "line E F G, line E F G\nIf FG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/589.jpg"
-  },
-  {
-    "id": 603,
-    "problem_id": 590,
-    "problem": "line E F G, line E F G\nIf FG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/590.jpg"
-  },
-  {
-    "id": 604,
-    "problem_id": 591,
-    "problem": "line E F G, line E F G\nIf FG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/591.jpg"
-  },
-  {
-    "id": 605,
-    "problem_id": 592,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the value of variable x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/592.jpg"
-  },
-  {
-    "id": 606,
-    "problem_id": 593,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the value of variable x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/593.jpg"
-  },
-  {
-    "id": 607,
-    "problem_id": 594,
-    "problem": "line K H M, line K J L, line M A L, line H A, line H J, line K H M, line K J L, line M A L, line H A, line H J\nJH is a midsegment of \\triangle KLM. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/594.jpg"
-  },
-  {
-    "id": 608,
-    "problem_id": 595,
-    "problem": "line K H M, line K J L, line M A L, line H A, line H J, line K H M, line K J L, line M A L, line H A, line H J\nJH is a midsegment of \\triangle KLM. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/595.jpg"
-  },
-  {
-    "id": 609,
-    "problem_id": 596,
-    "problem": "line K H M, line K J L, line M A L, line H A, line H J, line K H M, line K J L, line M A L, line H A, line H J\nJH is a midsegment of \\triangle KLM. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/596.jpg"
-  },
-  {
-    "id": 610,
-    "problem_id": 597,
-    "problem": "line K H M, line K J L, line M A L, line H A, line H J, line K H M, line K J L, line M A L, line H A, line H J\nJH is a midsegment of \\triangle KLM. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/597.jpg"
-  },
-  {
-    "id": 611,
-    "problem_id": 598,
-    "problem": "line K H M, line K J L, line M A L, line H A, line H J, line K H M, line K J L, line M A L, line H A, line H J\nJH is a midsegment of \\triangle KLM. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/598.jpg"
-  },
-  {
-    "id": 612,
-    "problem_id": 599,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/599.jpg"
-  },
-  {
-    "id": 614,
-    "problem_id": 600,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 1 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/600.jpg"
-  },
-  {
-    "id": 615,
-    "problem_id": 601,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 1 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/601.jpg"
-  },
-  {
-    "id": 616,
-    "problem_id": 602,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/602.jpg"
-  },
-  {
-    "id": 617,
-    "problem_id": 603,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/603.jpg"
-  },
-  {
-    "id": 618,
-    "problem_id": 604,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/604.jpg"
-  },
-  {
-    "id": 619,
-    "problem_id": 605,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/605.jpg"
-  },
-  {
-    "id": 620,
-    "problem_id": 606,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/606.jpg"
-  },
-  {
-    "id": 621,
-    "problem_id": 607,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/607.jpg"
-  },
-  {
-    "id": 622,
-    "problem_id": 608,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/608.jpg"
-  },
-  {
-    "id": 623,
-    "problem_id": 609,
-    "problem": "line C B, line K J, line C D, line L J, line B D, line K L, line C B, line K J, line C D, line L J, line B D, line K L\nGiven m \\angle K = m \\angle D and m \\angle J = m \\angle C, find the value of s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/609.jpg"
-  },
-  {
-    "id": 625,
-    "problem_id": 610,
-    "problem": "line C B, line K J, line C D, line L J, line B D, line K L, line C B, line K J, line C D, line L J, line B D, line K L\nGiven m \\angle K = m \\angle D and m \\angle J = m \\angle C, find the value of s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/610.jpg"
-  },
-  {
-    "id": 626,
-    "problem_id": 611,
-    "problem": "line C B, line K J, line C D, line L J, line B D, line K L, line C B, line K J, line C D, line L J, line B D, line K L\nGiven m \\angle K = m \\angle D and m \\angle J = m \\angle C, find the value of s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/611.jpg"
-  },
-  {
-    "id": 627,
-    "problem_id": 612,
-    "problem": "line A B C, line D B, line D C, line D A, line A B C, line D B, line D C, line D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/612.jpg"
-  },
-  {
-    "id": 628,
-    "problem_id": 613,
-    "problem": "line A B C, line D B, line D C, line D A, line A B C, line D B, line D C, line D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/613.jpg"
-  },
-  {
-    "id": 629,
-    "problem_id": 614,
-    "problem": "line A B C, line D B, line D C, line D A, line A B C, line D B, line D C, line D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/614.jpg"
-  },
-  {
-    "id": 630,
-    "problem_id": 615,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/615.jpg"
-  },
-  {
-    "id": 631,
-    "problem_id": 616,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/616.jpg"
-  },
-  {
-    "id": 632,
-    "problem_id": 617,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/617.jpg"
-  },
-  {
-    "id": 633,
-    "problem_id": 618,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/618.jpg"
-  },
-  {
-    "id": 634,
-    "problem_id": 619,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/619.jpg"
-  },
-  {
-    "id": 636,
-    "problem_id": 620,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/620.jpg"
-  },
-  {
-    "id": 637,
-    "problem_id": 621,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/621.jpg"
-  },
-  {
-    "id": 638,
-    "problem_id": 622,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/622.jpg"
-  },
-  {
-    "id": 639,
-    "problem_id": 623,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/623.jpg"
-  },
-  {
-    "id": 640,
-    "problem_id": 624,
-    "problem": "line Z Y, line Y X, line Z X, line Z Y, line Y X, line Z X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/624.jpg"
-  },
-  {
-    "id": 641,
-    "problem_id": 625,
-    "problem": "line Z Y, line Y X, line Z X, line Z Y, line Y X, line Z X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/625.jpg"
-  },
-  {
-    "id": 642,
-    "problem_id": 626,
-    "problem": "line Z Y, line Y X, line Z X, line Z Y, line Y X, line Z X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/626.jpg"
-  },
-  {
-    "id": 643,
-    "problem_id": 627,
-    "problem": "line Z Y, line Y X, line Z X, line Z Y, line Y X, line Z X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/627.jpg"
-  },
-  {
-    "id": 644,
-    "problem_id": 628,
-    "problem": "line Z Y, line Y X, line Z X, line Z Y, line Y X, line Z X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/628.jpg"
-  },
-  {
-    "id": 645,
-    "problem_id": 629,
-    "problem": "line B C D E, line E F, line A C G, \\odot H lieson A B G F D, line B C D E, line E F, line A C G, \\odot H lieson A B G F D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/629.jpg"
-  },
-  {
-    "id": 646,
-    "problem_id": 630,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/630.jpg"
-  },
-  {
-    "id": 647,
-    "problem_id": 631,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/631.jpg"
-  },
-  {
-    "id": 648,
-    "problem_id": 632,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/632.jpg"
-  },
-  {
-    "id": 649,
-    "problem_id": 633,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/633.jpg"
-  },
-  {
-    "id": 650,
-    "problem_id": 634,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/634.jpg"
-  },
-  {
-    "id": 651,
-    "problem_id": 635,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/635.jpg"
-  },
-  {
-    "id": 652,
-    "problem_id": 636,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/636.jpg"
-  },
-  {
-    "id": 653,
-    "problem_id": 637,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/637.jpg"
-  },
-  {
-    "id": 654,
-    "problem_id": 638,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/638.jpg"
-  },
-  {
-    "id": 655,
-    "problem_id": 639,
-    "problem": "line B C, line A D C, line A B, line D B, line B C, line A D C, line A B, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/639.jpg"
-  },
-  {
-    "id": 656,
-    "problem_id": 640,
-    "problem": "line R T, line S T, line S R, line R T, line S T, line S R\nWhat is m \\angle S?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/640.jpg"
-  },
-  {
-    "id": 657,
-    "problem_id": 641,
-    "problem": "line R T, line S T, line S R, line R T, line S T, line S R\nWhat is m \\angle S?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/641.jpg"
-  },
-  {
-    "id": 658,
-    "problem_id": 642,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the perimeter of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/642.jpg"
-  },
-  {
-    "id": 659,
-    "problem_id": 643,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the perimeter of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/643.jpg"
-  },
-  {
-    "id": 660,
-    "problem_id": 644,
-    "problem": "line A B, line B E, line C D E, line A C, line A D, line A B, line B E, line C D E, line A C, line A D\nFind the perimeter of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/644.jpg"
-  },
-  {
-    "id": 661,
-    "problem_id": 645,
-    "problem": "line H I C D, line G I B, line E C B, line F I A, line H I C D, line G I B, line E C B, line F I A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/645.jpg"
-  },
-  {
-    "id": 662,
-    "problem_id": 646,
-    "problem": "line H I C D, line G I B, line E C B, line F I A, line H I C D, line G I B, line E C B, line F I A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/646.jpg"
-  },
-  {
-    "id": 663,
-    "problem_id": 647,
-    "problem": "line H I C D, line G I B, line E C B, line F I A, line H I C D, line G I B, line E C B, line F I A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/647.jpg"
-  },
-  {
-    "id": 664,
-    "problem_id": 648,
-    "problem": "line H I C D, line G I B, line E C B, line F I A, line H I C D, line G I B, line E C B, line F I A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/648.jpg"
-  },
-  {
-    "id": 665,
-    "problem_id": 649,
-    "problem": "line H I C D, line G I B, line E C B, line F I A, line H I C D, line G I B, line E C B, line F I A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/649.jpg"
-  },
-  {
-    "id": 666,
-    "problem_id": 650,
-    "problem": "line A C E, line E D, line B C D, line B A, line A C E, line E D, line B C D, line B A\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/650.jpg"
-  },
-  {
-    "id": 667,
-    "problem_id": 651,
-    "problem": "line A C B, \\odot C lieson A B, line A C B, \\odot C lieson A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/651.jpg"
-  },
-  {
-    "id": 668,
-    "problem_id": 652,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind the measure of \\angle ADB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/652.jpg"
-  },
-  {
-    "id": 669,
-    "problem_id": 653,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/653.jpg"
-  },
-  {
-    "id": 670,
-    "problem_id": 654,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/654.jpg"
-  },
-  {
-    "id": 671,
-    "problem_id": 655,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/655.jpg"
-  },
-  {
-    "id": 672,
-    "problem_id": 656,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/656.jpg"
-  },
-  {
-    "id": 673,
-    "problem_id": 657,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/657.jpg"
-  },
-  {
-    "id": 674,
-    "problem_id": 658,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/658.jpg"
-  },
-  {
-    "id": 675,
-    "problem_id": 659,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/659.jpg"
-  },
-  {
-    "id": 677,
-    "problem_id": 660,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/660.jpg"
-  },
-  {
-    "id": 678,
-    "problem_id": 661,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/661.jpg"
-  },
-  {
-    "id": 679,
-    "problem_id": 662,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/662.jpg"
-  },
-  {
-    "id": 680,
-    "problem_id": 663,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/663.jpg"
-  },
-  {
-    "id": 681,
-    "problem_id": 664,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/664.jpg"
-  },
-  {
-    "id": 682,
-    "problem_id": 665,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/665.jpg"
-  },
-  {
-    "id": 683,
-    "problem_id": 666,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/666.jpg"
-  },
-  {
-    "id": 684,
-    "problem_id": 667,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/667.jpg"
-  },
-  {
-    "id": 685,
-    "problem_id": 668,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/668.jpg"
-  },
-  {
-    "id": 686,
-    "problem_id": 669,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/669.jpg"
-  },
-  {
-    "id": 687,
-    "problem_id": 670,
-    "problem": "line A B E F, line D E, line C B, line A B E F, line D E, line C B\nm \\angle 8 = m \\angle 5 and m \\angle 5 = 125. What is the measurement of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/670.jpg"
-  },
-  {
-    "id": 688,
-    "problem_id": 671,
-    "problem": "line A B E F, line D E, line C B, line A B E F, line D E, line C B\nm \\angle 8 = m \\angle 5 and m \\angle 5 = 125. What is the measurement of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/671.jpg"
-  },
-  {
-    "id": 689,
-    "problem_id": 672,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/672.jpg"
-  },
-  {
-    "id": 690,
-    "problem_id": 673,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/673.jpg"
-  },
-  {
-    "id": 691,
-    "problem_id": 674,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/674.jpg"
-  },
-  {
-    "id": 692,
-    "problem_id": 675,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/675.jpg"
-  },
-  {
-    "id": 693,
-    "problem_id": 676,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/676.jpg"
-  },
-  {
-    "id": 694,
-    "problem_id": 677,
-    "problem": "line F E, line C D, line D E, line C F, line F E, line C D, line D E, line C F\nEDCF is a rectangle. Find the length of EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/677.jpg"
-  },
-  {
-    "id": 695,
-    "problem_id": 678,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/678.jpg"
-  },
-  {
-    "id": 696,
-    "problem_id": 679,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/679.jpg"
-  },
-  {
-    "id": 697,
-    "problem_id": 680,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/680.jpg"
-  },
-  {
-    "id": 698,
-    "problem_id": 681,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/681.jpg"
-  },
-  {
-    "id": 699,
-    "problem_id": 682,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/682.jpg"
-  },
-  {
-    "id": 700,
-    "problem_id": 683,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/683.jpg"
-  },
-  {
-    "id": 701,
-    "problem_id": 684,
-    "problem": "line C D, line A B D, line C B, line A C, line C D, line A B D, line C B, line A C\nFind the value of p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/684.jpg"
-  },
-  {
-    "id": 702,
-    "problem_id": 685,
-    "problem": "line S R P, line U T P, line Q P, \\odot A lieson S U T R Q, line S R P, line U T P, line Q P, \\odot A lieson S U T R Q\nWhat is the length of PU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/685.jpg"
-  },
-  {
-    "id": 703,
-    "problem_id": 686,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/686.jpg"
-  },
-  {
-    "id": 704,
-    "problem_id": 687,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/687.jpg"
-  },
-  {
-    "id": 705,
-    "problem_id": 688,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/688.jpg"
-  },
-  {
-    "id": 706,
-    "problem_id": 689,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/689.jpg"
-  },
-  {
-    "id": 707,
-    "problem_id": 690,
-    "problem": "line E J G, line E H, line F G, line F J H, line F E, line G H, line E J G, line E H, line F G, line F J H, line F E, line G H\nEFGH is a parallelogram. Find HF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/690.jpg"
-  },
-  {
-    "id": 708,
-    "problem_id": 691,
-    "problem": "line E J G, line E H, line F G, line F J H, line F E, line G H, line E J G, line E H, line F G, line F J H, line F E, line G H\nEFGH is a parallelogram. Find HF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/691.jpg"
-  },
-  {
-    "id": 709,
-    "problem_id": 692,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line D E B, line A D, line D C, line B C, line A B, line A E C, line D E B\nWhat is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/692.jpg"
-  },
-  {
-    "id": 710,
-    "problem_id": 693,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line D E B, line A D, line D C, line B C, line A B, line A E C, line D E B\nWhat is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/693.jpg"
-  },
-  {
-    "id": 712,
-    "problem_id": 694,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line D E B, line A D, line D C, line B C, line A B, line A E C, line D E B\nWhat is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/694.jpg"
-  },
-  {
-    "id": 713,
-    "problem_id": 695,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line D E B, line A D, line D C, line B C, line A B, line A E C, line D E B\nWhat is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/695.jpg"
-  },
-  {
-    "id": 714,
-    "problem_id": 696,
-    "problem": "line C J L, line L M B, line L K A, line J M, line M K, line C J L, line L M B, line L K A, line J M, line M K\nWhat is the measure of \\angle KLM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/696.jpg"
-  },
-  {
-    "id": 715,
-    "problem_id": 697,
-    "problem": "line C J L, line L M B, line L K A, line J M, line M K, line C J L, line L M B, line L K A, line J M, line M K\nWhat is the measure of \\angle KLM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/697.jpg"
-  },
-  {
-    "id": 716,
-    "problem_id": 698,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/698.jpg"
-  },
-  {
-    "id": 717,
-    "problem_id": 699,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/699.jpg"
-  },
-  {
-    "id": 718,
-    "problem_id": 700,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/700.jpg"
-  },
-  {
-    "id": 719,
-    "problem_id": 701,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/701.jpg"
-  },
-  {
-    "id": 720,
-    "problem_id": 702,
-    "problem": "line C B, line B D, line C D E, line A E, line D A, line C B, line B D, line C D E, line A E, line D A\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/702.jpg"
-  },
-  {
-    "id": 721,
-    "problem_id": 703,
-    "problem": "line C B, line B D, line C D E, line A E, line D A, line C B, line B D, line C D E, line A E, line D A\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/703.jpg"
-  },
-  {
-    "id": 722,
-    "problem_id": 704,
-    "problem": "line C B, line B D, line C D E, line A E, line D A, line C B, line B D, line C D E, line A E, line D A\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/704.jpg"
-  },
-  {
-    "id": 723,
-    "problem_id": 705,
-    "problem": "line C B, line B D, line C D E, line A E, line D A, line C B, line B D, line C D E, line A E, line D A\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/705.jpg"
-  },
-  {
-    "id": 724,
-    "problem_id": 706,
-    "problem": "line X Y, line Y Z, line X Z, line X Y, line Y Z, line X Z\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/706.jpg"
-  },
-  {
-    "id": 725,
-    "problem_id": 707,
-    "problem": "line X Y, line Y Z, line X Z, line X Y, line Y Z, line X Z\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/707.jpg"
-  },
-  {
-    "id": 726,
-    "problem_id": 708,
-    "problem": "line X Y, line Y Z, line X Z, line X Y, line Y Z, line X Z\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/708.jpg"
-  },
-  {
-    "id": 727,
-    "problem_id": 709,
-    "problem": "line X Y, line Y Z, line X Z, line X Y, line Y Z, line X Z\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/709.jpg"
-  },
-  {
-    "id": 728,
-    "problem_id": 710,
-    "problem": "line X Y, line Y Z, line X Z, line X Y, line Y Z, line X Z\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/710.jpg"
-  },
-  {
-    "id": 729,
-    "problem_id": 711,
-    "problem": "line X Y, line Y Z, line X Z, line X Y, line Y Z, line X Z\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/711.jpg"
-  },
-  {
-    "id": 730,
-    "problem_id": 712,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AB = EF, EF = BC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/712.jpg"
-  },
-  {
-    "id": 731,
-    "problem_id": 713,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AB = EF, EF = BC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/713.jpg"
-  },
-  {
-    "id": 732,
-    "problem_id": 714,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AB = EF, EF = BC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/714.jpg"
-  },
-  {
-    "id": 733,
-    "problem_id": 715,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AB = EF, EF = BC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/715.jpg"
-  },
-  {
-    "id": 734,
-    "problem_id": 716,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AB = EF, EF = BC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/716.jpg"
-  },
-  {
-    "id": 735,
-    "problem_id": 717,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AB = EF, EF = BC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/717.jpg"
-  },
-  {
-    "id": 736,
-    "problem_id": 718,
-    "problem": "line A C, line A B E, line C D E, line B D, line A C, line A B E, line C D E, line B D\nFind f.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/718.jpg"
-  },
-  {
-    "id": 737,
-    "problem_id": 719,
-    "problem": "line G F, line D A, line D C, line A B, line C B, line E F, line H G, line H E, line G F, line D A, line D C, line A B, line C B, line E F, line H G, line H E\n\\parallelogram ABCD \\sim \\parallelogram EFGH. Find the perimeter of \\parallelogram EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/719.jpg"
-  },
-  {
-    "id": 739,
-    "problem_id": 720,
-    "problem": "line A B, line A C, line A D, line B D C, line A B, line A C, line A D, line B D C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/720.jpg"
-  },
-  {
-    "id": 740,
-    "problem_id": 721,
-    "problem": "line A B, line A C, line A D, line B D C, line A B, line A C, line A D, line B D C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/721.jpg"
-  },
-  {
-    "id": 741,
-    "problem_id": 722,
-    "problem": "line A B, line A C, line A D, line B D C, line A B, line A C, line A D, line B D C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/722.jpg"
-  },
-  {
-    "id": 742,
-    "problem_id": 723,
-    "problem": "line A B, line A C, line A D, line B D C, line A B, line A C, line A D, line B D C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/723.jpg"
-  },
-  {
-    "id": 743,
-    "problem_id": 724,
-    "problem": "line A B, line A C, line A D, line B D C, line A B, line A C, line A D, line B D C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/724.jpg"
-  },
-  {
-    "id": 744,
-    "problem_id": 725,
-    "problem": "line D C B, line A B, \\odot N lieson D C A, line D C B, line A B, \\odot N lieson D C A\nFind the value of variable z in \\odot N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/725.jpg"
-  },
-  {
-    "id": 745,
-    "problem_id": 726,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/726.jpg"
-  },
-  {
-    "id": 746,
-    "problem_id": 727,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/727.jpg"
-  },
-  {
-    "id": 747,
-    "problem_id": 728,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/728.jpg"
-  },
-  {
-    "id": 748,
-    "problem_id": 729,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/729.jpg"
-  },
-  {
-    "id": 749,
-    "problem_id": 730,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/730.jpg"
-  },
-  {
-    "id": 750,
-    "problem_id": 731,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/731.jpg"
-  },
-  {
-    "id": 751,
-    "problem_id": 732,
-    "problem": "line W V, line T U, line T W, line T V, line U V, line W V, line T U, line T W, line T V, line U V\nGiven that the perimeter of TUVW is 149 units, find VU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/732.jpg"
-  },
-  {
-    "id": 752,
-    "problem_id": 733,
-    "problem": "line W V, line T U, line T W, line T V, line U V, line W V, line T U, line T W, line T V, line U V\nGiven that the perimeter of TUVW is 149 units, find VU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/733.jpg"
-  },
-  {
-    "id": 753,
-    "problem_id": 734,
-    "problem": "line W V, line T U, line T W, line T V, line U V, line W V, line T U, line T W, line T V, line U V\nGiven that the perimeter of TUVW is 149 units, find VU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/734.jpg"
-  },
-  {
-    "id": 754,
-    "problem_id": 735,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find the length of PQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/735.jpg"
-  },
-  {
-    "id": 755,
-    "problem_id": 736,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find the length of PQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/736.jpg"
-  },
-  {
-    "id": 756,
-    "problem_id": 737,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find the length of PQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/737.jpg"
-  },
-  {
-    "id": 757,
-    "problem_id": 738,
-    "problem": "line A C D, line A B, line A E, line B C E, line B D, line E D, line A C D, line A B, line A E, line B C E, line B D, line E D\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/738.jpg"
-  },
-  {
-    "id": 758,
-    "problem_id": 739,
-    "problem": "line A C D, line A B, line A E, line B C E, line B D, line E D, line A C D, line A B, line A E, line B C E, line B D, line E D\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/739.jpg"
-  },
-  {
-    "id": 759,
-    "problem_id": 740,
-    "problem": "line A C D, line A B, line A E, line B C E, line B D, line E D, line A C D, line A B, line A E, line B C E, line B D, line E D\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/740.jpg"
-  },
-  {
-    "id": 760,
-    "problem_id": 741,
-    "problem": "line A C D, line A B, line A E, line B C E, line B D, line E D, line A C D, line A B, line A E, line B C E, line B D, line E D\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/741.jpg"
-  },
-  {
-    "id": 761,
-    "problem_id": 742,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/742.jpg"
-  },
-  {
-    "id": 762,
-    "problem_id": 743,
-    "problem": "line A B D, line C D, \\odot E lieson A C B, line A B D, line C D, \\odot E lieson A C B\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/743.jpg"
-  },
-  {
-    "id": 763,
-    "problem_id": 744,
-    "problem": "line A B D, line C D, \\odot E lieson A C B, line A B D, line C D, \\odot E lieson A C B\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/744.jpg"
-  },
-  {
-    "id": 764,
-    "problem_id": 745,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/745.jpg"
-  },
-  {
-    "id": 765,
-    "problem_id": 746,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/746.jpg"
-  },
-  {
-    "id": 766,
-    "problem_id": 747,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/747.jpg"
-  },
-  {
-    "id": 767,
-    "problem_id": 748,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/748.jpg"
-  },
-  {
-    "id": 768,
-    "problem_id": 749,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/749.jpg"
-  },
-  {
-    "id": 769,
-    "problem_id": 750,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/750.jpg"
-  },
-  {
-    "id": 770,
-    "problem_id": 751,
-    "problem": "line Q P, \\odot Q lieson P, line Q P, \\odot Q lieson P\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/751.jpg"
-  },
-  {
-    "id": 771,
-    "problem_id": 752,
-    "problem": "line C D G, line A G B, line A F C, line C E B, line A D E, line F D B, line C D G, line A G B, line A F C, line C E B, line A D E, line F D B\nAE, BF, and CG are medians. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/752.jpg"
-  },
-  {
-    "id": 772,
-    "problem_id": 753,
-    "problem": "line C D G, line A G B, line A F C, line C E B, line A D E, line F D B, line C D G, line A G B, line A F C, line C E B, line A D E, line F D B\nAE, BF, and CG are medians. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/753.jpg"
-  },
-  {
-    "id": 773,
-    "problem_id": 754,
-    "problem": "line W P Y, line X P Z, line Z Y, line W Z, line X W, line X Y, line W P Y, line X P Z, line Z Y, line W Z, line X W, line X Y\nIf WXYZ is a kite, find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/754.jpg"
-  },
-  {
-    "id": 774,
-    "problem_id": 755,
-    "problem": "line A B C, line B D E, \\odot D lieson E B, line A B C, line B D E, \\odot D lieson E B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/755.jpg"
-  },
-  {
-    "id": 775,
-    "problem_id": 756,
-    "problem": "line A B C, line B D E, \\odot D lieson E B, line A B C, line B D E, \\odot D lieson E B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/756.jpg"
-  },
-  {
-    "id": 776,
-    "problem_id": 757,
-    "problem": "line A B C, line B D E, \\odot D lieson E B, line A B C, line B D E, \\odot D lieson E B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/757.jpg"
-  },
-  {
-    "id": 777,
-    "problem_id": 758,
-    "problem": "line E P B, line F P C, line A P D, line A F E, line E D C, line A B C, line E P B, line F P C, line A P D, line A F E, line E D C, line A B C\nP is the incenter of \\triangle AEC. Find EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/758.jpg"
-  },
-  {
-    "id": 778,
-    "problem_id": 759,
-    "problem": "line E P B, line F P C, line A P D, line A F E, line E D C, line A B C, line E P B, line F P C, line A P D, line A F E, line E D C, line A B C\nP is the incenter of \\triangle AEC. Find EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/759.jpg"
-  },
-  {
-    "id": 779,
-    "problem_id": 760,
-    "problem": "line E P B, line F P C, line A P D, line A F E, line E D C, line A B C, line E P B, line F P C, line A P D, line A F E, line E D C, line A B C\nP is the incenter of \\triangle AEC. Find EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/760.jpg"
-  },
-  {
-    "id": 780,
-    "problem_id": 761,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/761.jpg"
-  },
-  {
-    "id": 781,
-    "problem_id": 762,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/762.jpg"
-  },
-  {
-    "id": 782,
-    "problem_id": 763,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/763.jpg"
-  },
-  {
-    "id": 783,
-    "problem_id": 764,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/764.jpg"
-  },
-  {
-    "id": 784,
-    "problem_id": 765,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/765.jpg"
-  },
-  {
-    "id": 785,
-    "problem_id": 766,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/766.jpg"
-  },
-  {
-    "id": 786,
-    "problem_id": 767,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/767.jpg"
-  },
-  {
-    "id": 787,
-    "problem_id": 768,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/768.jpg"
-  },
-  {
-    "id": 788,
-    "problem_id": 769,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/769.jpg"
-  },
-  {
-    "id": 789,
-    "problem_id": 770,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/770.jpg"
-  },
-  {
-    "id": 790,
-    "problem_id": 771,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/771.jpg"
-  },
-  {
-    "id": 791,
-    "problem_id": 772,
-    "problem": "line X W, line W Z, line X Y, line Y Z, line X W, line W Z, line X Y, line Y Z\nIf WXYZ is a kite, find m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/772.jpg"
-  },
-  {
-    "id": 792,
-    "problem_id": 773,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/773.jpg"
-  },
-  {
-    "id": 793,
-    "problem_id": 774,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/774.jpg"
-  },
-  {
-    "id": 794,
-    "problem_id": 775,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/775.jpg"
-  },
-  {
-    "id": 795,
-    "problem_id": 776,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/776.jpg"
-  },
-  {
-    "id": 796,
-    "problem_id": 777,
-    "problem": "line A D C, line B C, line B A, \\odot A lieson B D, line A D C, line B C, line B A, \\odot A lieson B D\nIf m \\angle A = 58, what is m \\angle ACB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/777.jpg"
-  },
-  {
-    "id": 797,
-    "problem_id": 778,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/778.jpg"
-  },
-  {
-    "id": 798,
-    "problem_id": 779,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/779.jpg"
-  },
-  {
-    "id": 799,
-    "problem_id": 780,
-    "problem": "line D C, line B C, line A B, line A D, line A C, line D C, line B C, line A B, line A D, line A C\nGiven parallelogram ABCD. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/780.jpg"
-  },
-  {
-    "id": 800,
-    "problem_id": 781,
-    "problem": "line D C, line B C, line A B, line A D, line A C, line D C, line B C, line A B, line A D, line A C\nGiven parallelogram ABCD. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/781.jpg"
-  },
-  {
-    "id": 801,
-    "problem_id": 782,
-    "problem": "line D C, line B C, line A B, line A D, line A C, line D C, line B C, line A B, line A D, line A C\nGiven parallelogram ABCD. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/782.jpg"
-  },
-  {
-    "id": 803,
-    "problem_id": 783,
-    "problem": "line D C, line B C, line A B, line A D, line A C, line D C, line B C, line A B, line A D, line A C\nGiven parallelogram ABCD. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/783.jpg"
-  },
-  {
-    "id": 804,
-    "problem_id": 784,
-    "problem": "line D C, line B C, line A B, line A D, line A C, line D C, line B C, line A B, line A D, line A C\nGiven parallelogram ABCD. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/784.jpg"
-  },
-  {
-    "id": 805,
-    "problem_id": 785,
-    "problem": "line D C, line B C, line A B, line A D, line A C, line D C, line B C, line A B, line A D, line A C\nGiven parallelogram ABCD. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/785.jpg"
-  },
-  {
-    "id": 806,
-    "problem_id": 786,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/786.jpg"
-  },
-  {
-    "id": 807,
-    "problem_id": 787,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/787.jpg"
-  },
-  {
-    "id": 808,
-    "problem_id": 788,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/788.jpg"
-  },
-  {
-    "id": 809,
-    "problem_id": 789,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/789.jpg"
-  },
-  {
-    "id": 810,
-    "problem_id": 790,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/790.jpg"
-  },
-  {
-    "id": 811,
-    "problem_id": 791,
-    "problem": "line J K, line K L, \\odot K lieson L J, line J K, line K L, \\odot K lieson L J\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/791.jpg"
-  },
-  {
-    "id": 812,
-    "problem_id": 792,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = x-4, m \\angle 12 = 2x-5, find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/792.jpg"
-  },
-  {
-    "id": 813,
-    "problem_id": 793,
-    "problem": "line G F, line E H F, line G E, line G H, line G F, line E H F, line G E, line G H\nFind HF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/793.jpg"
-  },
-  {
-    "id": 814,
-    "problem_id": 794,
-    "problem": "line G F, line E H F, line G E, line G H, line G F, line E H F, line G E, line G H\nFind HF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/794.jpg"
-  },
-  {
-    "id": 815,
-    "problem_id": 795,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind the perimeter of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/795.jpg"
-  },
-  {
-    "id": 816,
-    "problem_id": 796,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/796.jpg"
-  },
-  {
-    "id": 817,
-    "problem_id": 797,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/797.jpg"
-  },
-  {
-    "id": 818,
-    "problem_id": 798,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/798.jpg"
-  },
-  {
-    "id": 819,
-    "problem_id": 799,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/799.jpg"
-  },
-  {
-    "id": 820,
-    "problem_id": 800,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/800.jpg"
-  },
-  {
-    "id": 821,
-    "problem_id": 801,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/801.jpg"
-  },
-  {
-    "id": 822,
-    "problem_id": 802,
-    "problem": "line A P Q R S B, line A P Q R S B\nFind the measurement of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/802.jpg"
-  },
-  {
-    "id": 823,
-    "problem_id": 803,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/803.jpg"
-  },
-  {
-    "id": 824,
-    "problem_id": 804,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/804.jpg"
-  },
-  {
-    "id": 825,
-    "problem_id": 805,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/805.jpg"
-  },
-  {
-    "id": 826,
-    "problem_id": 806,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/806.jpg"
-  },
-  {
-    "id": 827,
-    "problem_id": 807,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/807.jpg"
-  },
-  {
-    "id": 828,
-    "problem_id": 808,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/808.jpg"
-  },
-  {
-    "id": 829,
-    "problem_id": 809,
-    "problem": "line A B, line E B, line A C F, line C B, \\odot B lieson A F E, line A B, line E B, line A C F, line C B, \\odot B lieson A F E\nWhat is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/809.jpg"
-  },
-  {
-    "id": 830,
-    "problem_id": 810,
-    "problem": "line A C, line A D, line C D, line B D, \\odot B lieson C D A, line A C, line A D, line C D, line B D, \\odot B lieson C D A\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/810.jpg"
-  },
-  {
-    "id": 831,
-    "problem_id": 811,
-    "problem": "line M A K, line H M, line J K, line J A, line H J, line M A K, line H M, line J K, line J A, line H J\nThe area of trapezoid HJKM is 90 square centimeters. What is the length of JK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/811.jpg"
-  },
-  {
-    "id": 832,
-    "problem_id": 812,
-    "problem": "line A C B, \\odot C lieson A B, line A C B, \\odot C lieson A B\nDetermine the radius of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/812.jpg"
-  },
-  {
-    "id": 833,
-    "problem_id": 813,
-    "problem": "line A C B, \\odot C lieson A B, line A C B, \\odot C lieson A B\nDetermine the radius of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/813.jpg"
-  },
-  {
-    "id": 834,
-    "problem_id": 814,
-    "problem": "line A C B, \\odot C lieson A B, line A C B, \\odot C lieson A B\nDetermine the radius of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/814.jpg"
-  },
-  {
-    "id": 835,
-    "problem_id": 815,
-    "problem": "line A C B, \\odot C lieson A B, line A C B, \\odot C lieson A B\nDetermine the radius of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/815.jpg"
-  },
-  {
-    "id": 836,
-    "problem_id": 816,
-    "problem": "line A C B, \\odot C lieson A B, line A C B, \\odot C lieson A B\nDetermine the radius of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/816.jpg"
-  },
-  {
-    "id": 837,
-    "problem_id": 817,
-    "problem": "line A B, line B F, line D E F, line A D, line C E, line A B, line B F, line D E F, line A D, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/817.jpg"
-  },
-  {
-    "id": 838,
-    "problem_id": 818,
-    "problem": "line A B, line B F, line D E F, line A D, line C E, line A B, line B F, line D E F, line A D, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/818.jpg"
-  },
-  {
-    "id": 839,
-    "problem_id": 819,
-    "problem": "line A B, line B F, line D E F, line A D, line C E, line A B, line B F, line D E F, line A D, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/819.jpg"
-  },
-  {
-    "id": 841,
-    "problem_id": 820,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/820.jpg"
-  },
-  {
-    "id": 842,
-    "problem_id": 821,
-    "problem": "line E F G, line B C G, line A D F, line A E, line A B, line C D, line E F G, line B C G, line A D F, line A E, line A B, line C D\nFind h in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/821.jpg"
-  },
-  {
-    "id": 843,
-    "problem_id": 822,
-    "problem": "line E F G, line B C G, line A D F, line A E, line A B, line C D, line E F G, line B C G, line A D F, line A E, line A B, line C D\nFind h in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/822.jpg"
-  },
-  {
-    "id": 844,
-    "problem_id": 823,
-    "problem": "line E F G, line B C G, line A D F, line A E, line A B, line C D, line E F G, line B C G, line A D F, line A E, line A B, line C D\nFind h in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/823.jpg"
-  },
-  {
-    "id": 845,
-    "problem_id": 824,
-    "problem": "line E F G, line B C G, line A D F, line A E, line A B, line C D, line E F G, line B C G, line A D F, line A E, line A B, line C D\nFind h in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/824.jpg"
-  },
-  {
-    "id": 846,
-    "problem_id": 825,
-    "problem": "line J M, line L M, line K L, line K J, line K M, line J M, line L M, line K L, line K J, line K M\nUse rhombus JKLM to find m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/825.jpg"
-  },
-  {
-    "id": 847,
-    "problem_id": 826,
-    "problem": "line J M, line L M, line K L, line K J, line K M, line J M, line L M, line K L, line K J, line K M\nUse rhombus JKLM to find m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/826.jpg"
-  },
-  {
-    "id": 848,
-    "problem_id": 827,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/827.jpg"
-  },
-  {
-    "id": 849,
-    "problem_id": 828,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/828.jpg"
-  },
-  {
-    "id": 850,
-    "problem_id": 829,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/829.jpg"
-  },
-  {
-    "id": 851,
-    "problem_id": 830,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/830.jpg"
-  },
-  {
-    "id": 852,
-    "problem_id": 831,
-    "problem": "line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G, line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G\nm \\widehat JH = 114. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/831.jpg"
-  },
-  {
-    "id": 853,
-    "problem_id": 832,
-    "problem": "line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G, line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G\nm \\widehat JH = 114. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/832.jpg"
-  },
-  {
-    "id": 854,
-    "problem_id": 833,
-    "problem": "line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G, line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G\nm \\widehat JH = 114. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/833.jpg"
-  },
-  {
-    "id": 855,
-    "problem_id": 834,
-    "problem": "line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G, line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G\nm \\widehat JH = 114. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/834.jpg"
-  },
-  {
-    "id": 856,
-    "problem_id": 835,
-    "problem": "line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G, line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G\nm \\widehat JH = 114. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/835.jpg"
-  },
-  {
-    "id": 857,
-    "problem_id": 836,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/836.jpg"
-  },
-  {
-    "id": 858,
-    "problem_id": 837,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/837.jpg"
-  },
-  {
-    "id": 859,
-    "problem_id": 838,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/838.jpg"
-  },
-  {
-    "id": 860,
-    "problem_id": 839,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/839.jpg"
-  },
-  {
-    "id": 861,
-    "problem_id": 840,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/840.jpg"
-  },
-  {
-    "id": 862,
-    "problem_id": 841,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/841.jpg"
-  },
-  {
-    "id": 863,
-    "problem_id": 842,
-    "problem": "line B C D, line A C E, \\odot F lieson A B E D, line B C D, line A C E, \\odot F lieson A B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/842.jpg"
-  },
-  {
-    "id": 864,
-    "problem_id": 843,
-    "problem": "line B A, line C A, \\odot A lieson B C, line B A, line C A, \\odot A lieson B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/843.jpg"
-  },
-  {
-    "id": 865,
-    "problem_id": 844,
-    "problem": "line N M, line L M, line L N, line S R, line R Q, line S Q, line N M, line L M, line L N, line S R, line R Q, line S Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/844.jpg"
-  },
-  {
-    "id": 866,
-    "problem_id": 845,
-    "problem": "line N M, line L M, line L N, line S R, line R Q, line S Q, line N M, line L M, line L N, line S R, line R Q, line S Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/845.jpg"
-  },
-  {
-    "id": 867,
-    "problem_id": 846,
-    "problem": "line N M, line L M, line L N, line S R, line R Q, line S Q, line N M, line L M, line L N, line S R, line R Q, line S Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/846.jpg"
-  },
-  {
-    "id": 868,
-    "problem_id": 847,
-    "problem": "line N M, line L M, line L N, line S R, line R Q, line S Q, line N M, line L M, line L N, line S R, line R Q, line S Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/847.jpg"
-  },
-  {
-    "id": 869,
-    "problem_id": 848,
-    "problem": "line N M, line L M, line L N, line S R, line R Q, line S Q, line N M, line L M, line L N, line S R, line R Q, line S Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/848.jpg"
-  },
-  {
-    "id": 870,
-    "problem_id": 849,
-    "problem": "line K N L, line B J N A, line J K, line J L, line K N L, line B J N A, line J K, line J L\nFind the measure of JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/849.jpg"
-  },
-  {
-    "id": 871,
-    "problem_id": 850,
-    "problem": "line K N L, line B J N A, line J K, line J L, line K N L, line B J N A, line J K, line J L\nFind the measure of JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/850.jpg"
-  },
-  {
-    "id": 872,
-    "problem_id": 851,
-    "problem": "line K N L, line B J N A, line J K, line J L, line K N L, line B J N A, line J K, line J L\nFind the measure of JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/851.jpg"
-  },
-  {
-    "id": 873,
-    "problem_id": 852,
-    "problem": "line K N L, line B J N A, line J K, line J L, line K N L, line B J N A, line J K, line J L\nFind the measure of JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/852.jpg"
-  },
-  {
-    "id": 874,
-    "problem_id": 853,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/853.jpg"
-  },
-  {
-    "id": 875,
-    "problem_id": 854,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/854.jpg"
-  },
-  {
-    "id": 876,
-    "problem_id": 855,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/855.jpg"
-  },
-  {
-    "id": 877,
-    "problem_id": 856,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/856.jpg"
-  },
-  {
-    "id": 878,
-    "problem_id": 857,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/857.jpg"
-  },
-  {
-    "id": 879,
-    "problem_id": 858,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/858.jpg"
-  },
-  {
-    "id": 880,
-    "problem_id": 859,
-    "problem": "line B A, line A C, line B C, line G H, line F H, line G F, line B A, line A C, line B C, line G H, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/859.jpg"
-  },
-  {
-    "id": 881,
-    "problem_id": 860,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nExpress the ratio of \\tan A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/860.jpg"
-  },
-  {
-    "id": 882,
-    "problem_id": 861,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nExpress the ratio of \\tan A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/861.jpg"
-  },
-  {
-    "id": 883,
-    "problem_id": 862,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nABCD is a parallelogram. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/862.jpg"
-  },
-  {
-    "id": 884,
-    "problem_id": 863,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nABCD is a parallelogram. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/863.jpg"
-  },
-  {
-    "id": 885,
-    "problem_id": 864,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nABCD is a parallelogram. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/864.jpg"
-  },
-  {
-    "id": 886,
-    "problem_id": 865,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nABCD is a parallelogram. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/865.jpg"
-  },
-  {
-    "id": 887,
-    "problem_id": 866,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nABCD is a parallelogram. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/866.jpg"
-  },
-  {
-    "id": 888,
-    "problem_id": 867,
-    "problem": "line A C, line B C, line A B, \\odot C lieson A B, line A C, line B C, line A B, \\odot C lieson A B\nFind the area of the shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/867.jpg"
-  },
-  {
-    "id": 889,
-    "problem_id": 868,
-    "problem": "line A C, line B C, line A B, \\odot C lieson A B, line A C, line B C, line A B, \\odot C lieson A B\nFind the area of the shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/868.jpg"
-  },
-  {
-    "id": 890,
-    "problem_id": 869,
-    "problem": "line A C, line B C, line A B, \\odot C lieson A B, line A C, line B C, line A B, \\odot C lieson A B\nFind the area of the shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/869.jpg"
-  },
-  {
-    "id": 891,
-    "problem_id": 870,
-    "problem": "line A C, line B C, line A B, \\odot C lieson A B, line A C, line B C, line A B, \\odot C lieson A B\nFind the area of the shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/870.jpg"
-  },
-  {
-    "id": 892,
-    "problem_id": 871,
-    "problem": "line A C, line B C, line A B, \\odot C lieson A B, line A C, line B C, line A B, \\odot C lieson A B\nFind the area of the shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/871.jpg"
-  },
-  {
-    "id": 893,
-    "problem_id": 872,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find DY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/872.jpg"
-  },
-  {
-    "id": 894,
-    "problem_id": 873,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find DY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/873.jpg"
-  },
-  {
-    "id": 895,
-    "problem_id": 874,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find DY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/874.jpg"
-  },
-  {
-    "id": 896,
-    "problem_id": 875,
-    "problem": "line B C D, line A D E, \\odot C lieson B D, line B C D, line A D E, \\odot C lieson B D\nWhat is m \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/875.jpg"
-  },
-  {
-    "id": 897,
-    "problem_id": 876,
-    "problem": "line A B C, line E C, line E A, line A D, line C D, line E B D, line A B C, line E C, line E A, line A D, line C D, line E B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/876.jpg"
-  },
-  {
-    "id": 898,
-    "problem_id": 877,
-    "problem": "line A B C, line E C, line E A, line A D, line C D, line E B D, line A B C, line E C, line E A, line A D, line C D, line E B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/877.jpg"
-  },
-  {
-    "id": 899,
-    "problem_id": 878,
-    "problem": "line A B C, line E C, line E A, line A D, line C D, line E B D, line A B C, line E C, line E A, line A D, line C D, line E B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/878.jpg"
-  },
-  {
-    "id": 900,
-    "problem_id": 879,
-    "problem": "line A B C, line E C, line E A, line A D, line C D, line E B D, line A B C, line E C, line E A, line A D, line C D, line E B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/879.jpg"
-  },
-  {
-    "id": 901,
-    "problem_id": 880,
-    "problem": "line A E B, line C B, line D A, line D C, line H F, line H I, line I J, line F G J, line H G, line D E, line A E B, line C B, line D A, line D C, line H F, line H I, line I J, line F G J, line H G, line D E\nFor the pair of similar figures, the area of the blue figure is 60 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/880.jpg"
-  },
-  {
-    "id": 902,
-    "problem_id": 881,
-    "problem": "line A E B, line C B, line D A, line D C, line H F, line H I, line I J, line F G J, line H G, line D E, line A E B, line C B, line D A, line D C, line H F, line H I, line I J, line F G J, line H G, line D E\nFor the pair of similar figures, the area of the blue figure is 60 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/881.jpg"
-  },
-  {
-    "id": 903,
-    "problem_id": 882,
-    "problem": "line C Q N, line B M N, line N P A, line Q P, line M Q, line C Q N, line B M N, line N P A, line Q P, line M Q\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/882.jpg"
-  },
-  {
-    "id": 904,
-    "problem_id": 883,
-    "problem": "line C Q N, line B M N, line N P A, line Q P, line M Q, line C Q N, line B M N, line N P A, line Q P, line M Q\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/883.jpg"
-  },
-  {
-    "id": 905,
-    "problem_id": 884,
-    "problem": "line C Q N, line B M N, line N P A, line Q P, line M Q, line C Q N, line B M N, line N P A, line Q P, line M Q\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/884.jpg"
-  },
-  {
-    "id": 906,
-    "problem_id": 885,
-    "problem": "line C Q N, line B M N, line N P A, line Q P, line M Q, line C Q N, line B M N, line N P A, line Q P, line M Q\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/885.jpg"
-  },
-  {
-    "id": 907,
-    "problem_id": 886,
-    "problem": "line C Q N, line B M N, line N P A, line Q P, line M Q, line C Q N, line B M N, line N P A, line Q P, line M Q\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/886.jpg"
-  },
-  {
-    "id": 908,
-    "problem_id": 887,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/887.jpg"
-  },
-  {
-    "id": 909,
-    "problem_id": 888,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/888.jpg"
-  },
-  {
-    "id": 910,
-    "problem_id": 889,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/889.jpg"
-  },
-  {
-    "id": 911,
-    "problem_id": 890,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/890.jpg"
-  },
-  {
-    "id": 912,
-    "problem_id": 891,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/891.jpg"
-  },
-  {
-    "id": 913,
-    "problem_id": 892,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/892.jpg"
-  },
-  {
-    "id": 914,
-    "problem_id": 893,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/893.jpg"
-  },
-  {
-    "id": 915,
-    "problem_id": 894,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/894.jpg"
-  },
-  {
-    "id": 916,
-    "problem_id": 895,
-    "problem": "line D F, line D E, line F E, \\odot E lieson D F, line D F, line D E, line F E, \\odot E lieson D F\nFind the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/895.jpg"
-  },
-  {
-    "id": 917,
-    "problem_id": 896,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/896.jpg"
-  },
-  {
-    "id": 918,
-    "problem_id": 897,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/897.jpg"
-  },
-  {
-    "id": 919,
-    "problem_id": 898,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/898.jpg"
-  },
-  {
-    "id": 920,
-    "problem_id": 899,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/899.jpg"
-  },
-  {
-    "id": 921,
-    "problem_id": 900,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/900.jpg"
-  },
-  {
-    "id": 922,
-    "problem_id": 901,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/901.jpg"
-  },
-  {
-    "id": 924,
-    "problem_id": 902,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/902.jpg"
-  },
-  {
-    "id": 925,
-    "problem_id": 903,
-    "problem": "line B G H J K A, line B G H J K A\nIf GK = 30, what is GH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/903.jpg"
-  },
-  {
-    "id": 926,
-    "problem_id": 904,
-    "problem": "line B G H J K A, line B G H J K A\nIf GK = 30, what is GH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/904.jpg"
-  },
-  {
-    "id": 927,
-    "problem_id": 905,
-    "problem": "line B G H J K A, line B G H J K A\nIf GK = 30, what is GH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/905.jpg"
-  },
-  {
-    "id": 928,
-    "problem_id": 906,
-    "problem": "line E A, line E D C, line D A, line A B, line C B, line E A, line E D C, line D A, line A B, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/906.jpg"
-  },
-  {
-    "id": 929,
-    "problem_id": 907,
-    "problem": "line E A, line E D C, line D A, line A B, line C B, line E A, line E D C, line D A, line A B, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/907.jpg"
-  },
-  {
-    "id": 931,
-    "problem_id": 908,
-    "problem": "line E A, line E D C, line D A, line A B, line C B, line E A, line E D C, line D A, line A B, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/908.jpg"
-  },
-  {
-    "id": 932,
-    "problem_id": 909,
-    "problem": "line E A, line E D C, line D A, line A B, line C B, line E A, line E D C, line D A, line A B, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/909.jpg"
-  },
-  {
-    "id": 933,
-    "problem_id": 910,
-    "problem": "line D C, line B C, line A B, line A D, line D B, line D C, line B C, line A B, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/910.jpg"
-  },
-  {
-    "id": 934,
-    "problem_id": 911,
-    "problem": "line D C, line B C, line A B, line A D, line D B, line D C, line B C, line A B, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/911.jpg"
-  },
-  {
-    "id": 935,
-    "problem_id": 912,
-    "problem": "line D C, line B C, line A B, line A D, line D B, line D C, line B C, line A B, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/912.jpg"
-  },
-  {
-    "id": 936,
-    "problem_id": 913,
-    "problem": "line D C, line B C, line A B, line A D, line D B, line D C, line B C, line A B, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/913.jpg"
-  },
-  {
-    "id": 937,
-    "problem_id": 914,
-    "problem": "line A M N P B, line C Q N, line A M N P B, line C Q N\nFind m \\angle MNQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/914.jpg"
-  },
-  {
-    "id": 938,
-    "problem_id": 915,
-    "problem": "line A M N P B, line C Q N, line A M N P B, line C Q N\nFind m \\angle MNQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/915.jpg"
-  },
-  {
-    "id": 939,
-    "problem_id": 916,
-    "problem": "line A M N P B, line C Q N, line A M N P B, line C Q N\nFind m \\angle MNQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/916.jpg"
-  },
-  {
-    "id": 941,
-    "problem_id": 917,
-    "problem": "line A M N P B, line C Q N, line A M N P B, line C Q N\nFind m \\angle MNQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/917.jpg"
-  },
-  {
-    "id": 942,
-    "problem_id": 918,
-    "problem": "line A M N P B, line C Q N, line A M N P B, line C Q N\nFind m \\angle MNQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/918.jpg"
-  },
-  {
-    "id": 943,
-    "problem_id": 919,
-    "problem": "line A E C, line D E B, \\odot F lieson D A B C, line A E C, line D E B, \\odot F lieson D A B C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/919.jpg"
-  },
-  {
-    "id": 944,
-    "problem_id": 920,
-    "problem": "line A E C, line D E B, \\odot F lieson D A B C, line A E C, line D E B, \\odot F lieson D A B C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/920.jpg"
-  },
-  {
-    "id": 945,
-    "problem_id": 921,
-    "problem": "line A E C, line D E B, \\odot F lieson D A B C, line A E C, line D E B, \\odot F lieson D A B C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/921.jpg"
-  },
-  {
-    "id": 946,
-    "problem_id": 922,
-    "problem": "line A E C, line D E B, \\odot F lieson D A B C, line A E C, line D E B, \\odot F lieson D A B C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/922.jpg"
-  },
-  {
-    "id": 947,
-    "problem_id": 923,
-    "problem": "line A B, line A C D, line B D, line C B, line A B, line A C D, line B D, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/923.jpg"
-  },
-  {
-    "id": 948,
-    "problem_id": 924,
-    "problem": "line W P Y, line X P Z, line Z Y, line W Z, line X W, line X Y, line W P Y, line X P Z, line Z Y, line W Z, line X W, line X Y\nIf WXYZ is a kite, find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/924.jpg"
-  },
-  {
-    "id": 949,
-    "problem_id": 925,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/925.jpg"
-  },
-  {
-    "id": 950,
-    "problem_id": 926,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/926.jpg"
-  },
-  {
-    "id": 951,
-    "problem_id": 927,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/927.jpg"
-  },
-  {
-    "id": 952,
-    "problem_id": 928,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/928.jpg"
-  },
-  {
-    "id": 953,
-    "problem_id": 929,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/929.jpg"
-  },
-  {
-    "id": 954,
-    "problem_id": 930,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/930.jpg"
-  },
-  {
-    "id": 955,
-    "problem_id": 931,
-    "problem": "line B A, line B C D, \\odot E lieson A C D, line B A, line B C D, \\odot E lieson A C D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/931.jpg"
-  },
-  {
-    "id": 956,
-    "problem_id": 932,
-    "problem": "line B A, line B C D, \\odot E lieson A C D, line B A, line B C D, \\odot E lieson A C D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/932.jpg"
-  },
-  {
-    "id": 957,
-    "problem_id": 933,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nIf c = 8, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/933.jpg"
-  },
-  {
-    "id": 958,
-    "problem_id": 934,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. What is GF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/934.jpg"
-  },
-  {
-    "id": 959,
-    "problem_id": 935,
-    "problem": "line L K, line L N M, line K N, \\odot K lieson L M, line L K, line L N M, line K N, \\odot K lieson L M\nWhat is the value of variable r?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/935.jpg"
-  },
-  {
-    "id": 960,
-    "problem_id": 936,
-    "problem": "line D F, line E F, line E D, line D F, line E F, line E D\nSolve for f.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/936.jpg"
-  },
-  {
-    "id": 961,
-    "problem_id": 937,
-    "problem": "line D F, line E F, line E D, line D F, line E F, line E D\nSolve for f.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/937.jpg"
-  },
-  {
-    "id": 962,
-    "problem_id": 938,
-    "problem": "line D F, line E F, line E D, line D F, line E F, line E D\nSolve for f.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/938.jpg"
-  },
-  {
-    "id": 963,
-    "problem_id": 939,
-    "problem": "line E B, line E D, line D C, line A B C, line E A, line E B, line E D, line D C, line A B C, line E A\nFind the base of the parallelogram given its area with 2000 square units.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/939.jpg"
-  },
-  {
-    "id": 964,
-    "problem_id": 940,
-    "problem": "line E B, line E D, line D C, line A B C, line E A, line E B, line E D, line D C, line A B C, line E A\nFind the base of the parallelogram given its area with 2000 square units.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/940.jpg"
-  },
-  {
-    "id": 965,
-    "problem_id": 941,
-    "problem": "line E B, line E D, line D C, line A B C, line E A, line E B, line E D, line D C, line A B C, line E A\nFind the base of the parallelogram given its area with 2000 square units.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/941.jpg"
-  },
-  {
-    "id": 966,
-    "problem_id": 942,
-    "problem": "line I C D H, line J B E K, line M A F L, line C B A, line N F E D G, line I C D H, line J B E K, line M A F L, line C B A, line N F E D G\nWhat is FD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/942.jpg"
-  },
-  {
-    "id": 967,
-    "problem_id": 943,
-    "problem": "line I C D H, line J B E K, line M A F L, line C B A, line N F E D G, line I C D H, line J B E K, line M A F L, line C B A, line N F E D G\nWhat is FD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/943.jpg"
-  },
-  {
-    "id": 968,
-    "problem_id": 944,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/944.jpg"
-  },
-  {
-    "id": 969,
-    "problem_id": 945,
-    "problem": "line W U, line T U, line S W, line S T, line W U, line T U, line S W, line S T\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/945.jpg"
-  },
-  {
-    "id": 970,
-    "problem_id": 946,
-    "problem": "line W U, line T U, line S W, line S T, line W U, line T U, line S W, line S T\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/946.jpg"
-  },
-  {
-    "id": 971,
-    "problem_id": 947,
-    "problem": "line W U, line T U, line S W, line S T, line W U, line T U, line S W, line S T\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/947.jpg"
-  },
-  {
-    "id": 972,
-    "problem_id": 948,
-    "problem": "line W U, line T U, line S W, line S T, line W U, line T U, line S W, line S T\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/948.jpg"
-  },
-  {
-    "id": 973,
-    "problem_id": 949,
-    "problem": "line W U, line T U, line S W, line S T, line W U, line T U, line S W, line S T\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/949.jpg"
-  },
-  {
-    "id": 974,
-    "problem_id": 950,
-    "problem": "line W U, line T U, line S W, line S T, line W U, line T U, line S W, line S T\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/950.jpg"
-  },
-  {
-    "id": 975,
-    "problem_id": 951,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/951.jpg"
-  },
-  {
-    "id": 976,
-    "problem_id": 952,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/952.jpg"
-  },
-  {
-    "id": 977,
-    "problem_id": 953,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/953.jpg"
-  },
-  {
-    "id": 978,
-    "problem_id": 954,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/954.jpg"
-  },
-  {
-    "id": 979,
-    "problem_id": 955,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/955.jpg"
-  },
-  {
-    "id": 980,
-    "problem_id": 956,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/956.jpg"
-  },
-  {
-    "id": 981,
-    "problem_id": 957,
-    "problem": "line A B, line A P C, line B C, line C D, \\odot P lieson B C A, line A B, line A P C, line B C, line C D, \\odot P lieson B C A\nWhat is m \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/957.jpg"
-  },
-  {
-    "id": 982,
-    "problem_id": 958,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/958.jpg"
-  },
-  {
-    "id": 985,
-    "problem_id": 959,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/959.jpg"
-  },
-  {
-    "id": 986,
-    "problem_id": 960,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/960.jpg"
-  },
-  {
-    "id": 987,
-    "problem_id": 961,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/961.jpg"
-  },
-  {
-    "id": 988,
-    "problem_id": 962,
-    "problem": "line X Z Y, line X Z Y\nIf ZY = 42, what is the length of ZX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/962.jpg"
-  },
-  {
-    "id": 989,
-    "problem_id": 963,
-    "problem": "line X Z Y, line X Z Y\nIf ZY = 42, what is the length of ZX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/963.jpg"
-  },
-  {
-    "id": 990,
-    "problem_id": 964,
-    "problem": "line X Z Y, line X Z Y\nIf ZY = 42, what is the length of ZX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/964.jpg"
-  },
-  {
-    "id": 991,
-    "problem_id": 965,
-    "problem": "line X Z Y, line X Z Y\nIf ZY = 42, what is the length of ZX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/965.jpg"
-  },
-  {
-    "id": 992,
-    "problem_id": 966,
-    "problem": "line X Z Y, line X Z Y\nIf ZY = 42, what is the length of ZX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/966.jpg"
-  },
-  {
-    "id": 993,
-    "problem_id": 967,
-    "problem": "line X Z Y, line X Z Y\nIf ZY = 42, what is the length of ZX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/967.jpg"
-  },
-  {
-    "id": 994,
-    "problem_id": 968,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/968.jpg"
-  },
-  {
-    "id": 995,
-    "problem_id": 969,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/969.jpg"
-  },
-  {
-    "id": 996,
-    "problem_id": 970,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/970.jpg"
-  },
-  {
-    "id": 997,
-    "problem_id": 971,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/971.jpg"
-  },
-  {
-    "id": 998,
-    "problem_id": 972,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/972.jpg"
-  },
-  {
-    "id": 999,
-    "problem_id": 973,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/973.jpg"
-  },
-  {
-    "id": 1000,
-    "problem_id": 974,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/974.jpg"
-  },
-  {
-    "id": 1001,
-    "problem_id": 975,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/975.jpg"
-  },
-  {
-    "id": 1002,
-    "problem_id": 976,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/976.jpg"
-  },
-  {
-    "id": 1003,
-    "problem_id": 977,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/977.jpg"
-  },
-  {
-    "id": 1004,
-    "problem_id": 978,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/978.jpg"
-  },
-  {
-    "id": 1006,
-    "problem_id": 979,
-    "problem": "line B E G, line A D H, line C D E F, line B E G, line A D H, line C D E F\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/979.jpg"
-  },
-  {
-    "id": 1007,
-    "problem_id": 980,
-    "problem": "line B E G, line A D H, line C D E F, line B E G, line A D H, line C D E F\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/980.jpg"
-  },
-  {
-    "id": 1008,
-    "problem_id": 981,
-    "problem": "line K J, line J L, line K M L, line J M, line E D, line E G C, line D C, line D G, line K J, line J L, line K M L, line J M, line E D, line E G C, line D C, line D G\nFind DC if DG and JM are altitudes and \\triangle KJL \\sim \\triangle EDC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/981.jpg"
-  },
-  {
-    "id": 1009,
-    "problem_id": 982,
-    "problem": "line A E C, line D E B, line D C, line B C, line A B, line A D, line A E C, line D E B, line D C, line B C, line A B, line A D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/982.jpg"
-  },
-  {
-    "id": 1010,
-    "problem_id": 983,
-    "problem": "line A E C, line D E B, line D C, line B C, line A B, line A D, line A E C, line D E B, line D C, line B C, line A B, line A D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/983.jpg"
-  },
-  {
-    "id": 1011,
-    "problem_id": 984,
-    "problem": "line A E C, line D E B, line D C, line B C, line A B, line A D, line A E C, line D E B, line D C, line B C, line A B, line A D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/984.jpg"
-  },
-  {
-    "id": 1012,
-    "problem_id": 985,
-    "problem": "line A E C, line D E B, line D C, line B C, line A B, line A D, line A E C, line D E B, line D C, line B C, line A B, line A D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/985.jpg"
-  },
-  {
-    "id": 1013,
-    "problem_id": 986,
-    "problem": "line A E C, line D E B, line D C, line B C, line A B, line A D, line A E C, line D E B, line D C, line B C, line A B, line A D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/986.jpg"
-  },
-  {
-    "id": 1014,
-    "problem_id": 987,
-    "problem": "line A C D, line B D, line B A, line B C, line A C D, line B D, line B A, line B C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/987.jpg"
-  },
-  {
-    "id": 1015,
-    "problem_id": 988,
-    "problem": "line A C D, line B D, line B A, line B C, line A C D, line B D, line B A, line B C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/988.jpg"
-  },
-  {
-    "id": 1016,
-    "problem_id": 989,
-    "problem": "line A C D, line B D, line B A, line B C, line A C D, line B D, line B A, line B C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/989.jpg"
-  },
-  {
-    "id": 1017,
-    "problem_id": 990,
-    "problem": "line A C D, line B D, line B A, line B C, line A C D, line B D, line B A, line B C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/990.jpg"
-  },
-  {
-    "id": 1018,
-    "problem_id": 991,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If m \\angle 2 = 18x-8 and m \\angle 5 = 70-4x, find m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/991.jpg"
-  },
-  {
-    "id": 1019,
-    "problem_id": 992,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If m \\angle 2 = 18x-8 and m \\angle 5 = 70-4x, find m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/992.jpg"
-  },
-  {
-    "id": 1020,
-    "problem_id": 993,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If m \\angle 2 = 18x-8 and m \\angle 5 = 70-4x, find m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/993.jpg"
-  },
-  {
-    "id": 1021,
-    "problem_id": 994,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If m \\angle 2 = 18x-8 and m \\angle 5 = 70-4x, find m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/994.jpg"
-  },
-  {
-    "id": 1022,
-    "problem_id": 995,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If m \\angle 2 = 18x-8 and m \\angle 5 = 70-4x, find m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/995.jpg"
-  },
-  {
-    "id": 1023,
-    "problem_id": 996,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle C of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/996.jpg"
-  },
-  {
-    "id": 1025,
-    "problem_id": 997,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle C of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/997.jpg"
-  },
-  {
-    "id": 1026,
-    "problem_id": 998,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle C of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/998.jpg"
-  },
-  {
-    "id": 1027,
-    "problem_id": 999,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle C of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/999.jpg"
-  },
-  {
-    "id": 1028,
-    "problem_id": 1000,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle C of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1000.jpg"
-  },
-  {
-    "id": 1029,
-    "problem_id": 1001,
-    "problem": "line J A I, line G J, line H I, line G A, line G H, line J A I, line G J, line H I, line G A, line G H\nThe area of trapezoid GHIJ is 103.5 square centimeters. Find the height of trapezoid GHIJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1001.jpg"
-  },
-  {
-    "id": 1030,
-    "problem_id": 1002,
-    "problem": "line J A I, line G J, line H I, line G A, line G H, line J A I, line G J, line H I, line G A, line G H\nThe area of trapezoid GHIJ is 103.5 square centimeters. Find the height of trapezoid GHIJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1002.jpg"
-  },
-  {
-    "id": 1031,
-    "problem_id": 1003,
-    "problem": "line J A I, line G J, line H I, line G A, line G H, line J A I, line G J, line H I, line G A, line G H\nThe area of trapezoid GHIJ is 103.5 square centimeters. Find the height of trapezoid GHIJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1003.jpg"
-  },
-  {
-    "id": 1032,
-    "problem_id": 1004,
-    "problem": "line E G F, line B E, line B A, line A C, line C F, line D F, line D G, line E G F, line B E, line B A, line A C, line C F, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1004.jpg"
-  },
-  {
-    "id": 1033,
-    "problem_id": 1005,
-    "problem": "line E G F, line B E, line B A, line A C, line C F, line D F, line D G, line E G F, line B E, line B A, line A C, line C F, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1005.jpg"
-  },
-  {
-    "id": 1034,
-    "problem_id": 1006,
-    "problem": "line E G F, line B E, line B A, line A C, line C F, line D F, line D G, line E G F, line B E, line B A, line A C, line C F, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1006.jpg"
-  },
-  {
-    "id": 1035,
-    "problem_id": 1007,
-    "problem": "line C D E, line A C, line B D, line B E, line A B, line C D E, line A C, line B D, line B E, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1007.jpg"
-  },
-  {
-    "id": 1036,
-    "problem_id": 1008,
-    "problem": "line C D E, line A C, line B D, line B E, line A B, line C D E, line A C, line B D, line B E, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1008.jpg"
-  },
-  {
-    "id": 1037,
-    "problem_id": 1009,
-    "problem": "line C D E, line A C, line B D, line B E, line A B, line C D E, line A C, line B D, line B E, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1009.jpg"
-  },
-  {
-    "id": 1038,
-    "problem_id": 1010,
-    "problem": "line B D, line C B, \\odot B lieson C D, line B D, line C B, \\odot B lieson C D\nFind m \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1010.jpg"
-  },
-  {
-    "id": 1039,
-    "problem_id": 1011,
-    "problem": "line B D, line C B, \\odot B lieson C D, line B D, line C B, \\odot B lieson C D\nFind m \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1011.jpg"
-  },
-  {
-    "id": 1040,
-    "problem_id": 1012,
-    "problem": "line B D, line C B, \\odot B lieson C D, line B D, line C B, \\odot B lieson C D\nFind m \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1012.jpg"
-  },
-  {
-    "id": 1041,
-    "problem_id": 1013,
-    "problem": "line B D, line C B, \\odot B lieson C D, line B D, line C B, \\odot B lieson C D\nFind m \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1013.jpg"
-  },
-  {
-    "id": 1042,
-    "problem_id": 1014,
-    "problem": "line B D, line C B, \\odot B lieson C D, line B D, line C B, \\odot B lieson C D\nFind m \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1014.jpg"
-  },
-  {
-    "id": 1043,
-    "problem_id": 1015,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of variable y. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1015.jpg"
-  },
-  {
-    "id": 1044,
-    "problem_id": 1016,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of variable y. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1016.jpg"
-  },
-  {
-    "id": 1045,
-    "problem_id": 1017,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of variable y. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1017.jpg"
-  },
-  {
-    "id": 1046,
-    "problem_id": 1018,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of variable y. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1018.jpg"
-  },
-  {
-    "id": 1047,
-    "problem_id": 1019,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of variable y. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1019.jpg"
-  },
-  {
-    "id": 1048,
-    "problem_id": 1020,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of variable y. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1020.jpg"
-  },
-  {
-    "id": 1049,
-    "problem_id": 1021,
-    "problem": "line T G, line T N R, line G R, line N G, line T G, line T N R, line G R, line N G\nFind NG in \\triangle TGR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1021.jpg"
-  },
-  {
-    "id": 1050,
-    "problem_id": 1022,
-    "problem": "line T G, line T N R, line G R, line N G, line T G, line T N R, line G R, line N G\nFind NG in \\triangle TGR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1022.jpg"
-  },
-  {
-    "id": 1051,
-    "problem_id": 1023,
-    "problem": "line B C D, line A B, line A D, line A C, line B C D, line A B, line A D, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1023.jpg"
-  },
-  {
-    "id": 1052,
-    "problem_id": 1024,
-    "problem": "line B C D, line A B, line A D, line A C, line B C D, line A B, line A D, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1024.jpg"
-  },
-  {
-    "id": 1053,
-    "problem_id": 1025,
-    "problem": "line B C D, line A B, line A D, line A C, line B C D, line A B, line A D, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1025.jpg"
-  },
-  {
-    "id": 1054,
-    "problem_id": 1026,
-    "problem": "line B C D, line A B, line A D, line A C, line B C D, line A B, line A D, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1026.jpg"
-  },
-  {
-    "id": 1055,
-    "problem_id": 1027,
-    "problem": "line B C D, line A B, line A D, line A C, line B C D, line A B, line A D, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1027.jpg"
-  },
-  {
-    "id": 1056,
-    "problem_id": 1028,
-    "problem": "line B C D, line A B, line A D, line A C, line B C D, line A B, line A D, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1028.jpg"
-  },
-  {
-    "id": 1057,
-    "problem_id": 1029,
-    "problem": "line C B A, line C D, line A D, line B D, line C B A, line C D, line A D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1029.jpg"
-  },
-  {
-    "id": 1058,
-    "problem_id": 1030,
-    "problem": "line C B A, line C D, line A D, line B D, line C B A, line C D, line A D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1030.jpg"
-  },
-  {
-    "id": 1059,
-    "problem_id": 1031,
-    "problem": "line C B A, line C D, line A D, line B D, line C B A, line C D, line A D, line B D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1031.jpg"
-  },
-  {
-    "id": 1060,
-    "problem_id": 1032,
-    "problem": "line A D, line B A, line B C, line C D E, line A D, line B A, line B C, line C D E\nSolve for the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1032.jpg"
-  },
-  {
-    "id": 1062,
-    "problem_id": 1033,
-    "problem": "line A D, line B A, line B C, line C D E, line A D, line B A, line B C, line C D E\nSolve for the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1033.jpg"
-  },
-  {
-    "id": 1063,
-    "problem_id": 1034,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1034.jpg"
-  },
-  {
-    "id": 1064,
-    "problem_id": 1035,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1035.jpg"
-  },
-  {
-    "id": 1065,
-    "problem_id": 1036,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1036.jpg"
-  },
-  {
-    "id": 1066,
-    "problem_id": 1037,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the diameter of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1037.jpg"
-  },
-  {
-    "id": 1067,
-    "problem_id": 1038,
-    "problem": "line A C D, line B D, line E C B, line A E, line A C D, line B D, line E C B, line A E\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1038.jpg"
-  },
-  {
-    "id": 1068,
-    "problem_id": 1039,
-    "problem": "line A C D, line B D, line E C B, line A E, line A C D, line B D, line E C B, line A E\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1039.jpg"
-  },
-  {
-    "id": 1069,
-    "problem_id": 1040,
-    "problem": "line A C D, line B D, line E C B, line A E, line A C D, line B D, line E C B, line A E\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1040.jpg"
-  },
-  {
-    "id": 1070,
-    "problem_id": 1041,
-    "problem": "line B A, \\odot A lieson M B P N, line B A, \\odot A lieson M B P N\nFind the length of \\widehat MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1041.jpg"
-  },
-  {
-    "id": 1071,
-    "problem_id": 1042,
-    "problem": "line B A, \\odot A lieson M B P N, line B A, \\odot A lieson M B P N\nFind the length of \\widehat MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1042.jpg"
-  },
-  {
-    "id": 1072,
-    "problem_id": 1043,
-    "problem": "line A C E F, line B C D, \\odot E lieson B F D A, line A C E F, line B C D, \\odot E lieson B F D A\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1043.jpg"
-  },
-  {
-    "id": 1073,
-    "problem_id": 1044,
-    "problem": "line A C E F, line B C D, \\odot E lieson B F D A, line A C E F, line B C D, \\odot E lieson B F D A\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1044.jpg"
-  },
-  {
-    "id": 1074,
-    "problem_id": 1045,
-    "problem": "line A C E F, line B C D, \\odot E lieson B F D A, line A C E F, line B C D, \\odot E lieson B F D A\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1045.jpg"
-  },
-  {
-    "id": 1075,
-    "problem_id": 1046,
-    "problem": "line M P, line P N, line N O, \\odot A lieson M N O P, line M P, line P N, line N O, \\odot A lieson M N O P\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1046.jpg"
-  },
-  {
-    "id": 1076,
-    "problem_id": 1047,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1047.jpg"
-  },
-  {
-    "id": 1077,
-    "problem_id": 1048,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1048.jpg"
-  },
-  {
-    "id": 1078,
-    "problem_id": 1049,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1049.jpg"
-  },
-  {
-    "id": 1079,
-    "problem_id": 1050,
-    "problem": "line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J, line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J\nP is the incenter of \\angle XYZ. Find m \\angle KYJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1050.jpg"
-  },
-  {
-    "id": 1080,
-    "problem_id": 1051,
-    "problem": "line B C, line B D, line A C, line B A, line D C, line B C, line B D, line A C, line B A, line D C\nDetermine m \\angle 3 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1051.jpg"
-  },
-  {
-    "id": 1081,
-    "problem_id": 1052,
-    "problem": "line K L H, line J L F, line L G, \\odot L lieson K F G H J, line K L H, line J L F, line L G, \\odot L lieson K F G H J\nFind m \\widehat JFH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1052.jpg"
-  },
-  {
-    "id": 1082,
-    "problem_id": 1053,
-    "problem": "line W J, line W L, line L J, line Q V, line B V, line Q B, line W J, line W L, line L J, line Q V, line B V, line Q B\n\\triangle WLJ \\sim \\triangle QBV. Find the scale factor of \\triangle WLJ to \\triangle QBV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1053.jpg"
-  },
-  {
-    "id": 1083,
-    "problem_id": 1054,
-    "problem": "line W J, line W L, line L J, line Q V, line B V, line Q B, line W J, line W L, line L J, line Q V, line B V, line Q B\n\\triangle WLJ \\sim \\triangle QBV. Find the scale factor of \\triangle WLJ to \\triangle QBV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1054.jpg"
-  },
-  {
-    "id": 1084,
-    "problem_id": 1055,
-    "problem": "line C D, line A B D, line C A, line C B, line C D, line A B D, line C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1055.jpg"
-  },
-  {
-    "id": 1085,
-    "problem_id": 1056,
-    "problem": "line C D, line A B D, line C A, line C B, line C D, line A B D, line C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1056.jpg"
-  },
-  {
-    "id": 1086,
-    "problem_id": 1057,
-    "problem": "line C D, line A B D, line C A, line C B, line C D, line A B D, line C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1057.jpg"
-  },
-  {
-    "id": 1087,
-    "problem_id": 1058,
-    "problem": "line C D, line A B D, line C A, line C B, line C D, line A B D, line C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1058.jpg"
-  },
-  {
-    "id": 1088,
-    "problem_id": 1059,
-    "problem": "line C D, line A B D, line C A, line C B, line C D, line A B D, line C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1059.jpg"
-  },
-  {
-    "id": 1089,
-    "problem_id": 1060,
-    "problem": "line C D, line A B D, line C A, line C B, line C D, line A B D, line C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1060.jpg"
-  },
-  {
-    "id": 1091,
-    "problem_id": 1061,
-    "problem": "line C B, line A D B, line A C, line C D, line C B, line A D B, line A C, line C D\nFind the length of BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1061.jpg"
-  },
-  {
-    "id": 1092,
-    "problem_id": 1062,
-    "problem": "line C B, line A D B, line A C, line C D, line C B, line A D B, line A C, line C D\nFind the length of BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1062.jpg"
-  },
-  {
-    "id": 1093,
-    "problem_id": 1063,
-    "problem": "line C B, line A D B, line A C, line C D, line C B, line A D B, line A C, line C D\nFind the length of BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1063.jpg"
-  },
-  {
-    "id": 1094,
-    "problem_id": 1064,
-    "problem": "line A B, line C B, \\odot B lieson A C, line A B, line C B, \\odot B lieson A C\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1064.jpg"
-  },
-  {
-    "id": 1095,
-    "problem_id": 1065,
-    "problem": "line K P L, line K N M, line M Q L, line N Q, line N P, line K P L, line K N M, line M Q L, line N Q, line N P\nWhat is NQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1065.jpg"
-  },
-  {
-    "id": 1096,
-    "problem_id": 1066,
-    "problem": "line A C, line A D, line B D C, line A B, line A C, line A D, line B D C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1066.jpg"
-  },
-  {
-    "id": 1097,
-    "problem_id": 1067,
-    "problem": "line A C, line A D, line B D C, line A B, line A C, line A D, line B D C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1067.jpg"
-  },
-  {
-    "id": 1098,
-    "problem_id": 1068,
-    "problem": "line A C, line A D, line B D C, line A B, line A C, line A D, line B D C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1068.jpg"
-  },
-  {
-    "id": 1099,
-    "problem_id": 1069,
-    "problem": "line A C, line A D, line B D C, line A B, line A C, line A D, line B D C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1069.jpg"
-  },
-  {
-    "id": 1100,
-    "problem_id": 1070,
-    "problem": "line A C, line A D, line B D C, line A B, line A C, line A D, line B D C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1070.jpg"
-  },
-  {
-    "id": 1101,
-    "problem_id": 1071,
-    "problem": "line A C, line A D, line B D C, line A B, line A C, line A D, line B D C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1071.jpg"
-  },
-  {
-    "id": 1102,
-    "problem_id": 1072,
-    "problem": "line C E, line A E, line A D, line D B, line E B, \\odot D lieson E B A, line C E, line A E, line A D, line D B, line E B, \\odot D lieson E B A\nFind the value of variable a. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1072.jpg"
-  },
-  {
-    "id": 1103,
-    "problem_id": 1073,
-    "problem": "line A C, line A D, line A B, line C D B, line A C, line A D, line A B, line C D B\nFind CD if AD is an altitude of \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1073.jpg"
-  },
-  {
-    "id": 1104,
-    "problem_id": 1074,
-    "problem": "line P M, line A Q M, \\odot B lieson P R M, line P M, line A Q M, \\odot B lieson P R M\nFind m \\widehat PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1074.jpg"
-  },
-  {
-    "id": 1105,
-    "problem_id": 1075,
-    "problem": "line P M, line A Q M, \\odot B lieson P R M, line P M, line A Q M, \\odot B lieson P R M\nFind m \\widehat PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1075.jpg"
-  },
-  {
-    "id": 1106,
-    "problem_id": 1076,
-    "problem": "line P M, line A Q M, \\odot B lieson P R M, line P M, line A Q M, \\odot B lieson P R M\nFind m \\widehat PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1076.jpg"
-  },
-  {
-    "id": 1107,
-    "problem_id": 1077,
-    "problem": "line P M, line A Q M, \\odot B lieson P R M, line P M, line A Q M, \\odot B lieson P R M\nFind m \\widehat PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1077.jpg"
-  },
-  {
-    "id": 1108,
-    "problem_id": 1078,
-    "problem": "line P M, line A Q M, \\odot B lieson P R M, line P M, line A Q M, \\odot B lieson P R M\nFind m \\widehat PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1078.jpg"
-  },
-  {
-    "id": 1109,
-    "problem_id": 1079,
-    "problem": "line E C D, line C G J, line G H I, line B F H, line A D F, line E C D, line C G J, line G H I, line B F H, line A D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1079.jpg"
-  },
-  {
-    "id": 1110,
-    "problem_id": 1080,
-    "problem": "line E C D, line C G J, line G H I, line B F H, line A D F, line E C D, line C G J, line G H I, line B F H, line A D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1080.jpg"
-  },
-  {
-    "id": 1111,
-    "problem_id": 1081,
-    "problem": "line E C D, line C G J, line G H I, line B F H, line A D F, line E C D, line C G J, line G H I, line B F H, line A D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1081.jpg"
-  },
-  {
-    "id": 1112,
-    "problem_id": 1082,
-    "problem": "line E C D, line C G J, line G H I, line B F H, line A D F, line E C D, line C G J, line G H I, line B F H, line A D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1082.jpg"
-  },
-  {
-    "id": 1113,
-    "problem_id": 1083,
-    "problem": "line E C D, line C G J, line G H I, line B F H, line A D F, line E C D, line C G J, line G H I, line B F H, line A D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1083.jpg"
-  },
-  {
-    "id": 1114,
-    "problem_id": 1084,
-    "problem": "line E C D, line C G J, line G H I, line B F H, line A D F, line E C D, line C G J, line G H I, line B F H, line A D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1084.jpg"
-  },
-  {
-    "id": 1115,
-    "problem_id": 1085,
-    "problem": "line F G H, line B C D, line G E, line A C, line F G H, line B C D, line G E, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1085.jpg"
-  },
-  {
-    "id": 1116,
-    "problem_id": 1086,
-    "problem": "line F G H, line B C D, line G E, line A C, line F G H, line B C D, line G E, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1086.jpg"
-  },
-  {
-    "id": 1117,
-    "problem_id": 1087,
-    "problem": "line F G H, line B C D, line G E, line A C, line F G H, line B C D, line G E, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1087.jpg"
-  },
-  {
-    "id": 1118,
-    "problem_id": 1088,
-    "problem": "line F G H, line B C D, line G E, line A C, line F G H, line B C D, line G E, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1088.jpg"
-  },
-  {
-    "id": 1119,
-    "problem_id": 1089,
-    "problem": "line A Q, line Q B, \\odot Q lieson A B, line A Q, line Q B, \\odot Q lieson A B\nWhat is the length of \\widehat AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1089.jpg"
-  },
-  {
-    "id": 1120,
-    "problem_id": 1090,
-    "problem": "line A B E, line C E, line D E, line A D, line A C, line D B C, line A B E, line C E, line D E, line A D, line A C, line D B C\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1090.jpg"
-  },
-  {
-    "id": 1121,
-    "problem_id": 1091,
-    "problem": "line A B E, line C E, line D E, line A D, line A C, line D B C, line A B E, line C E, line D E, line A D, line A C, line D B C\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1091.jpg"
-  },
-  {
-    "id": 1122,
-    "problem_id": 1092,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nDetermine the length of HE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1092.jpg"
-  },
-  {
-    "id": 1123,
-    "problem_id": 1093,
-    "problem": "line M N, line M P, line N P, line J L, line K L, line J K, line M N, line M P, line N P, line J L, line K L, line J K\n\\triangle JKL \\sim \\triangle MNP. Find m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1093.jpg"
-  },
-  {
-    "id": 1124,
-    "problem_id": 1094,
-    "problem": "line L N, line L M, line N M, \\odot N lieson M L, line L N, line L M, line N M, \\odot N lieson M L\nFind the area of the shaded region in the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1094.jpg"
-  },
-  {
-    "id": 1125,
-    "problem_id": 1095,
-    "problem": "line L N, line L M, line N M, \\odot N lieson M L, line L N, line L M, line N M, \\odot N lieson M L\nFind the area of the shaded region in the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1095.jpg"
-  },
-  {
-    "id": 1126,
-    "problem_id": 1096,
-    "problem": "line L N, line L M, line N M, \\odot N lieson M L, line L N, line L M, line N M, \\odot N lieson M L\nFind the area of the shaded region in the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1096.jpg"
-  },
-  {
-    "id": 1127,
-    "problem_id": 1097,
-    "problem": "line F B A H, line I B, line G A, line F G, line G H, line F I, line I H, line F B A H, line I B, line G A, line F G, line G H, line F I, line I H\nFind the area of the quadrilateral if FH = 37.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1097.jpg"
-  },
-  {
-    "id": 1128,
-    "problem_id": 1098,
-    "problem": "line F B A H, line I B, line G A, line F G, line G H, line F I, line I H, line F B A H, line I B, line G A, line F G, line G H, line F I, line I H\nFind the area of the quadrilateral if FH = 37.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1098.jpg"
-  },
-  {
-    "id": 1129,
-    "problem_id": 1099,
-    "problem": "line E B, line D C, line D E A, line C B A, line E B, line D C, line D E A, line C B A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1099.jpg"
-  },
-  {
-    "id": 1130,
-    "problem_id": 1100,
-    "problem": "line E B, line D C, line D E A, line C B A, line E B, line D C, line D E A, line C B A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1100.jpg"
-  },
-  {
-    "id": 1131,
-    "problem_id": 1101,
-    "problem": "line E B, line D C, line D E A, line C B A, line E B, line D C, line D E A, line C B A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1101.jpg"
-  },
-  {
-    "id": 1132,
-    "problem_id": 1102,
-    "problem": "line E B, line D C, line D E A, line C B A, line E B, line D C, line D E A, line C B A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1102.jpg"
-  },
-  {
-    "id": 1133,
-    "problem_id": 1103,
-    "problem": "line E B, line D C, line D E A, line C B A, line E B, line D C, line D E A, line C B A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1103.jpg"
-  },
-  {
-    "id": 1134,
-    "problem_id": 1104,
-    "problem": "line E B, line D C, line D E A, line C B A, line E B, line D C, line D E A, line C B A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1104.jpg"
-  },
-  {
-    "id": 1135,
-    "problem_id": 1105,
-    "problem": "line Z Y, line X Y, line M N, line P N, line Z X, line M P, line Z Y, line X Y, line M N, line P N, line Z X, line M P\n\\triangle MNP \\sim \\triangle XYZ. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1105.jpg"
-  },
-  {
-    "id": 1136,
-    "problem_id": 1106,
-    "problem": "line Z Y, line X Y, line M N, line P N, line Z X, line M P, line Z Y, line X Y, line M N, line P N, line Z X, line M P\n\\triangle MNP \\sim \\triangle XYZ. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1106.jpg"
-  },
-  {
-    "id": 1137,
-    "problem_id": 1107,
-    "problem": "line Z Y, line X Y, line M N, line P N, line Z X, line M P, line Z Y, line X Y, line M N, line P N, line Z X, line M P\n\\triangle MNP \\sim \\triangle XYZ. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1107.jpg"
-  },
-  {
-    "id": 1138,
-    "problem_id": 1108,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind m \\widehat JHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1108.jpg"
-  },
-  {
-    "id": 1139,
-    "problem_id": 1109,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind m \\widehat JHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1109.jpg"
-  },
-  {
-    "id": 1140,
-    "problem_id": 1110,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind m \\widehat JHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1110.jpg"
-  },
-  {
-    "id": 1141,
-    "problem_id": 1111,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind m \\widehat JHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1111.jpg"
-  },
-  {
-    "id": 1142,
-    "problem_id": 1112,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nWhat is \\sin B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1112.jpg"
-  },
-  {
-    "id": 1143,
-    "problem_id": 1113,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nWhat is \\sin B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1113.jpg"
-  },
-  {
-    "id": 1144,
-    "problem_id": 1114,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nWhat is \\sin B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1114.jpg"
-  },
-  {
-    "id": 1145,
-    "problem_id": 1115,
-    "problem": "line R S, line R U, line R T, line S T U, line R S, line R U, line R T, line S T U\nWhat is m \\angle TRU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1115.jpg"
-  },
-  {
-    "id": 1146,
-    "problem_id": 1116,
-    "problem": "line R S, line R U, line R T, line S T U, line R S, line R U, line R T, line S T U\nWhat is m \\angle TRU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1116.jpg"
-  },
-  {
-    "id": 1147,
-    "problem_id": 1117,
-    "problem": "line R S, line R U, line R T, line S T U, line R S, line R U, line R T, line S T U\nWhat is m \\angle TRU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1117.jpg"
-  },
-  {
-    "id": 1148,
-    "problem_id": 1118,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1118.jpg"
-  },
-  {
-    "id": 1149,
-    "problem_id": 1119,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1119.jpg"
-  },
-  {
-    "id": 1150,
-    "problem_id": 1120,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1120.jpg"
-  },
-  {
-    "id": 1151,
-    "problem_id": 1121,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1121.jpg"
-  },
-  {
-    "id": 1152,
-    "problem_id": 1122,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1122.jpg"
-  },
-  {
-    "id": 1153,
-    "problem_id": 1123,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1123.jpg"
-  },
-  {
-    "id": 1154,
-    "problem_id": 1124,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1124.jpg"
-  },
-  {
-    "id": 1155,
-    "problem_id": 1125,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1125.jpg"
-  },
-  {
-    "id": 1156,
-    "problem_id": 1126,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1126.jpg"
-  },
-  {
-    "id": 1157,
-    "problem_id": 1127,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1127.jpg"
-  },
-  {
-    "id": 1158,
-    "problem_id": 1128,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1128.jpg"
-  },
-  {
-    "id": 1159,
-    "problem_id": 1129,
-    "problem": "line D F, line G D, line G F, line H K, line M K, line M H, line D F, line G D, line G F, line H K, line M K, line M H\n\\triangle DFG \\sim \\triangle HKM. Determine the length of MK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1129.jpg"
-  },
-  {
-    "id": 1160,
-    "problem_id": 1130,
-    "problem": "line T W, line U V, line V W, line U T, line T W, line U V, line V W, line U T\nTUVW is a parallelogram. Find m \\angle W.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1130.jpg"
-  },
-  {
-    "id": 1161,
-    "problem_id": 1131,
-    "problem": "line C B D, line E F G, line A B F H, line C B D, line E F G, line A B F H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1131.jpg"
-  },
-  {
-    "id": 1162,
-    "problem_id": 1132,
-    "problem": "line C B D, line E F G, line A B F H, line C B D, line E F G, line A B F H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1132.jpg"
-  },
-  {
-    "id": 1163,
-    "problem_id": 1133,
-    "problem": "line A G C, line B F C, line E D C, line B E A, line A D F, line B D G, line A G C, line B F C, line E D C, line B E A, line A D F, line B D G\nGiven that D is the centroid of \\triangle ABC, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1133.jpg"
-  },
-  {
-    "id": 1164,
-    "problem_id": 1134,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1134.jpg"
-  },
-  {
-    "id": 1165,
-    "problem_id": 1135,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1135.jpg"
-  },
-  {
-    "id": 1166,
-    "problem_id": 1136,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1136.jpg"
-  },
-  {
-    "id": 1167,
-    "problem_id": 1137,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1137.jpg"
-  },
-  {
-    "id": 1168,
-    "problem_id": 1138,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1138.jpg"
-  },
-  {
-    "id": 1169,
-    "problem_id": 1139,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1139.jpg"
-  },
-  {
-    "id": 1170,
-    "problem_id": 1140,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1140.jpg"
-  },
-  {
-    "id": 1171,
-    "problem_id": 1141,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1141.jpg"
-  },
-  {
-    "id": 1172,
-    "problem_id": 1142,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1142.jpg"
-  },
-  {
-    "id": 1173,
-    "problem_id": 1143,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1143.jpg"
-  },
-  {
-    "id": 1174,
-    "problem_id": 1144,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1144.jpg"
-  },
-  {
-    "id": 1175,
-    "problem_id": 1145,
-    "problem": "line A B C D, line A B C D\nFind the measurement of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1145.jpg"
-  },
-  {
-    "id": 1176,
-    "problem_id": 1146,
-    "problem": "line A C, line C D B, line A B, \\odot C lieson D A, line A C, line C D B, line A B, \\odot C lieson D A\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1146.jpg"
-  },
-  {
-    "id": 1177,
-    "problem_id": 1147,
-    "problem": "line A C, line C D B, line A B, \\odot C lieson D A, line A C, line C D B, line A B, \\odot C lieson D A\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1147.jpg"
-  },
-  {
-    "id": 1178,
-    "problem_id": 1148,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind m \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1148.jpg"
-  },
-  {
-    "id": 1179,
-    "problem_id": 1149,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind m \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1149.jpg"
-  },
-  {
-    "id": 1180,
-    "problem_id": 1150,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind m \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1150.jpg"
-  },
-  {
-    "id": 1181,
-    "problem_id": 1151,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind m \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1151.jpg"
-  },
-  {
-    "id": 1182,
-    "problem_id": 1152,
-    "problem": "line D C, line A B, line B C, line A D, line D C, line A B, line B C, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1152.jpg"
-  },
-  {
-    "id": 1183,
-    "problem_id": 1153,
-    "problem": "line D C, line A B, line B C, line A D, line D C, line A B, line B C, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1153.jpg"
-  },
-  {
-    "id": 1184,
-    "problem_id": 1154,
-    "problem": "line D C, line A B, line B C, line A D, line D C, line A B, line B C, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1154.jpg"
-  },
-  {
-    "id": 1185,
-    "problem_id": 1155,
-    "problem": "line D C, line A B, line B C, line A D, line D C, line A B, line B C, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1155.jpg"
-  },
-  {
-    "id": 1186,
-    "problem_id": 1156,
-    "problem": "line B C, line A B, \\odot D lieson C A, line B C, line A B, \\odot D lieson C A\nFind BC. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1156.jpg"
-  },
-  {
-    "id": 1187,
-    "problem_id": 1157,
-    "problem": "line A B C, line C E H, line G I H, line A D G, \\odot F lieson B D I E, line A B C, line C E H, line G I H, line A D G, \\odot F lieson B D I E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1157.jpg"
-  },
-  {
-    "id": 1188,
-    "problem_id": 1158,
-    "problem": "line A B C, line C E H, line G I H, line A D G, \\odot F lieson B D I E, line A B C, line C E H, line G I H, line A D G, \\odot F lieson B D I E\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1158.jpg"
-  },
-  {
-    "id": 1190,
-    "problem_id": 1159,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1159.jpg"
-  },
-  {
-    "id": 1191,
-    "problem_id": 1160,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1160.jpg"
-  },
-  {
-    "id": 1192,
-    "problem_id": 1161,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1161.jpg"
-  },
-  {
-    "id": 1193,
-    "problem_id": 1162,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1162.jpg"
-  },
-  {
-    "id": 1194,
-    "problem_id": 1163,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1163.jpg"
-  },
-  {
-    "id": 1195,
-    "problem_id": 1164,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1164.jpg"
-  },
-  {
-    "id": 1196,
-    "problem_id": 1165,
-    "problem": "line A D, line D C, line C B, line A B, line A C, line A D, line D C, line C B, line A B, line A C\n\\triangle ACD \\cong \\triangle ACB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1165.jpg"
-  },
-  {
-    "id": 1197,
-    "problem_id": 1166,
-    "problem": "line A D, line D C, line C B, line A B, line A C, line A D, line D C, line C B, line A B, line A C\n\\triangle ACD \\cong \\triangle ACB. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1166.jpg"
-  },
-  {
-    "id": 1198,
-    "problem_id": 1167,
-    "problem": "line W Z, line X Y, line X W, line Y Z, line W Z, line X Y, line X W, line Y Z\nWXYZ is a parallelogram. What is the measure of WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1167.jpg"
-  },
-  {
-    "id": 1199,
-    "problem_id": 1168,
-    "problem": "line W Z, line X Y, line X W, line Y Z, line W Z, line X Y, line X W, line Y Z\nWXYZ is a parallelogram. What is the measure of WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1168.jpg"
-  },
-  {
-    "id": 1200,
-    "problem_id": 1169,
-    "problem": "line W Z, line X Y, line X W, line Y Z, line W Z, line X Y, line X W, line Y Z\nWXYZ is a parallelogram. What is the measure of WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1169.jpg"
-  },
-  {
-    "id": 1201,
-    "problem_id": 1170,
-    "problem": "line W Z, line X Y, line X W, line Y Z, line W Z, line X Y, line X W, line Y Z\nWXYZ is a parallelogram. What is the measure of WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1170.jpg"
-  },
-  {
-    "id": 1202,
-    "problem_id": 1171,
-    "problem": "line K M B, line K L C, line A J K, line M L, line J M, line K M B, line K L C, line A J K, line M L, line J M\nFind ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1171.jpg"
-  },
-  {
-    "id": 1203,
-    "problem_id": 1172,
-    "problem": "line K M B, line K L C, line A J K, line M L, line J M, line K M B, line K L C, line A J K, line M L, line J M\nFind ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1172.jpg"
-  },
-  {
-    "id": 1204,
-    "problem_id": 1173,
-    "problem": "line K M B, line K L C, line A J K, line M L, line J M, line K M B, line K L C, line A J K, line M L, line J M\nFind ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1173.jpg"
-  },
-  {
-    "id": 1205,
-    "problem_id": 1174,
-    "problem": "line K M B, line K L C, line A J K, line M L, line J M, line K M B, line K L C, line A J K, line M L, line J M\nFind ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1174.jpg"
-  },
-  {
-    "id": 1206,
-    "problem_id": 1175,
-    "problem": "line A B, line C B, line E A, line E D C, line D B, line A B, line C B, line E A, line E D C, line D B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1175.jpg"
-  },
-  {
-    "id": 1207,
-    "problem_id": 1176,
-    "problem": "line A B, line C B, line E A, line E D C, line D B, line A B, line C B, line E A, line E D C, line D B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1176.jpg"
-  },
-  {
-    "id": 1208,
-    "problem_id": 1177,
-    "problem": "line A B, line C B, line E A, line E D C, line D B, line A B, line C B, line E A, line E D C, line D B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1177.jpg"
-  },
-  {
-    "id": 1209,
-    "problem_id": 1178,
-    "problem": "line A B, line C B, line E A, line E D C, line D B, line A B, line C B, line E A, line E D C, line D B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1178.jpg"
-  },
-  {
-    "id": 1210,
-    "problem_id": 1179,
-    "problem": "line J P, line L M, line N M, line J K, line P N, line K L, line J P, line L M, line N M, line J K, line P N, line K L\nWhat is the measure of \\angle K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1179.jpg"
-  },
-  {
-    "id": 1211,
-    "problem_id": 1180,
-    "problem": "line J P, line L M, line N M, line J K, line P N, line K L, line J P, line L M, line N M, line J K, line P N, line K L\nWhat is the measure of \\angle K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1180.jpg"
-  },
-  {
-    "id": 1212,
-    "problem_id": 1181,
-    "problem": "line J P, line L M, line N M, line J K, line P N, line K L, line J P, line L M, line N M, line J K, line P N, line K L\nWhat is the measure of \\angle K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1181.jpg"
-  },
-  {
-    "id": 1213,
-    "problem_id": 1182,
-    "problem": "line J P, line L M, line N M, line J K, line P N, line K L, line J P, line L M, line N M, line J K, line P N, line K L\nWhat is the measure of \\angle K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1182.jpg"
-  },
-  {
-    "id": 1214,
-    "problem_id": 1183,
-    "problem": "line J P, line L M, line N M, line J K, line P N, line K L, line J P, line L M, line N M, line J K, line P N, line K L\nWhat is the measure of \\angle K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1183.jpg"
-  },
-  {
-    "id": 1215,
-    "problem_id": 1184,
-    "problem": "line T Q R, line Q S A, line T Q R, line Q S A\n\\angle RQT is a straight angle. What is m \\angle RQS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1184.jpg"
-  },
-  {
-    "id": 1216,
-    "problem_id": 1185,
-    "problem": "line A C, line B A, \\odot A lieson C B, line A C, line B A, \\odot A lieson C B\nFind the area of the sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1185.jpg"
-  },
-  {
-    "id": 1217,
-    "problem_id": 1186,
-    "problem": "line A C, line B A, \\odot A lieson C B, line A C, line B A, \\odot A lieson C B\nFind the area of the sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1186.jpg"
-  },
-  {
-    "id": 1218,
-    "problem_id": 1187,
-    "problem": "line B C, line A F, line E F, line D E, line C D, line B A, line B C, line A F, line E F, line D E, line C D, line B A\nWhat is m \\angle D?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1187.jpg"
-  },
-  {
-    "id": 1219,
-    "problem_id": 1188,
-    "problem": "line B C, line A F, line E F, line D E, line C D, line B A, line B C, line A F, line E F, line D E, line C D, line B A\nWhat is m \\angle D?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1188.jpg"
-  },
-  {
-    "id": 1221,
-    "problem_id": 1189,
-    "problem": "line B C, line A F, line E F, line D E, line C D, line B A, line B C, line A F, line E F, line D E, line C D, line B A\nWhat is m \\angle D?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1189.jpg"
-  },
-  {
-    "id": 1222,
-    "problem_id": 1190,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1190.jpg"
-  },
-  {
-    "id": 1223,
-    "problem_id": 1191,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1191.jpg"
-  },
-  {
-    "id": 1224,
-    "problem_id": 1192,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1192.jpg"
-  },
-  {
-    "id": 1225,
-    "problem_id": 1193,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1193.jpg"
-  },
-  {
-    "id": 1226,
-    "problem_id": 1194,
-    "problem": "line A B C, line L K B, line I J K, line J H G, line H E F, line E C D, line A B C, line L K B, line I J K, line J H G, line H E F, line E C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1194.jpg"
-  },
-  {
-    "id": 1227,
-    "problem_id": 1195,
-    "problem": "line A B C, line L K B, line I J K, line J H G, line H E F, line E C D, line A B C, line L K B, line I J K, line J H G, line H E F, line E C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1195.jpg"
-  },
-  {
-    "id": 1228,
-    "problem_id": 1196,
-    "problem": "line A B C, line L K B, line I J K, line J H G, line H E F, line E C D, line A B C, line L K B, line I J K, line J H G, line H E F, line E C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1196.jpg"
-  },
-  {
-    "id": 1229,
-    "problem_id": 1197,
-    "problem": "line A B C, line L K B, line I J K, line J H G, line H E F, line E C D, line A B C, line L K B, line I J K, line J H G, line H E F, line E C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1197.jpg"
-  },
-  {
-    "id": 1230,
-    "problem_id": 1198,
-    "problem": "line B A, line B C, \\odot D lieson B C A, line B A, line B C, \\odot D lieson B C A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1198.jpg"
-  },
-  {
-    "id": 1231,
-    "problem_id": 1199,
-    "problem": "line B A, line B C, \\odot D lieson B C A, line B A, line B C, \\odot D lieson B C A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1199.jpg"
-  },
-  {
-    "id": 1232,
-    "problem_id": 1200,
-    "problem": "line B A, line B C, \\odot D lieson B C A, line B A, line B C, \\odot D lieson B C A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1200.jpg"
-  },
-  {
-    "id": 1233,
-    "problem_id": 1201,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1201.jpg"
-  },
-  {
-    "id": 1234,
-    "problem_id": 1202,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1202.jpg"
-  },
-  {
-    "id": 1235,
-    "problem_id": 1203,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the perimeter of quadrilateral ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1203.jpg"
-  },
-  {
-    "id": 1236,
-    "problem_id": 1204,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the perimeter of quadrilateral ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1204.jpg"
-  },
-  {
-    "id": 1237,
-    "problem_id": 1205,
-    "problem": "line B C A, line D C, line C E, line B C A, line D C, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1205.jpg"
-  },
-  {
-    "id": 1238,
-    "problem_id": 1206,
-    "problem": "line B C A, line D C, line C E, line B C A, line D C, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1206.jpg"
-  },
-  {
-    "id": 1239,
-    "problem_id": 1207,
-    "problem": "line B C D, line A D, line B E F, line A B, line A C, line D F, line C E, line B C D, line A D, line B E F, line A B, line A C, line D F, line C E\nFind the length of EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1207.jpg"
-  },
-  {
-    "id": 1240,
-    "problem_id": 1208,
-    "problem": "line B C D, line A D, line B E F, line A B, line A C, line D F, line C E, line B C D, line A D, line B E F, line A B, line A C, line D F, line C E\nFind the length of EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1208.jpg"
-  },
-  {
-    "id": 1241,
-    "problem_id": 1209,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1209.jpg"
-  },
-  {
-    "id": 1242,
-    "problem_id": 1210,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1210.jpg"
-  },
-  {
-    "id": 1243,
-    "problem_id": 1211,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1211.jpg"
-  },
-  {
-    "id": 1244,
-    "problem_id": 1212,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1212.jpg"
-  },
-  {
-    "id": 1245,
-    "problem_id": 1213,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1213.jpg"
-  },
-  {
-    "id": 1247,
-    "problem_id": 1214,
-    "problem": "line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E, line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1214.jpg"
-  },
-  {
-    "id": 1248,
-    "problem_id": 1215,
-    "problem": "line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E, line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1215.jpg"
-  },
-  {
-    "id": 1249,
-    "problem_id": 1216,
-    "problem": "line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E, line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1216.jpg"
-  },
-  {
-    "id": 1250,
-    "problem_id": 1217,
-    "problem": "line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E, line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1217.jpg"
-  },
-  {
-    "id": 1251,
-    "problem_id": 1218,
-    "problem": "line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E, line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1218.jpg"
-  },
-  {
-    "id": 1252,
-    "problem_id": 1219,
-    "problem": "line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E, line I E, line E F, line G F, line H G, line A H, line B A, line B C, line C D, line D E\nFind the perimeter of the regular polygon figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1219.jpg"
-  },
-  {
-    "id": 1253,
-    "problem_id": 1220,
-    "problem": "line l lieson A S R B, line P S Q, line Q R, line P R, line l lieson A S R B, line P S Q, line Q R, line P R\nWhat is the length of PR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1220.jpg"
-  },
-  {
-    "id": 1254,
-    "problem_id": 1221,
-    "problem": "line l lieson A S R B, line P S Q, line Q R, line P R, line l lieson A S R B, line P S Q, line Q R, line P R\nWhat is the length of PR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1221.jpg"
-  },
-  {
-    "id": 1255,
-    "problem_id": 1222,
-    "problem": "line l lieson A S R B, line P S Q, line Q R, line P R, line l lieson A S R B, line P S Q, line Q R, line P R\nWhat is the length of PR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1222.jpg"
-  },
-  {
-    "id": 1256,
-    "problem_id": 1223,
-    "problem": "line A B, line A P C, line B C, line C D, \\odot P lieson B C A, line A B, line A P C, line B C, line C D, \\odot P lieson B C A\nWhat is m \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1223.jpg"
-  },
-  {
-    "id": 1257,
-    "problem_id": 1224,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1224.jpg"
-  },
-  {
-    "id": 1258,
-    "problem_id": 1225,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1225.jpg"
-  },
-  {
-    "id": 1259,
-    "problem_id": 1226,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1226.jpg"
-  },
-  {
-    "id": 1260,
-    "problem_id": 1227,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1227.jpg"
-  },
-  {
-    "id": 1261,
-    "problem_id": 1228,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1228.jpg"
-  },
-  {
-    "id": 1262,
-    "problem_id": 1229,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find m \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1229.jpg"
-  },
-  {
-    "id": 1263,
-    "problem_id": 1230,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find m \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1230.jpg"
-  },
-  {
-    "id": 1264,
-    "problem_id": 1231,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find m \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1231.jpg"
-  },
-  {
-    "id": 1265,
-    "problem_id": 1232,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find m \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1232.jpg"
-  },
-  {
-    "id": 1266,
-    "problem_id": 1233,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find m \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1233.jpg"
-  },
-  {
-    "id": 1267,
-    "problem_id": 1234,
-    "problem": "line G R J, line H Q J, line H P G, line P Q, line Q R, line G R J, line H Q J, line H P G, line P Q, line Q R\nFind m \\angle GPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1234.jpg"
-  },
-  {
-    "id": 1268,
-    "problem_id": 1235,
-    "problem": "line G R J, line H Q J, line H P G, line P Q, line Q R, line G R J, line H Q J, line H P G, line P Q, line Q R\nFind m \\angle GPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1235.jpg"
-  },
-  {
-    "id": 1269,
-    "problem_id": 1236,
-    "problem": "line G R J, line H Q J, line H P G, line P Q, line Q R, line G R J, line H Q J, line H P G, line P Q, line Q R\nFind m \\angle GPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1236.jpg"
-  },
-  {
-    "id": 1270,
-    "problem_id": 1237,
-    "problem": "line G R J, line H Q J, line H P G, line P Q, line Q R, line G R J, line H Q J, line H P G, line P Q, line Q R\nFind m \\angle GPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1237.jpg"
-  },
-  {
-    "id": 1271,
-    "problem_id": 1238,
-    "problem": "line G R J, line H Q J, line H P G, line P Q, line Q R, line G R J, line H Q J, line H P G, line P Q, line Q R\nFind m \\angle GPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1238.jpg"
-  },
-  {
-    "id": 1272,
-    "problem_id": 1239,
-    "problem": "line G R J, line H Q J, line H P G, line P Q, line Q R, line G R J, line H Q J, line H P G, line P Q, line Q R\nFind m \\angle GPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1239.jpg"
-  },
-  {
-    "id": 1273,
-    "problem_id": 1240,
-    "problem": "line H K A, line G K J, line K I, \\odot K lieson H G A J I, line H K A, line G K J, line K I, \\odot K lieson H G A J I\nSolve for m \\angle GKI.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1240.jpg"
-  },
-  {
-    "id": 1274,
-    "problem_id": 1241,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1241.jpg"
-  },
-  {
-    "id": 1275,
-    "problem_id": 1242,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1242.jpg"
-  },
-  {
-    "id": 1276,
-    "problem_id": 1243,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1243.jpg"
-  },
-  {
-    "id": 1277,
-    "problem_id": 1244,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1244.jpg"
-  },
-  {
-    "id": 1278,
-    "problem_id": 1245,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1245.jpg"
-  },
-  {
-    "id": 1279,
-    "problem_id": 1246,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 2 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1246.jpg"
-  },
-  {
-    "id": 1280,
-    "problem_id": 1247,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 2 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1247.jpg"
-  },
-  {
-    "id": 1281,
-    "problem_id": 1248,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 2 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1248.jpg"
-  },
-  {
-    "id": 1282,
-    "problem_id": 1249,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 2 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1249.jpg"
-  },
-  {
-    "id": 1283,
-    "problem_id": 1250,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 2 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1250.jpg"
-  },
-  {
-    "id": 1284,
-    "problem_id": 1251,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nDetermine the measurement of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1251.jpg"
-  },
-  {
-    "id": 1285,
-    "problem_id": 1252,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nDetermine the measurement of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1252.jpg"
-  },
-  {
-    "id": 1286,
-    "problem_id": 1253,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nDetermine the measurement of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1253.jpg"
-  },
-  {
-    "id": 1287,
-    "problem_id": 1254,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nDetermine the measurement of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1254.jpg"
-  },
-  {
-    "id": 1288,
-    "problem_id": 1255,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nDetermine the measurement of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1255.jpg"
-  },
-  {
-    "id": 1289,
-    "problem_id": 1256,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nDetermine the measurement of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1256.jpg"
-  },
-  {
-    "id": 1290,
-    "problem_id": 1257,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1257.jpg"
-  },
-  {
-    "id": 1291,
-    "problem_id": 1258,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1258.jpg"
-  },
-  {
-    "id": 1292,
-    "problem_id": 1259,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1259.jpg"
-  },
-  {
-    "id": 1293,
-    "problem_id": 1260,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1260.jpg"
-  },
-  {
-    "id": 1294,
-    "problem_id": 1261,
-    "problem": "line A D, line B D, line B A, line C A, line C D, line A D, line B D, line B A, line C A, line C D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1261.jpg"
-  },
-  {
-    "id": 1295,
-    "problem_id": 1262,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nIf b = 18, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1262.jpg"
-  },
-  {
-    "id": 1296,
-    "problem_id": 1263,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nIf b = 18, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1263.jpg"
-  },
-  {
-    "id": 1297,
-    "problem_id": 1264,
-    "problem": "line S T, line R T, line R S, line S T, line R T, line R S\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1264.jpg"
-  },
-  {
-    "id": 1298,
-    "problem_id": 1265,
-    "problem": "line S T, line R T, line R S, line S T, line R T, line R S\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1265.jpg"
-  },
-  {
-    "id": 1299,
-    "problem_id": 1266,
-    "problem": "line S T, line R T, line R S, line S T, line R T, line R S\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1266.jpg"
-  },
-  {
-    "id": 1300,
-    "problem_id": 1267,
-    "problem": "line S T, line R T, line R S, line S T, line R T, line R S\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1267.jpg"
-  },
-  {
-    "id": 1301,
-    "problem_id": 1268,
-    "problem": "line K P L, line K N M, line M Q L, line N Q, line N P, line K P L, line K N M, line M Q L, line N Q, line N P\nWhat is m \\angle NQL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1268.jpg"
-  },
-  {
-    "id": 1302,
-    "problem_id": 1269,
-    "problem": "line A B, line C B, line C D, line E D, line F E, line F A, line A B, line C B, line C D, line E D, line F E, line F A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1269.jpg"
-  },
-  {
-    "id": 1303,
-    "problem_id": 1270,
-    "problem": "line A B, line C B, line C D, line E D, line F E, line F A, line A B, line C B, line C D, line E D, line F E, line F A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1270.jpg"
-  },
-  {
-    "id": 1304,
-    "problem_id": 1271,
-    "problem": "line A B, line C B, line C D, line E D, line F E, line F A, line A B, line C B, line C D, line E D, line F E, line F A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1271.jpg"
-  },
-  {
-    "id": 1305,
-    "problem_id": 1272,
-    "problem": "line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J, line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J\nP is the incenter of \\angle XYZ. Find PX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1272.jpg"
-  },
-  {
-    "id": 1306,
-    "problem_id": 1273,
-    "problem": "line K J, line K L, line J L, line K J, line K L, line J L\nFind m \\angle KLJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1273.jpg"
-  },
-  {
-    "id": 1307,
-    "problem_id": 1274,
-    "problem": "line K J, line K L, line J L, line K J, line K L, line J L\nFind m \\angle KLJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1274.jpg"
-  },
-  {
-    "id": 1308,
-    "problem_id": 1275,
-    "problem": "line K J, line K L, line J L, line K J, line K L, line J L\nFind m \\angle KLJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1275.jpg"
-  },
-  {
-    "id": 1309,
-    "problem_id": 1276,
-    "problem": "line E B C, line A C, line C D F, \\odot G lieson A C B, line E B C, line A C, line C D F, \\odot G lieson A C B\nFind m \\angle BCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1276.jpg"
-  },
-  {
-    "id": 1310,
-    "problem_id": 1277,
-    "problem": "line G F C B, line l lieson E F H, line m lieson A C D, line G F C B, line l lieson E F H, line m lieson A C D\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1277.jpg"
-  },
-  {
-    "id": 1311,
-    "problem_id": 1278,
-    "problem": "line G F C B, line l lieson E F H, line m lieson A C D, line G F C B, line l lieson E F H, line m lieson A C D\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1278.jpg"
-  },
-  {
-    "id": 1312,
-    "problem_id": 1279,
-    "problem": "line G F C B, line l lieson E F H, line m lieson A C D, line G F C B, line l lieson E F H, line m lieson A C D\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1279.jpg"
-  },
-  {
-    "id": 1313,
-    "problem_id": 1280,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 4 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1280.jpg"
-  },
-  {
-    "id": 1314,
-    "problem_id": 1281,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 4 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1281.jpg"
-  },
-  {
-    "id": 1315,
-    "problem_id": 1282,
-    "problem": "line B C D, line A C E F, \\odot E lieson B F D A, line B C D, line A C E F, \\odot E lieson B F D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1282.jpg"
-  },
-  {
-    "id": 1316,
-    "problem_id": 1283,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1283.jpg"
-  },
-  {
-    "id": 1317,
-    "problem_id": 1284,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1284.jpg"
-  },
-  {
-    "id": 1318,
-    "problem_id": 1285,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1285.jpg"
-  },
-  {
-    "id": 1319,
-    "problem_id": 1286,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1286.jpg"
-  },
-  {
-    "id": 1320,
-    "problem_id": 1287,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nThe area of the triangle is 52 square centimeters. Find the height.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1287.jpg"
-  },
-  {
-    "id": 1321,
-    "problem_id": 1288,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nThe area of the triangle is 52 square centimeters. Find the height.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1288.jpg"
-  },
-  {
-    "id": 1322,
-    "problem_id": 1289,
-    "problem": "line A C D, line B C E, line D E, line B A, line A C D, line B C E, line D E, line B A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1289.jpg"
-  },
-  {
-    "id": 1323,
-    "problem_id": 1290,
-    "problem": "line Q P, line N P, line M N, line M Q, line Q P, line N P, line M N, line M Q\nParallelogram MNPQ is shown. Solve for m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1290.jpg"
-  },
-  {
-    "id": 1324,
-    "problem_id": 1291,
-    "problem": "line B P C N E, line A M C Q D, \\odot F lieson M P Q N, line B P C N E, line A M C Q D, \\odot F lieson M P Q N\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1291.jpg"
-  },
-  {
-    "id": 1325,
-    "problem_id": 1292,
-    "problem": "line B P C N E, line A M C Q D, \\odot F lieson M P Q N, line B P C N E, line A M C Q D, \\odot F lieson M P Q N\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1292.jpg"
-  },
-  {
-    "id": 1326,
-    "problem_id": 1293,
-    "problem": "line B P C N E, line A M C Q D, \\odot F lieson M P Q N, line B P C N E, line A M C Q D, \\odot F lieson M P Q N\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1293.jpg"
-  },
-  {
-    "id": 1327,
-    "problem_id": 1294,
-    "problem": "line B C, line A D C, line B A, line B D, line B C, line A D C, line B A, line B D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1294.jpg"
-  },
-  {
-    "id": 1328,
-    "problem_id": 1295,
-    "problem": "line B C, line A D C, line B A, line B D, line B C, line A D C, line B A, line B D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1295.jpg"
-  },
-  {
-    "id": 1329,
-    "problem_id": 1296,
-    "problem": "line B C, line A D C, line B A, line B D, line B C, line A D C, line B A, line B D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1296.jpg"
-  },
-  {
-    "id": 1330,
-    "problem_id": 1297,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1297.jpg"
-  },
-  {
-    "id": 1331,
-    "problem_id": 1298,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1298.jpg"
-  },
-  {
-    "id": 1332,
-    "problem_id": 1299,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1299.jpg"
-  },
-  {
-    "id": 1333,
-    "problem_id": 1300,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1300.jpg"
-  },
-  {
-    "id": 1334,
-    "problem_id": 1301,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1301.jpg"
-  },
-  {
-    "id": 1336,
-    "problem_id": 1302,
-    "problem": "line H G E F, line F W W' A, line B C D F, line D W, line E D, line G C, line C W', line H G E F, line F W W' A, line B C D F, line D W, line E D, line G C, line C W'\nFind the scale factor from W to W'.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1302.jpg"
-  },
-  {
-    "id": 1337,
-    "problem_id": 1303,
-    "problem": "line H G E F, line F W W' A, line B C D F, line D W, line E D, line G C, line C W', line H G E F, line F W W' A, line B C D F, line D W, line E D, line G C, line C W'\nFind the scale factor from W to W'.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1303.jpg"
-  },
-  {
-    "id": 1338,
-    "problem_id": 1304,
-    "problem": "line A D, line D C, line B C, line A B, line A D, line D C, line B C, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1304.jpg"
-  },
-  {
-    "id": 1339,
-    "problem_id": 1305,
-    "problem": "line A D, line D C, line B C, line A B, line A D, line D C, line B C, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1305.jpg"
-  },
-  {
-    "id": 1340,
-    "problem_id": 1306,
-    "problem": "line A D, line D C, line B C, line A B, line A D, line D C, line B C, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1306.jpg"
-  },
-  {
-    "id": 1341,
-    "problem_id": 1307,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1307.jpg"
-  },
-  {
-    "id": 1342,
-    "problem_id": 1308,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1308.jpg"
-  },
-  {
-    "id": 1343,
-    "problem_id": 1309,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1309.jpg"
-  },
-  {
-    "id": 1344,
-    "problem_id": 1310,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1310.jpg"
-  },
-  {
-    "id": 1345,
-    "problem_id": 1311,
-    "problem": "line A E, line A B, line B F, line E D F, line C D, line A E, line A B, line B F, line E D F, line C D\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1311.jpg"
-  },
-  {
-    "id": 1346,
-    "problem_id": 1312,
-    "problem": "line A E, line A B, line B F, line E D F, line C D, line A E, line A B, line B F, line E D F, line C D\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1312.jpg"
-  },
-  {
-    "id": 1347,
-    "problem_id": 1313,
-    "problem": "line A E, line A B, line B F, line E D F, line C D, line A E, line A B, line B F, line E D F, line C D\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1313.jpg"
-  },
-  {
-    "id": 1348,
-    "problem_id": 1314,
-    "problem": "line A E, line A B, line B F, line E D F, line C D, line A E, line A B, line B F, line E D F, line C D\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1314.jpg"
-  },
-  {
-    "id": 1349,
-    "problem_id": 1315,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1315.jpg"
-  },
-  {
-    "id": 1350,
-    "problem_id": 1316,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1316.jpg"
-  },
-  {
-    "id": 1351,
-    "problem_id": 1317,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1317.jpg"
-  },
-  {
-    "id": 1352,
-    "problem_id": 1318,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1318.jpg"
-  },
-  {
-    "id": 1353,
-    "problem_id": 1319,
-    "problem": "line A B, line C D, line D H, line C G, line G H, line B F, line A E, line E F, line A B, line C D, line D H, line C G, line G H, line B F, line A E, line E F\nABFE \\sim CDHG. Determine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1319.jpg"
-  },
-  {
-    "id": 1354,
-    "problem_id": 1320,
-    "problem": "line Q P A, line Q S B, line Q R C, line P S, line S R, line Q P A, line Q S B, line Q R C, line P S, line S R\nFind m \\angle PQS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1320.jpg"
-  },
-  {
-    "id": 1355,
-    "problem_id": 1321,
-    "problem": "line Q P A, line Q S B, line Q R C, line P S, line S R, line Q P A, line Q S B, line Q R C, line P S, line S R\nFind m \\angle PQS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1321.jpg"
-  },
-  {
-    "id": 1356,
-    "problem_id": 1322,
-    "problem": "line P Q R, line P Q R\nQ is the midpoint of PR. What is RQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1322.jpg"
-  },
-  {
-    "id": 1357,
-    "problem_id": 1323,
-    "problem": "line P Q R, line P Q R\nQ is the midpoint of PR. What is RQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1323.jpg"
-  },
-  {
-    "id": 1358,
-    "problem_id": 1324,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind CB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1324.jpg"
-  },
-  {
-    "id": 1359,
-    "problem_id": 1325,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind CB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1325.jpg"
-  },
-  {
-    "id": 1360,
-    "problem_id": 1326,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind CB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1326.jpg"
-  },
-  {
-    "id": 1361,
-    "problem_id": 1327,
-    "problem": "line A Z X W, line B Y W, \\odot C lieson V Z X Y, line A Z X W, line B Y W, \\odot C lieson V Z X Y\nFind the measure of \\widehat ZX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1327.jpg"
-  },
-  {
-    "id": 1362,
-    "problem_id": 1328,
-    "problem": "line L K, line J K, line L J, line L K, line J K, line L J\nFind \\sin J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1328.jpg"
-  },
-  {
-    "id": 1363,
-    "problem_id": 1329,
-    "problem": "line L K, line J K, line L J, line L K, line J K, line L J\nFind \\sin J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1329.jpg"
-  },
-  {
-    "id": 1364,
-    "problem_id": 1330,
-    "problem": "line Q P, line P R, \\odot P lieson Q R S, line Q P, line P R, \\odot P lieson Q R S\nWhat is the length of \\widehat QSR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1330.jpg"
-  },
-  {
-    "id": 1365,
-    "problem_id": 1331,
-    "problem": "line Q P, line P R, \\odot P lieson Q R S, line Q P, line P R, \\odot P lieson Q R S\nWhat is the length of \\widehat QSR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1331.jpg"
-  },
-  {
-    "id": 1367,
-    "problem_id": 1332,
-    "problem": "line A B, line B D F, line F G, line A C D E G, line C B, line F E, line A B, line B D F, line F G, line A C D E G, line C B, line F E\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1332.jpg"
-  },
-  {
-    "id": 1368,
-    "problem_id": 1333,
-    "problem": "line A B, line B D F, line F G, line A C D E G, line C B, line F E, line A B, line B D F, line F G, line A C D E G, line C B, line F E\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1333.jpg"
-  },
-  {
-    "id": 1369,
-    "problem_id": 1334,
-    "problem": "line A B, line B D F, line F G, line A C D E G, line C B, line F E, line A B, line B D F, line F G, line A C D E G, line C B, line F E\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1334.jpg"
-  },
-  {
-    "id": 1370,
-    "problem_id": 1335,
-    "problem": "line A B, line B D F, line F G, line A C D E G, line C B, line F E, line A B, line B D F, line F G, line A C D E G, line C B, line F E\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1335.jpg"
-  },
-  {
-    "id": 1371,
-    "problem_id": 1336,
-    "problem": "line B A, line A C, line C E, line F E, line D F, line B D, line B A, line A C, line C E, line F E, line D F, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1336.jpg"
-  },
-  {
-    "id": 1372,
-    "problem_id": 1337,
-    "problem": "line B A, line A C, line C E, line F E, line D F, line B D, line B A, line A C, line C E, line F E, line D F, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1337.jpg"
-  },
-  {
-    "id": 1373,
-    "problem_id": 1338,
-    "problem": "line B A, line A C, line C E, line F E, line D F, line B D, line B A, line A C, line C E, line F E, line D F, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1338.jpg"
-  },
-  {
-    "id": 1374,
-    "problem_id": 1339,
-    "problem": "line B A, line A C, line C E, line F E, line D F, line B D, line B A, line A C, line C E, line F E, line D F, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1339.jpg"
-  },
-  {
-    "id": 1375,
-    "problem_id": 1340,
-    "problem": "line B A, line A C, line C E, line F E, line D F, line B D, line B A, line A C, line C E, line F E, line D F, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1340.jpg"
-  },
-  {
-    "id": 1376,
-    "problem_id": 1341,
-    "problem": "line A B, \\odot B lieson A, line A B, \\odot B lieson A\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1341.jpg"
-  },
-  {
-    "id": 1377,
-    "problem_id": 1342,
-    "problem": "line A B, \\odot B lieson A, line A B, \\odot B lieson A\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1342.jpg"
-  },
-  {
-    "id": 1378,
-    "problem_id": 1343,
-    "problem": "line A B, \\odot B lieson A, line A B, \\odot B lieson A\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1343.jpg"
-  },
-  {
-    "id": 1379,
-    "problem_id": 1344,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1344.jpg"
-  },
-  {
-    "id": 1380,
-    "problem_id": 1345,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1345.jpg"
-  },
-  {
-    "id": 1381,
-    "problem_id": 1346,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1346.jpg"
-  },
-  {
-    "id": 1382,
-    "problem_id": 1347,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1347.jpg"
-  },
-  {
-    "id": 1383,
-    "problem_id": 1348,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1348.jpg"
-  },
-  {
-    "id": 1384,
-    "problem_id": 1349,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1349.jpg"
-  },
-  {
-    "id": 1385,
-    "problem_id": 1350,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1350.jpg"
-  },
-  {
-    "id": 1386,
-    "problem_id": 1351,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1351.jpg"
-  },
-  {
-    "id": 1387,
-    "problem_id": 1352,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1352.jpg"
-  },
-  {
-    "id": 1388,
-    "problem_id": 1353,
-    "problem": "line N P, line P Q, line N Q, line N P, line P Q, line N Q\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1353.jpg"
-  },
-  {
-    "id": 1389,
-    "problem_id": 1354,
-    "problem": "line N P, line P Q, line N Q, line N P, line P Q, line N Q\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1354.jpg"
-  },
-  {
-    "id": 1390,
-    "problem_id": 1355,
-    "problem": "line N P, line P Q, line N Q, line N P, line P Q, line N Q\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1355.jpg"
-  },
-  {
-    "id": 1391,
-    "problem_id": 1356,
-    "problem": "line N P, line P Q, line N Q, line N P, line P Q, line N Q\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1356.jpg"
-  },
-  {
-    "id": 1392,
-    "problem_id": 1357,
-    "problem": "line R T, line T S, line R S, line W V, line W U, line V U, line R T, line T S, line R S, line W V, line W U, line V U\nEach pair of polygons is similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1357.jpg"
-  },
-  {
-    "id": 1393,
-    "problem_id": 1358,
-    "problem": "line R T, line T S, line R S, line W V, line W U, line V U, line R T, line T S, line R S, line W V, line W U, line V U\nEach pair of polygons is similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1358.jpg"
-  },
-  {
-    "id": 1394,
-    "problem_id": 1359,
-    "problem": "line R T, line T S, line R S, line W V, line W U, line V U, line R T, line T S, line R S, line W V, line W U, line V U\nEach pair of polygons is similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1359.jpg"
-  },
-  {
-    "id": 1395,
-    "problem_id": 1360,
-    "problem": "line R T, line T S, line R S, line W V, line W U, line V U, line R T, line T S, line R S, line W V, line W U, line V U\nEach pair of polygons is similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1360.jpg"
-  },
-  {
-    "id": 1396,
-    "problem_id": 1361,
-    "problem": "line P A M, line N B M, line N C P, line Q P, line Q A, line B Q, line Q M, line C Q, line N Q, line P A M, line N B M, line N C P, line Q P, line Q A, line B Q, line Q M, line C Q, line N Q\nThe perpendicular bisectors of \\triangle MNP meet at point Q. Find QM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1361.jpg"
-  },
-  {
-    "id": 1397,
-    "problem_id": 1362,
-    "problem": "line J K, line J H, line K H, line J K, line J H, line K H\nFind the length of KH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1362.jpg"
-  },
-  {
-    "id": 1398,
-    "problem_id": 1363,
-    "problem": "line J K, line J H, line K H, line J K, line J H, line K H\nFind the length of KH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1363.jpg"
-  },
-  {
-    "id": 1399,
-    "problem_id": 1364,
-    "problem": "line J K, line J H, line K H, line J K, line J H, line K H\nFind the length of KH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1364.jpg"
-  },
-  {
-    "id": 1400,
-    "problem_id": 1365,
-    "problem": "line J K, line J H, line K H, line J K, line J H, line K H\nFind the length of KH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1365.jpg"
-  },
-  {
-    "id": 1401,
-    "problem_id": 1366,
-    "problem": "line J K, line J H, line K H, line J K, line J H, line K H\nFind the length of KH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1366.jpg"
-  },
-  {
-    "id": 1402,
-    "problem_id": 1367,
-    "problem": "line J K, line J H, line K H, line J K, line J H, line K H\nFind the length of KH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1367.jpg"
-  },
-  {
-    "id": 1404,
-    "problem_id": 1368,
-    "problem": "line S W, line T W, line S T, line S W, line T W, line S T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1368.jpg"
-  },
-  {
-    "id": 1405,
-    "problem_id": 1369,
-    "problem": "line S W, line T W, line S T, line S W, line T W, line S T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1369.jpg"
-  },
-  {
-    "id": 1406,
-    "problem_id": 1370,
-    "problem": "line S W, line T W, line S T, line S W, line T W, line S T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1370.jpg"
-  },
-  {
-    "id": 1407,
-    "problem_id": 1371,
-    "problem": "line S W, line T W, line S T, line S W, line T W, line S T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1371.jpg"
-  },
-  {
-    "id": 1408,
-    "problem_id": 1372,
-    "problem": "line Y X O, line A X B, \\odot O lieson Y A B, line Y X O, line A X B, \\odot O lieson Y A B\nCircle O has a radius of 10, AB = 10 and m \\widehat AB = 60. Find m \\widehat AY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1372.jpg"
-  },
-  {
-    "id": 1409,
-    "problem_id": 1373,
-    "problem": "line Y X O, line A X B, \\odot O lieson Y A B, line Y X O, line A X B, \\odot O lieson Y A B\nCircle O has a radius of 10, AB = 10 and m \\widehat AB = 60. Find m \\widehat AY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1373.jpg"
-  },
-  {
-    "id": 1410,
-    "problem_id": 1374,
-    "problem": "line C B A, line C F E, line C D G, line F D, line B F, line C B A, line C F E, line C D G, line F D, line B F\nWhat is the length of FB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1374.jpg"
-  },
-  {
-    "id": 1411,
-    "problem_id": 1375,
-    "problem": "line C B A, line C F E, line C D G, line F D, line B F, line C B A, line C F E, line C D G, line F D, line B F\nWhat is the length of FB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1375.jpg"
-  },
-  {
-    "id": 1412,
-    "problem_id": 1376,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1376.jpg"
-  },
-  {
-    "id": 1413,
-    "problem_id": 1377,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1377.jpg"
-  },
-  {
-    "id": 1414,
-    "problem_id": 1378,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1378.jpg"
-  },
-  {
-    "id": 1415,
-    "problem_id": 1379,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1379.jpg"
-  },
-  {
-    "id": 1416,
-    "problem_id": 1380,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1380.jpg"
-  },
-  {
-    "id": 1417,
-    "problem_id": 1381,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1381.jpg"
-  },
-  {
-    "id": 1418,
-    "problem_id": 1382,
-    "problem": "line N P, line M Q P, line M N, line N Q, line N P, line M Q P, line M N, line N Q\nWhat is the length of MP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1382.jpg"
-  },
-  {
-    "id": 1419,
-    "problem_id": 1383,
-    "problem": "line N P, line M Q P, line M N, line N Q, line N P, line M Q P, line M N, line N Q\nWhat is the length of MP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1383.jpg"
-  },
-  {
-    "id": 1420,
-    "problem_id": 1384,
-    "problem": "line N P, line M Q P, line M N, line N Q, line N P, line M Q P, line M N, line N Q\nWhat is the length of MP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1384.jpg"
-  },
-  {
-    "id": 1421,
-    "problem_id": 1385,
-    "problem": "line N P, line M Q P, line M N, line N Q, line N P, line M Q P, line M N, line N Q\nWhat is the length of MP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1385.jpg"
-  },
-  {
-    "id": 1422,
-    "problem_id": 1386,
-    "problem": "line K L, line M P L, line J M, line J N K, line N P, line K L, line M P L, line J M, line J N K, line N P\nIn the trapezoid, NP = 15. What is the length of KL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1386.jpg"
-  },
-  {
-    "id": 1423,
-    "problem_id": 1387,
-    "problem": "line K L, line M P L, line J M, line J N K, line N P, line K L, line M P L, line J M, line J N K, line N P\nIn the trapezoid, NP = 15. What is the length of KL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1387.jpg"
-  },
-  {
-    "id": 1424,
-    "problem_id": 1388,
-    "problem": "line S A T, line R B T, line R C S, \\odot D lieson C A B, line S A T, line R B T, line R C S, \\odot D lieson C A B\nTriangle RST is circumscribed about the circle. What is RT?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1388.jpg"
-  },
-  {
-    "id": 1425,
-    "problem_id": 1389,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1389.jpg"
-  },
-  {
-    "id": 1426,
-    "problem_id": 1390,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1390.jpg"
-  },
-  {
-    "id": 1427,
-    "problem_id": 1391,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1391.jpg"
-  },
-  {
-    "id": 1428,
-    "problem_id": 1392,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1392.jpg"
-  },
-  {
-    "id": 1429,
-    "problem_id": 1393,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 11.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1393.jpg"
-  },
-  {
-    "id": 1430,
-    "problem_id": 1394,
-    "problem": "line B L N A, line M N P, line L P, line L M, line B L N A, line M N P, line L P, line L M\nFind LP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1394.jpg"
-  },
-  {
-    "id": 1431,
-    "problem_id": 1395,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle L of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1395.jpg"
-  },
-  {
-    "id": 1432,
-    "problem_id": 1396,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle L of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1396.jpg"
-  },
-  {
-    "id": 1433,
-    "problem_id": 1397,
-    "problem": "line B C, line C A, line B E A, line E C, line B C, line C A, line B E A, line E C\nIf x = 7\\sqrt{3}, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1397.jpg"
-  },
-  {
-    "id": 1434,
-    "problem_id": 1398,
-    "problem": "line B C, line C A, line B E A, line E C, line B C, line C A, line B E A, line E C\nIf x = 7\\sqrt{3}, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1398.jpg"
-  },
-  {
-    "id": 1435,
-    "problem_id": 1399,
-    "problem": "line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X, line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X\nFind b in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1399.jpg"
-  },
-  {
-    "id": 1436,
-    "problem_id": 1400,
-    "problem": "line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X, line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X\nFind b in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1400.jpg"
-  },
-  {
-    "id": 1437,
-    "problem_id": 1401,
-    "problem": "line A B D, line B C, line A B D, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1401.jpg"
-  },
-  {
-    "id": 1438,
-    "problem_id": 1402,
-    "problem": "line A B D, line B C, line A B D, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1402.jpg"
-  },
-  {
-    "id": 1439,
-    "problem_id": 1403,
-    "problem": "line A B D, line B C, line A B D, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1403.jpg"
-  },
-  {
-    "id": 1440,
-    "problem_id": 1404,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1404.jpg"
-  },
-  {
-    "id": 1441,
-    "problem_id": 1405,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1405.jpg"
-  },
-  {
-    "id": 1442,
-    "problem_id": 1406,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1406.jpg"
-  },
-  {
-    "id": 1443,
-    "problem_id": 1407,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1407.jpg"
-  },
-  {
-    "id": 1444,
-    "problem_id": 1408,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1408.jpg"
-  },
-  {
-    "id": 1445,
-    "problem_id": 1409,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1409.jpg"
-  },
-  {
-    "id": 1446,
-    "problem_id": 1410,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1410.jpg"
-  },
-  {
-    "id": 1447,
-    "problem_id": 1411,
-    "problem": "line B C D, line A D, line B A, line C A, line B C D, line A D, line B A, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1411.jpg"
-  },
-  {
-    "id": 1448,
-    "problem_id": 1412,
-    "problem": "line B C D, line A D, line B A, line C A, line B C D, line A D, line B A, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1412.jpg"
-  },
-  {
-    "id": 1449,
-    "problem_id": 1413,
-    "problem": "line S T, line R V T, line S V, line R S, line S T, line R V T, line S V, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1413.jpg"
-  },
-  {
-    "id": 1450,
-    "problem_id": 1414,
-    "problem": "line S T, line R V T, line S V, line R S, line S T, line R V T, line S V, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1414.jpg"
-  },
-  {
-    "id": 1451,
-    "problem_id": 1415,
-    "problem": "line S T, line R V T, line S V, line R S, line S T, line R V T, line S V, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1415.jpg"
-  },
-  {
-    "id": 1452,
-    "problem_id": 1416,
-    "problem": "line S T, line R V T, line S V, line R S, line S T, line R V T, line S V, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1416.jpg"
-  },
-  {
-    "id": 1453,
-    "problem_id": 1417,
-    "problem": "line S T, line R V T, line S V, line R S, line S T, line R V T, line S V, line R S\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1417.jpg"
-  },
-  {
-    "id": 1454,
-    "problem_id": 1418,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1418.jpg"
-  },
-  {
-    "id": 1455,
-    "problem_id": 1419,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1419.jpg"
-  },
-  {
-    "id": 1456,
-    "problem_id": 1420,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1420.jpg"
-  },
-  {
-    "id": 1457,
-    "problem_id": 1421,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1421.jpg"
-  },
-  {
-    "id": 1458,
-    "problem_id": 1422,
-    "problem": "line E F, line B F, line A E, line A D B, line C D, line C A, line C B, line E F, line B F, line A E, line A D B, line C D, line C A, line C B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1422.jpg"
-  },
-  {
-    "id": 1459,
-    "problem_id": 1423,
-    "problem": "line E F, line B F, line A E, line A D B, line C D, line C A, line C B, line E F, line B F, line A E, line A D B, line C D, line C A, line C B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1423.jpg"
-  },
-  {
-    "id": 1460,
-    "problem_id": 1424,
-    "problem": "line B A, line D A, line A C, line B D C, line B A, line D A, line A C, line B D C\nFind x if AD is a median of \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1424.jpg"
-  },
-  {
-    "id": 1461,
-    "problem_id": 1425,
-    "problem": "line B A, line D A, line A C, line B D C, line B A, line D A, line A C, line B D C\nFind x if AD is a median of \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1425.jpg"
-  },
-  {
-    "id": 1462,
-    "problem_id": 1426,
-    "problem": "line E D, line A E, line A B C, line C D, line B D, line E D, line A E, line A B C, line C D, line B D\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1426.jpg"
-  },
-  {
-    "id": 1463,
-    "problem_id": 1427,
-    "problem": "line E D, line A E, line A B C, line C D, line B D, line E D, line A E, line A B C, line C D, line B D\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1427.jpg"
-  },
-  {
-    "id": 1464,
-    "problem_id": 1428,
-    "problem": "line E D, line A E, line A B C, line C D, line B D, line E D, line A E, line A B C, line C D, line B D\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1428.jpg"
-  },
-  {
-    "id": 1465,
-    "problem_id": 1429,
-    "problem": "line E D, line A E, line A B C, line C D, line B D, line E D, line A E, line A B C, line C D, line B D\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1429.jpg"
-  },
-  {
-    "id": 1466,
-    "problem_id": 1430,
-    "problem": "line E D, line A E, line A B C, line C D, line B D, line E D, line A E, line A B C, line C D, line B D\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1430.jpg"
-  },
-  {
-    "id": 1467,
-    "problem_id": 1431,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1431.jpg"
-  },
-  {
-    "id": 1468,
-    "problem_id": 1432,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1432.jpg"
-  },
-  {
-    "id": 1469,
-    "problem_id": 1433,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1433.jpg"
-  },
-  {
-    "id": 1470,
-    "problem_id": 1434,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1434.jpg"
-  },
-  {
-    "id": 1471,
-    "problem_id": 1435,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1435.jpg"
-  },
-  {
-    "id": 1472,
-    "problem_id": 1436,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1436.jpg"
-  },
-  {
-    "id": 1473,
-    "problem_id": 1437,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1437.jpg"
-  },
-  {
-    "id": 1474,
-    "problem_id": 1438,
-    "problem": "line A C, line A B, line B D, line C D, line A E D, line B E C, line A C, line A B, line B D, line C D, line A E D, line B E C\nQuadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1438.jpg"
-  },
-  {
-    "id": 1475,
-    "problem_id": 1439,
-    "problem": "line A C, line A B, line B D, line C D, line A E D, line B E C, line A C, line A B, line B D, line C D, line A E D, line B E C\nQuadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1439.jpg"
-  },
-  {
-    "id": 1476,
-    "problem_id": 1440,
-    "problem": "line A C, line A B, line B D, line C D, line A E D, line B E C, line A C, line A B, line B D, line C D, line A E D, line B E C\nQuadrilateral ABDC is a rectangle. m \\angle 2 = 40. Find m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1440.jpg"
-  },
-  {
-    "id": 1477,
-    "problem_id": 1441,
-    "problem": "line M N, line R U, line S T, line T N U, line S M R, line M N, line R U, line S T, line T N U, line S M R\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1441.jpg"
-  },
-  {
-    "id": 1478,
-    "problem_id": 1442,
-    "problem": "line M N, line R U, line S T, line T N U, line S M R, line M N, line R U, line S T, line T N U, line S M R\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1442.jpg"
-  },
-  {
-    "id": 1479,
-    "problem_id": 1443,
-    "problem": "line M N, line R U, line S T, line T N U, line S M R, line M N, line R U, line S T, line T N U, line S M R\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1443.jpg"
-  },
-  {
-    "id": 1480,
-    "problem_id": 1444,
-    "problem": "line M N, line R U, line S T, line T N U, line S M R, line M N, line R U, line S T, line T N U, line S M R\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1444.jpg"
-  },
-  {
-    "id": 1481,
-    "problem_id": 1445,
-    "problem": "line M N, line R U, line S T, line T N U, line S M R, line M N, line R U, line S T, line T N U, line S M R\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1445.jpg"
-  },
-  {
-    "id": 1482,
-    "problem_id": 1446,
-    "problem": "line D B, line A B E, line D E, line B C, line A C, line D B, line A B E, line D E, line B C, line A C\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1446.jpg"
-  },
-  {
-    "id": 1484,
-    "problem_id": 1447,
-    "problem": "line D B, line A B E, line D E, line B C, line A C, line D B, line A B E, line D E, line B C, line A C\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1447.jpg"
-  },
-  {
-    "id": 1485,
-    "problem_id": 1448,
-    "problem": "line R A T, line S C T, line S B R, line S D A, line R D C, line B D T, line R A T, line S C T, line S B R, line S D A, line R D C, line B D T\nThe perpendicular bisectors of \\triangle RST meet at point D. Find ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1448.jpg"
-  },
-  {
-    "id": 1486,
-    "problem_id": 1449,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOC = 7x-2, m \\angle DOC = 2x+8, m \\angle EOD = 27. Find m \\angle AOB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1449.jpg"
-  },
-  {
-    "id": 1487,
-    "problem_id": 1450,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOC = 7x-2, m \\angle DOC = 2x+8, m \\angle EOD = 27. Find m \\angle AOB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1450.jpg"
-  },
-  {
-    "id": 1488,
-    "problem_id": 1451,
-    "problem": "line J K, line K L, \\odot K lieson L J, line J K, line K L, \\odot K lieson L J\nFind the length of \\widehat JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1451.jpg"
-  },
-  {
-    "id": 1490,
-    "problem_id": 1452,
-    "problem": "line J K, line K L, \\odot K lieson L J, line J K, line K L, \\odot K lieson L J\nFind the length of \\widehat JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1452.jpg"
-  },
-  {
-    "id": 1491,
-    "problem_id": 1453,
-    "problem": "line J K, line K L, \\odot K lieson L J, line J K, line K L, \\odot K lieson L J\nFind the length of \\widehat JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1453.jpg"
-  },
-  {
-    "id": 1492,
-    "problem_id": 1454,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1454.jpg"
-  },
-  {
-    "id": 1493,
-    "problem_id": 1455,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1455.jpg"
-  },
-  {
-    "id": 1494,
-    "problem_id": 1456,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1456.jpg"
-  },
-  {
-    "id": 1495,
-    "problem_id": 1457,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1457.jpg"
-  },
-  {
-    "id": 1496,
-    "problem_id": 1458,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1458.jpg"
-  },
-  {
-    "id": 1497,
-    "problem_id": 1459,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1459.jpg"
-  },
-  {
-    "id": 1498,
-    "problem_id": 1460,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1460.jpg"
-  },
-  {
-    "id": 1499,
-    "problem_id": 1461,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nWhat is the length of LM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1461.jpg"
-  },
-  {
-    "id": 1500,
-    "problem_id": 1462,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nWhat is the length of LM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1462.jpg"
-  },
-  {
-    "id": 1501,
-    "problem_id": 1463,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nWhat is the length of LM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1463.jpg"
-  },
-  {
-    "id": 1502,
-    "problem_id": 1464,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nWhat is the length of LM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1464.jpg"
-  },
-  {
-    "id": 1503,
-    "problem_id": 1465,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nWhat is the length of LM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1465.jpg"
-  },
-  {
-    "id": 1504,
-    "problem_id": 1466,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nWhat is the length of LM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1466.jpg"
-  },
-  {
-    "id": 1505,
-    "problem_id": 1467,
-    "problem": "line Q T R, line P U R, line P S Q, line S T, line U T, line S U, line Q T R, line P U R, line P S Q, line S T, line U T, line S U\nm \\angle QST = 40. What is m \\angle STU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1467.jpg"
-  },
-  {
-    "id": 1506,
-    "problem_id": 1468,
-    "problem": "line Q T R, line P U R, line P S Q, line S T, line U T, line S U, line Q T R, line P U R, line P S Q, line S T, line U T, line S U\nm \\angle QST = 40. What is m \\angle STU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1468.jpg"
-  },
-  {
-    "id": 1507,
-    "problem_id": 1469,
-    "problem": "line A B C, line C D, line B D, line B E, line A E, line A B C, line C D, line B D, line B E, line A E\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1469.jpg"
-  },
-  {
-    "id": 1508,
-    "problem_id": 1470,
-    "problem": "line A B C, line C D, line B D, line B E, line A E, line A B C, line C D, line B D, line B E, line A E\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1470.jpg"
-  },
-  {
-    "id": 1509,
-    "problem_id": 1471,
-    "problem": "line A B C, line C D, line B D, line B E, line A E, line A B C, line C D, line B D, line B E, line A E\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1471.jpg"
-  },
-  {
-    "id": 1510,
-    "problem_id": 1472,
-    "problem": "line A B C, line C D, line B D, line B E, line A E, line A B C, line C D, line B D, line B E, line A E\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1472.jpg"
-  },
-  {
-    "id": 1511,
-    "problem_id": 1473,
-    "problem": "line A B C, line C D, line B D, line B E, line A E, line A B C, line C D, line B D, line B E, line A E\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1473.jpg"
-  },
-  {
-    "id": 1512,
-    "problem_id": 1474,
-    "problem": "line A B C, line C D, line B D, line B E, line A E, line A B C, line C D, line B D, line B E, line A E\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1474.jpg"
-  },
-  {
-    "id": 1513,
-    "problem_id": 1475,
-    "problem": "line A U, line A V B, line O A, line O V U, line A U, line A V B, line O A, line O V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1475.jpg"
-  },
-  {
-    "id": 1514,
-    "problem_id": 1476,
-    "problem": "line A U, line A V B, line O A, line O V U, line A U, line A V B, line O A, line O V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1476.jpg"
-  },
-  {
-    "id": 1515,
-    "problem_id": 1477,
-    "problem": "line A U, line A V B, line O A, line O V U, line A U, line A V B, line O A, line O V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1477.jpg"
-  },
-  {
-    "id": 1516,
-    "problem_id": 1478,
-    "problem": "line A D, line C B D, line C A, line A B, line A D, line C B D, line C A, line A B\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1478.jpg"
-  },
-  {
-    "id": 1517,
-    "problem_id": 1479,
-    "problem": "line A B, line C B, line D C, line E D, line E A, line A B, line C B, line D C, line E D, line E A\nThe perimeter of this polygon is 60 centimeters. Find the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1479.jpg"
-  },
-  {
-    "id": 1518,
-    "problem_id": 1480,
-    "problem": "line A B, line C B, line D C, line E D, line E A, line A B, line C B, line D C, line E D, line E A\nThe perimeter of this polygon is 60 centimeters. Find the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1480.jpg"
-  },
-  {
-    "id": 1519,
-    "problem_id": 1481,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1481.jpg"
-  },
-  {
-    "id": 1520,
-    "problem_id": 1482,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1482.jpg"
-  },
-  {
-    "id": 1521,
-    "problem_id": 1483,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1483.jpg"
-  },
-  {
-    "id": 1522,
-    "problem_id": 1484,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1484.jpg"
-  },
-  {
-    "id": 1523,
-    "problem_id": 1485,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1485.jpg"
-  },
-  {
-    "id": 1524,
-    "problem_id": 1486,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1486.jpg"
-  },
-  {
-    "id": 1525,
-    "problem_id": 1487,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1487.jpg"
-  },
-  {
-    "id": 1526,
-    "problem_id": 1488,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1488.jpg"
-  },
-  {
-    "id": 1527,
-    "problem_id": 1489,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x for given rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1489.jpg"
-  },
-  {
-    "id": 1528,
-    "problem_id": 1490,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x for given rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1490.jpg"
-  },
-  {
-    "id": 1529,
-    "problem_id": 1491,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x for given rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1491.jpg"
-  },
-  {
-    "id": 1530,
-    "problem_id": 1492,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x for given rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1492.jpg"
-  },
-  {
-    "id": 1531,
-    "problem_id": 1493,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x for given rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1493.jpg"
-  },
-  {
-    "id": 1532,
-    "problem_id": 1494,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x for given rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1494.jpg"
-  },
-  {
-    "id": 1533,
-    "problem_id": 1495,
-    "problem": "line B A, line A C, line C F, line E F, line D E, line B D, line B A, line A C, line C F, line E F, line D E, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1495.jpg"
-  },
-  {
-    "id": 1534,
-    "problem_id": 1496,
-    "problem": "line B A, line A C, line C F, line E F, line D E, line B D, line B A, line A C, line C F, line E F, line D E, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1496.jpg"
-  },
-  {
-    "id": 1535,
-    "problem_id": 1497,
-    "problem": "line B A, line A C, line C F, line E F, line D E, line B D, line B A, line A C, line C F, line E F, line D E, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1497.jpg"
-  },
-  {
-    "id": 1536,
-    "problem_id": 1498,
-    "problem": "line B A, line A C, line C F, line E F, line D E, line B D, line B A, line A C, line C F, line E F, line D E, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1498.jpg"
-  },
-  {
-    "id": 1537,
-    "problem_id": 1499,
-    "problem": "line B A, line A C, line C F, line E F, line D E, line B D, line B A, line A C, line C F, line E F, line D E, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1499.jpg"
-  },
-  {
-    "id": 1538,
-    "problem_id": 1500,
-    "problem": "line B A, line A C, line C F, line E F, line D E, line B D, line B A, line A C, line C F, line E F, line D E, line B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1500.jpg"
-  },
-  {
-    "id": 1539,
-    "problem_id": 1501,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nWhat is the circumference of the circle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1501.jpg"
-  },
-  {
-    "id": 1540,
-    "problem_id": 1502,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1502.jpg"
-  },
-  {
-    "id": 1541,
-    "problem_id": 1503,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1503.jpg"
-  },
-  {
-    "id": 1542,
-    "problem_id": 1504,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1504.jpg"
-  },
-  {
-    "id": 1543,
-    "problem_id": 1505,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1505.jpg"
-  },
-  {
-    "id": 1544,
-    "problem_id": 1506,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1506.jpg"
-  },
-  {
-    "id": 1545,
-    "problem_id": 1507,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1507.jpg"
-  },
-  {
-    "id": 1546,
-    "problem_id": 1508,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind BC if \\triangle ABC is an isosceles triangle with AB = BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1508.jpg"
-  },
-  {
-    "id": 1547,
-    "problem_id": 1509,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind BC if \\triangle ABC is an isosceles triangle with AB = BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1509.jpg"
-  },
-  {
-    "id": 1548,
-    "problem_id": 1510,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind BC if \\triangle ABC is an isosceles triangle with AB = BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1510.jpg"
-  },
-  {
-    "id": 1549,
-    "problem_id": 1511,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nFind BC if \\triangle ABC is an isosceles triangle with AB = BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1511.jpg"
-  },
-  {
-    "id": 1550,
-    "problem_id": 1512,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1512.jpg"
-  },
-  {
-    "id": 1551,
-    "problem_id": 1513,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1513.jpg"
-  },
-  {
-    "id": 1552,
-    "problem_id": 1514,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1514.jpg"
-  },
-  {
-    "id": 1553,
-    "problem_id": 1515,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1515.jpg"
-  },
-  {
-    "id": 1554,
-    "problem_id": 1516,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1516.jpg"
-  },
-  {
-    "id": 1555,
-    "problem_id": 1517,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1517.jpg"
-  },
-  {
-    "id": 1556,
-    "problem_id": 1518,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nSolve for the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1518.jpg"
-  },
-  {
-    "id": 1557,
-    "problem_id": 1519,
-    "problem": "line A C D, line B C E, line A C D, line B C E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1519.jpg"
-  },
-  {
-    "id": 1558,
-    "problem_id": 1520,
-    "problem": "line A C D, line B C E, line A C D, line B C E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1520.jpg"
-  },
-  {
-    "id": 1559,
-    "problem_id": 1521,
-    "problem": "line A C D, line B C E, line A C D, line B C E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1521.jpg"
-  },
-  {
-    "id": 1560,
-    "problem_id": 1522,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1522.jpg"
-  },
-  {
-    "id": 1561,
-    "problem_id": 1523,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1523.jpg"
-  },
-  {
-    "id": 1562,
-    "problem_id": 1524,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1524.jpg"
-  },
-  {
-    "id": 1563,
-    "problem_id": 1525,
-    "problem": "line N M, line K L, line L M, line K N, line N M, line K L, line L M, line K N\nKLMN is a rectangle. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1525.jpg"
-  },
-  {
-    "id": 1564,
-    "problem_id": 1526,
-    "problem": "line N M, line K L, line L M, line K N, line N M, line K L, line L M, line K N\nKLMN is a rectangle. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1526.jpg"
-  },
-  {
-    "id": 1565,
-    "problem_id": 1527,
-    "problem": "line N M, line K L, line L M, line K N, line N M, line K L, line L M, line K N\nKLMN is a rectangle. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1527.jpg"
-  },
-  {
-    "id": 1566,
-    "problem_id": 1528,
-    "problem": "line N M, line K L, line L M, line K N, line N M, line K L, line L M, line K N\nKLMN is a rectangle. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1528.jpg"
-  },
-  {
-    "id": 1567,
-    "problem_id": 1529,
-    "problem": "line T A Q, line P T, line P Q, line P A R, line Q R, line T A Q, line P T, line P Q, line P A R, line Q R\nFind the measure of \\angle 5 if PQ \\perp QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1529.jpg"
-  },
-  {
-    "id": 1568,
-    "problem_id": 1530,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable m in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1530.jpg"
-  },
-  {
-    "id": 1569,
-    "problem_id": 1531,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable m in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1531.jpg"
-  },
-  {
-    "id": 1570,
-    "problem_id": 1532,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable m in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1532.jpg"
-  },
-  {
-    "id": 1571,
-    "problem_id": 1533,
-    "problem": "line D C, line A D, line A B, line B C, line A C, line D C, line A D, line A B, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1533.jpg"
-  },
-  {
-    "id": 1572,
-    "problem_id": 1534,
-    "problem": "line D C, line A D, line A B, line B C, line A C, line D C, line A D, line A B, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1534.jpg"
-  },
-  {
-    "id": 1573,
-    "problem_id": 1535,
-    "problem": "line D C, line A D, line A B, line B C, line A C, line D C, line A D, line A B, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1535.jpg"
-  },
-  {
-    "id": 1574,
-    "problem_id": 1536,
-    "problem": "line D C, line A D, line A B, line B C, line A C, line D C, line A D, line A B, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1536.jpg"
-  },
-  {
-    "id": 1575,
-    "problem_id": 1537,
-    "problem": "line A D E, line A B C, line A F, \\odot G lieson F D B C E, line A D E, line A B C, line A F, \\odot G lieson F D B C E\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1537.jpg"
-  },
-  {
-    "id": 1576,
-    "problem_id": 1538,
-    "problem": "line A D E, line A B C, line A F, \\odot G lieson F D B C E, line A D E, line A B C, line A F, \\odot G lieson F D B C E\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1538.jpg"
-  },
-  {
-    "id": 1577,
-    "problem_id": 1539,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1539.jpg"
-  },
-  {
-    "id": 1578,
-    "problem_id": 1540,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1540.jpg"
-  },
-  {
-    "id": 1580,
-    "problem_id": 1541,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1541.jpg"
-  },
-  {
-    "id": 1581,
-    "problem_id": 1542,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1542.jpg"
-  },
-  {
-    "id": 1582,
-    "problem_id": 1543,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1543.jpg"
-  },
-  {
-    "id": 1583,
-    "problem_id": 1544,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1544.jpg"
-  },
-  {
-    "id": 1584,
-    "problem_id": 1545,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1545.jpg"
-  },
-  {
-    "id": 1585,
-    "problem_id": 1546,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1546.jpg"
-  },
-  {
-    "id": 1586,
-    "problem_id": 1547,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1547.jpg"
-  },
-  {
-    "id": 1587,
-    "problem_id": 1548,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1548.jpg"
-  },
-  {
-    "id": 1588,
-    "problem_id": 1549,
-    "problem": "line B C E, line A E, line A C D, line D E, line B D, line B A, line B C E, line A E, line A C D, line D E, line B D, line B A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1549.jpg"
-  },
-  {
-    "id": 1589,
-    "problem_id": 1550,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1550.jpg"
-  },
-  {
-    "id": 1590,
-    "problem_id": 1551,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1551.jpg"
-  },
-  {
-    "id": 1591,
-    "problem_id": 1552,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1552.jpg"
-  },
-  {
-    "id": 1592,
-    "problem_id": 1553,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1553.jpg"
-  },
-  {
-    "id": 1593,
-    "problem_id": 1554,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1554.jpg"
-  },
-  {
-    "id": 1594,
-    "problem_id": 1555,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1555.jpg"
-  },
-  {
-    "id": 1595,
-    "problem_id": 1556,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1556.jpg"
-  },
-  {
-    "id": 1596,
-    "problem_id": 1557,
-    "problem": "line G A E B, line D E F, line B C H, \\odot I lieson A F B D, line G A E B, line D E F, line B C H, \\odot I lieson A F B D\nFind m \\angle DEB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1557.jpg"
-  },
-  {
-    "id": 1597,
-    "problem_id": 1558,
-    "problem": "line B C, line A C, line B D, line A D, line l lieson F D E, \\odot C lieson B D A, line B C, line A C, line B D, line A D, line l lieson F D E, \\odot C lieson B D A\nDetermine the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1558.jpg"
-  },
-  {
-    "id": 1598,
-    "problem_id": 1559,
-    "problem": "line B C, line A C, line B D, line A D, line l lieson F D E, \\odot C lieson B D A, line B C, line A C, line B D, line A D, line l lieson F D E, \\odot C lieson B D A\nDetermine the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1559.jpg"
-  },
-  {
-    "id": 1599,
-    "problem_id": 1560,
-    "problem": "line B C, line A C, line B D, line A D, line l lieson F D E, \\odot C lieson B D A, line B C, line A C, line B D, line A D, line l lieson F D E, \\odot C lieson B D A\nDetermine the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1560.jpg"
-  },
-  {
-    "id": 1600,
-    "problem_id": 1561,
-    "problem": "line A D B, line C B, line C D, \\odot C lieson A B, line A D B, line C B, line C D, \\odot C lieson A B\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1561.jpg"
-  },
-  {
-    "id": 1601,
-    "problem_id": 1562,
-    "problem": "line A D B, line C B, line C D, \\odot C lieson A B, line A D B, line C B, line C D, \\odot C lieson A B\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1562.jpg"
-  },
-  {
-    "id": 1602,
-    "problem_id": 1563,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1563.jpg"
-  },
-  {
-    "id": 1603,
-    "problem_id": 1564,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1564.jpg"
-  },
-  {
-    "id": 1604,
-    "problem_id": 1565,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1565.jpg"
-  },
-  {
-    "id": 1605,
-    "problem_id": 1566,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1566.jpg"
-  },
-  {
-    "id": 1606,
-    "problem_id": 1567,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1567.jpg"
-  },
-  {
-    "id": 1607,
-    "problem_id": 1568,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1568.jpg"
-  },
-  {
-    "id": 1608,
-    "problem_id": 1569,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1569.jpg"
-  },
-  {
-    "id": 1609,
-    "problem_id": 1570,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1570.jpg"
-  },
-  {
-    "id": 1610,
-    "problem_id": 1571,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1571.jpg"
-  },
-  {
-    "id": 1611,
-    "problem_id": 1572,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1572.jpg"
-  },
-  {
-    "id": 1612,
-    "problem_id": 1573,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1573.jpg"
-  },
-  {
-    "id": 1613,
-    "problem_id": 1574,
-    "problem": "line R S, line S T, line U T, line R U, \\odot P lieson R U T S, line R S, line S T, line U T, line R U, \\odot P lieson R U T S\nQuadrilateral RSTU is inscribed in circle P. Find the measure of \\widehat TUR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1574.jpg"
-  },
-  {
-    "id": 1614,
-    "problem_id": 1575,
-    "problem": "line A B, \\odot A lieson B H G, line A B, \\odot A lieson B H G\nWhat is the length of diameter?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1575.jpg"
-  },
-  {
-    "id": 1616,
-    "problem_id": 1576,
-    "problem": "line A B, \\odot A lieson B H G, line A B, \\odot A lieson B H G\nWhat is the length of diameter?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1576.jpg"
-  },
-  {
-    "id": 1617,
-    "problem_id": 1577,
-    "problem": "line A B, \\odot A lieson B H G, line A B, \\odot A lieson B H G\nWhat is the length of diameter?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1577.jpg"
-  },
-  {
-    "id": 1618,
-    "problem_id": 1578,
-    "problem": "line A D, line D E, line B E, line B A, line A C E, line B C D, line A D, line D E, line B E, line B A, line A C E, line B C D\nSolve for the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1578.jpg"
-  },
-  {
-    "id": 1619,
-    "problem_id": 1579,
-    "problem": "line A D, line D E, line B E, line B A, line A C E, line B C D, line A D, line D E, line B E, line B A, line A C E, line B C D\nSolve for the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1579.jpg"
-  },
-  {
-    "id": 1620,
-    "problem_id": 1580,
-    "problem": "line A D, line D E, line B E, line B A, line A C E, line B C D, line A D, line D E, line B E, line B A, line A C E, line B C D\nSolve for the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1580.jpg"
-  },
-  {
-    "id": 1621,
-    "problem_id": 1581,
-    "problem": "line A D, line D E, line B E, line B A, line A C E, line B C D, line A D, line D E, line B E, line B A, line A C E, line B C D\nSolve for the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1581.jpg"
-  },
-  {
-    "id": 1622,
-    "problem_id": 1582,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1582.jpg"
-  },
-  {
-    "id": 1623,
-    "problem_id": 1583,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1583.jpg"
-  },
-  {
-    "id": 1624,
-    "problem_id": 1584,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1584.jpg"
-  },
-  {
-    "id": 1625,
-    "problem_id": 1585,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1585.jpg"
-  },
-  {
-    "id": 1626,
-    "problem_id": 1586,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1586.jpg"
-  },
-  {
-    "id": 1627,
-    "problem_id": 1587,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1587.jpg"
-  },
-  {
-    "id": 1628,
-    "problem_id": 1588,
-    "problem": "line U S, line A S B, \\odot C lieson U T S, line U S, line A S B, \\odot C lieson U T S\nFind m \\widehat US.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1588.jpg"
-  },
-  {
-    "id": 1629,
-    "problem_id": 1589,
-    "problem": "line U S, line A S B, \\odot C lieson U T S, line U S, line A S B, \\odot C lieson U T S\nFind m \\widehat US.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1589.jpg"
-  },
-  {
-    "id": 1630,
-    "problem_id": 1590,
-    "problem": "line U S, line A S B, \\odot C lieson U T S, line U S, line A S B, \\odot C lieson U T S\nFind m \\widehat US.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1590.jpg"
-  },
-  {
-    "id": 1631,
-    "problem_id": 1591,
-    "problem": "line B A, line B C, \\odot D lieson B A C, line B A, line B C, \\odot D lieson B A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1591.jpg"
-  },
-  {
-    "id": 1632,
-    "problem_id": 1592,
-    "problem": "line B A, line B C, \\odot D lieson B A C, line B A, line B C, \\odot D lieson B A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1592.jpg"
-  },
-  {
-    "id": 1633,
-    "problem_id": 1593,
-    "problem": "line B A, line B C, \\odot D lieson B A C, line B A, line B C, \\odot D lieson B A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1593.jpg"
-  },
-  {
-    "id": 1634,
-    "problem_id": 1594,
-    "problem": "line B Z E, line C Y Z D, line A W Y F, line B Z E, line C Y Z D, line A W Y F\nFind m \\angle WYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1594.jpg"
-  },
-  {
-    "id": 1635,
-    "problem_id": 1595,
-    "problem": "line K L M, line K L M\nIf LM = 35, find the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1595.jpg"
-  },
-  {
-    "id": 1636,
-    "problem_id": 1596,
-    "problem": "line K L M, line K L M\nIf LM = 35, find the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1596.jpg"
-  },
-  {
-    "id": 1637,
-    "problem_id": 1597,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1597.jpg"
-  },
-  {
-    "id": 1638,
-    "problem_id": 1598,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1598.jpg"
-  },
-  {
-    "id": 1639,
-    "problem_id": 1599,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1599.jpg"
-  },
-  {
-    "id": 1640,
-    "problem_id": 1600,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1600.jpg"
-  },
-  {
-    "id": 1641,
-    "problem_id": 1601,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1601.jpg"
-  },
-  {
-    "id": 1642,
-    "problem_id": 1602,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1602.jpg"
-  },
-  {
-    "id": 1643,
-    "problem_id": 1603,
-    "problem": "line A C F, line B C D, \\odot E lieson A B F D, line A C F, line B C D, \\odot E lieson A B F D\nFind the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1603.jpg"
-  },
-  {
-    "id": 1644,
-    "problem_id": 1604,
-    "problem": "line A C F, line B C D, \\odot E lieson A B F D, line A C F, line B C D, \\odot E lieson A B F D\nFind the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1604.jpg"
-  },
-  {
-    "id": 1645,
-    "problem_id": 1605,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1605.jpg"
-  },
-  {
-    "id": 1646,
-    "problem_id": 1606,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1606.jpg"
-  },
-  {
-    "id": 1647,
-    "problem_id": 1607,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1607.jpg"
-  },
-  {
-    "id": 1648,
-    "problem_id": 1608,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1608.jpg"
-  },
-  {
-    "id": 1649,
-    "problem_id": 1609,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1609.jpg"
-  },
-  {
-    "id": 1650,
-    "problem_id": 1610,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1610.jpg"
-  },
-  {
-    "id": 1651,
-    "problem_id": 1611,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle EJG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1611.jpg"
-  },
-  {
-    "id": 1652,
-    "problem_id": 1612,
-    "problem": "line E B D, line A B C F, \\odot C lieson E A D F, line E B D, line A B C F, \\odot C lieson E A D F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1612.jpg"
-  },
-  {
-    "id": 1653,
-    "problem_id": 1613,
-    "problem": "line E B D, line A B C F, \\odot C lieson E A D F, line E B D, line A B C F, \\odot C lieson E A D F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1613.jpg"
-  },
-  {
-    "id": 1654,
-    "problem_id": 1614,
-    "problem": "line E B D, line A B C F, \\odot C lieson E A D F, line E B D, line A B C F, \\odot C lieson E A D F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1614.jpg"
-  },
-  {
-    "id": 1655,
-    "problem_id": 1615,
-    "problem": "line C B, line C D, \\odot C lieson D B, line C B, line C D, \\odot C lieson D B\nWhat is the length of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1615.jpg"
-  },
-  {
-    "id": 1656,
-    "problem_id": 1616,
-    "problem": "line C B, line C D, \\odot C lieson D B, line C B, line C D, \\odot C lieson D B\nWhat is the length of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1616.jpg"
-  },
-  {
-    "id": 1657,
-    "problem_id": 1617,
-    "problem": "line C B, line C D, \\odot C lieson D B, line C B, line C D, \\odot C lieson D B\nWhat is the length of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1617.jpg"
-  },
-  {
-    "id": 1658,
-    "problem_id": 1618,
-    "problem": "line C B, line C D, \\odot C lieson D B, line C B, line C D, \\odot C lieson D B\nWhat is the length of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1618.jpg"
-  },
-  {
-    "id": 1659,
-    "problem_id": 1619,
-    "problem": "line C B, line C D, \\odot C lieson D B, line C B, line C D, \\odot C lieson D B\nWhat is the length of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1619.jpg"
-  },
-  {
-    "id": 1660,
-    "problem_id": 1620,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1620.jpg"
-  },
-  {
-    "id": 1661,
-    "problem_id": 1621,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1621.jpg"
-  },
-  {
-    "id": 1662,
-    "problem_id": 1622,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1622.jpg"
-  },
-  {
-    "id": 1663,
-    "problem_id": 1623,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1623.jpg"
-  },
-  {
-    "id": 1664,
-    "problem_id": 1624,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1624.jpg"
-  },
-  {
-    "id": 1665,
-    "problem_id": 1625,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1625.jpg"
-  },
-  {
-    "id": 1666,
-    "problem_id": 1626,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 10?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1626.jpg"
-  },
-  {
-    "id": 1667,
-    "problem_id": 1627,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1627.jpg"
-  },
-  {
-    "id": 1668,
-    "problem_id": 1628,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1628.jpg"
-  },
-  {
-    "id": 1669,
-    "problem_id": 1629,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1629.jpg"
-  },
-  {
-    "id": 1670,
-    "problem_id": 1630,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1630.jpg"
-  },
-  {
-    "id": 1671,
-    "problem_id": 1631,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1631.jpg"
-  },
-  {
-    "id": 1672,
-    "problem_id": 1632,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1632.jpg"
-  },
-  {
-    "id": 1673,
-    "problem_id": 1633,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle BAC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1633.jpg"
-  },
-  {
-    "id": 1674,
-    "problem_id": 1634,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle BAC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1634.jpg"
-  },
-  {
-    "id": 1675,
-    "problem_id": 1635,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle BAC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1635.jpg"
-  },
-  {
-    "id": 1676,
-    "problem_id": 1636,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle BAC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1636.jpg"
-  },
-  {
-    "id": 1677,
-    "problem_id": 1637,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle BAC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1637.jpg"
-  },
-  {
-    "id": 1678,
-    "problem_id": 1638,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle BAC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1638.jpg"
-  },
-  {
-    "id": 1679,
-    "problem_id": 1639,
-    "problem": "line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B, line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B\nFind the perimeter of the inscribed regular polygon shown.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1639.jpg"
-  },
-  {
-    "id": 1680,
-    "problem_id": 1640,
-    "problem": "line W Z, line T Z, line R T, line W R, \\odot A lieson W Z T R, line W Z, line T Z, line R T, line W R, \\odot A lieson W Z T R\nFind the measure of \\widehat WZT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1640.jpg"
-  },
-  {
-    "id": 1681,
-    "problem_id": 1641,
-    "problem": "line W Z, line T Z, line R T, line W R, \\odot A lieson W Z T R, line W Z, line T Z, line R T, line W R, \\odot A lieson W Z T R\nFind the measure of \\widehat WZT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1641.jpg"
-  },
-  {
-    "id": 1682,
-    "problem_id": 1642,
-    "problem": "line W Z, line T Z, line R T, line W R, \\odot A lieson W Z T R, line W Z, line T Z, line R T, line W R, \\odot A lieson W Z T R\nFind the measure of \\widehat WZT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1642.jpg"
-  },
-  {
-    "id": 1683,
-    "problem_id": 1643,
-    "problem": "line B A, line B C, line A D, line C E D, \\odot E lieson D C, line B A, line B C, line A D, line C E D, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1643.jpg"
-  },
-  {
-    "id": 1684,
-    "problem_id": 1644,
-    "problem": "line B A, line B C, line A D, line C E D, \\odot E lieson D C, line B A, line B C, line A D, line C E D, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1644.jpg"
-  },
-  {
-    "id": 1685,
-    "problem_id": 1645,
-    "problem": "line B A, line B C, line A D, line C E D, \\odot E lieson D C, line B A, line B C, line A D, line C E D, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1645.jpg"
-  },
-  {
-    "id": 1686,
-    "problem_id": 1646,
-    "problem": "line B A, line B C, line A D, line C E D, \\odot E lieson D C, line B A, line B C, line A D, line C E D, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1646.jpg"
-  },
-  {
-    "id": 1687,
-    "problem_id": 1647,
-    "problem": "line Q T, line T S, line P T R, \\odot T lieson P S R Q, line Q T, line T S, line P T R, \\odot T lieson P S R Q\nWhat is the measure of \\widehat RS in \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1647.jpg"
-  },
-  {
-    "id": 1688,
-    "problem_id": 1648,
-    "problem": "line Y B, line Y X, line B X, line Y B, line Y X, line B X\nSolve for m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1648.jpg"
-  },
-  {
-    "id": 1690,
-    "problem_id": 1649,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1649.jpg"
-  },
-  {
-    "id": 1691,
-    "problem_id": 1650,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1650.jpg"
-  },
-  {
-    "id": 1692,
-    "problem_id": 1651,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1651.jpg"
-  },
-  {
-    "id": 1693,
-    "problem_id": 1652,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1652.jpg"
-  },
-  {
-    "id": 1694,
-    "problem_id": 1653,
-    "problem": "line A B, line E D B, line A C E, line C D, line A B, line E D B, line A C E, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1653.jpg"
-  },
-  {
-    "id": 1695,
-    "problem_id": 1654,
-    "problem": "line A B, line E D B, line A C E, line C D, line A B, line E D B, line A C E, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1654.jpg"
-  },
-  {
-    "id": 1697,
-    "problem_id": 1655,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1655.jpg"
-  },
-  {
-    "id": 1698,
-    "problem_id": 1656,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1656.jpg"
-  },
-  {
-    "id": 1699,
-    "problem_id": 1657,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1657.jpg"
-  },
-  {
-    "id": 1700,
-    "problem_id": 1658,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1658.jpg"
-  },
-  {
-    "id": 1701,
-    "problem_id": 1659,
-    "problem": "line A B, line D A, line D C, line C B, line A B, line D A, line D C, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1659.jpg"
-  },
-  {
-    "id": 1702,
-    "problem_id": 1660,
-    "problem": "line A B, line D A, line D C, line C B, line A B, line D A, line D C, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1660.jpg"
-  },
-  {
-    "id": 1704,
-    "problem_id": 1661,
-    "problem": "line A B C, line D C E, line G E F, line B G H, line A B C, line D C E, line G E F, line B G H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1661.jpg"
-  },
-  {
-    "id": 1705,
-    "problem_id": 1662,
-    "problem": "line A B C, line D C E, line G E F, line B G H, line A B C, line D C E, line G E F, line B G H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1662.jpg"
-  },
-  {
-    "id": 1706,
-    "problem_id": 1663,
-    "problem": "line A B C, line D C E, line G E F, line B G H, line A B C, line D C E, line G E F, line B G H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1663.jpg"
-  },
-  {
-    "id": 1707,
-    "problem_id": 1664,
-    "problem": "line A B C, line D C E, line G E F, line B G H, line A B C, line D C E, line G E F, line B G H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1664.jpg"
-  },
-  {
-    "id": 1708,
-    "problem_id": 1665,
-    "problem": "line A B C, line D C E, line G E F, line B G H, line A B C, line D C E, line G E F, line B G H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1665.jpg"
-  },
-  {
-    "id": 1709,
-    "problem_id": 1666,
-    "problem": "line X Y, line W X, line W P Y, line W Z, line Y Z, line X P Z, line X Y, line W X, line W P Y, line W Z, line Y Z, line X P Z\nIf WXYZ is a kite, find WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1666.jpg"
-  },
-  {
-    "id": 1710,
-    "problem_id": 1667,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind MN if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1667.jpg"
-  },
-  {
-    "id": 1711,
-    "problem_id": 1668,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind MN if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1668.jpg"
-  },
-  {
-    "id": 1712,
-    "problem_id": 1669,
-    "problem": "line A C D, line E D, line C E, line A B E, line C B, line A C D, line E D, line C E, line A B E, line C B\nIf EC is an altitude of \\triangle AED, m \\angle 1 = 2x+7, and m \\angle 2 = 3x+13, find m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1669.jpg"
-  },
-  {
-    "id": 1713,
-    "problem_id": 1670,
-    "problem": "line V U T, line R S T, line P W V, line P Q R, \\odot Z lieson W U S Q, line V U T, line R S T, line P W V, line P Q R, \\odot Z lieson W U S Q\nFind VU. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1670.jpg"
-  },
-  {
-    "id": 1714,
-    "problem_id": 1671,
-    "problem": "line A E, line D E, line A C D, line B C E, line B A, line A E, line D E, line A C D, line B C E, line B A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1671.jpg"
-  },
-  {
-    "id": 1715,
-    "problem_id": 1672,
-    "problem": "line A E, line D E, line A C D, line B C E, line B A, line A E, line D E, line A C D, line B C E, line B A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1672.jpg"
-  },
-  {
-    "id": 1716,
-    "problem_id": 1673,
-    "problem": "line A E, line D E, line A C D, line B C E, line B A, line A E, line D E, line A C D, line B C E, line B A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1673.jpg"
-  },
-  {
-    "id": 1717,
-    "problem_id": 1674,
-    "problem": "line A E, line D E, line A C D, line B C E, line B A, line A E, line D E, line A C D, line B C E, line B A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1674.jpg"
-  },
-  {
-    "id": 1718,
-    "problem_id": 1675,
-    "problem": "line A B, line B C, \\odot B lieson C A, line A B, line B C, \\odot B lieson C A\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1675.jpg"
-  },
-  {
-    "id": 1719,
-    "problem_id": 1676,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1676.jpg"
-  },
-  {
-    "id": 1720,
-    "problem_id": 1677,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1677.jpg"
-  },
-  {
-    "id": 1721,
-    "problem_id": 1678,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nW is the midpoint of XY. Solve for the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1678.jpg"
-  },
-  {
-    "id": 1722,
-    "problem_id": 1679,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nW is the midpoint of XY. Solve for the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1679.jpg"
-  },
-  {
-    "id": 1723,
-    "problem_id": 1680,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nW is the midpoint of XY. Solve for the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1680.jpg"
-  },
-  {
-    "id": 1724,
-    "problem_id": 1681,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nW is the midpoint of XY. Solve for the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1681.jpg"
-  },
-  {
-    "id": 1725,
-    "problem_id": 1682,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nW is the midpoint of XY. Solve for the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1682.jpg"
-  },
-  {
-    "id": 1726,
-    "problem_id": 1683,
-    "problem": "line Q U R V, line P A R, line T V, line P Q, line T A U, line Q U R V, line P A R, line T V, line P Q, line T A U\nWhat is the length of TU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1683.jpg"
-  },
-  {
-    "id": 1727,
-    "problem_id": 1684,
-    "problem": "line Q U R V, line P A R, line T V, line P Q, line T A U, line Q U R V, line P A R, line T V, line P Q, line T A U\nWhat is the length of TU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1684.jpg"
-  },
-  {
-    "id": 1728,
-    "problem_id": 1685,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the measure of \\angle 1 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1685.jpg"
-  },
-  {
-    "id": 1729,
-    "problem_id": 1686,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the measure of \\angle 1 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1686.jpg"
-  },
-  {
-    "id": 1730,
-    "problem_id": 1687,
-    "problem": "line A B, line B D, line A C D, \\odot D lieson C B, line A B, line B D, line A C D, \\odot D lieson C B\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1687.jpg"
-  },
-  {
-    "id": 1731,
-    "problem_id": 1688,
-    "problem": "line A B, line B D, line A C D, \\odot D lieson C B, line A B, line B D, line A C D, \\odot D lieson C B\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1688.jpg"
-  },
-  {
-    "id": 1732,
-    "problem_id": 1689,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PM in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1689.jpg"
-  },
-  {
-    "id": 1733,
-    "problem_id": 1690,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PM in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1690.jpg"
-  },
-  {
-    "id": 1734,
-    "problem_id": 1691,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PM in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1691.jpg"
-  },
-  {
-    "id": 1735,
-    "problem_id": 1692,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PM in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1692.jpg"
-  },
-  {
-    "id": 1736,
-    "problem_id": 1693,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nFind m \\angle BGF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1693.jpg"
-  },
-  {
-    "id": 1737,
-    "problem_id": 1694,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nFind m \\angle BGF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1694.jpg"
-  },
-  {
-    "id": 1738,
-    "problem_id": 1695,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nFind m \\angle BGF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1695.jpg"
-  },
-  {
-    "id": 1739,
-    "problem_id": 1696,
-    "problem": "line C A, line A B, line B E, line D E, line C D, line C A, line A B, line B E, line D E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1696.jpg"
-  },
-  {
-    "id": 1740,
-    "problem_id": 1697,
-    "problem": "line C A, line A B, line B E, line D E, line C D, line C A, line A B, line B E, line D E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1697.jpg"
-  },
-  {
-    "id": 1741,
-    "problem_id": 1698,
-    "problem": "line C A, line A B, line B E, line D E, line C D, line C A, line A B, line B E, line D E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1698.jpg"
-  },
-  {
-    "id": 1742,
-    "problem_id": 1699,
-    "problem": "line C A, line A B, line B E, line D E, line C D, line C A, line A B, line B E, line D E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1699.jpg"
-  },
-  {
-    "id": 1743,
-    "problem_id": 1700,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1700.jpg"
-  },
-  {
-    "id": 1744,
-    "problem_id": 1701,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1701.jpg"
-  },
-  {
-    "id": 1745,
-    "problem_id": 1702,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1702.jpg"
-  },
-  {
-    "id": 1746,
-    "problem_id": 1703,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1703.jpg"
-  },
-  {
-    "id": 1747,
-    "problem_id": 1704,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1704.jpg"
-  },
-  {
-    "id": 1748,
-    "problem_id": 1705,
-    "problem": "line B C D, line E D, line A D, line A C E, line B E, line A B, line B C D, line E D, line A D, line A C E, line B E, line A B\nWhat is the area of the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1705.jpg"
-  },
-  {
-    "id": 1749,
-    "problem_id": 1706,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1706.jpg"
-  },
-  {
-    "id": 1750,
-    "problem_id": 1707,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1707.jpg"
-  },
-  {
-    "id": 1751,
-    "problem_id": 1708,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1708.jpg"
-  },
-  {
-    "id": 1752,
-    "problem_id": 1709,
-    "problem": "line B C, line D C, line A D, line A B, line B C, line D C, line A D, line A B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1709.jpg"
-  },
-  {
-    "id": 1753,
-    "problem_id": 1710,
-    "problem": "line B C, line D C, line A D, line A B, line B C, line D C, line A D, line A B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1710.jpg"
-  },
-  {
-    "id": 1754,
-    "problem_id": 1711,
-    "problem": "line C D, line A D, line B E D, line B A, line B C, line A E C, line C D, line A D, line B E D, line B A, line B C, line A E C\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1711.jpg"
-  },
-  {
-    "id": 1755,
-    "problem_id": 1712,
-    "problem": "line C D, line A D, line B E D, line B A, line B C, line A E C, line C D, line A D, line B E D, line B A, line B C, line A E C\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1712.jpg"
-  },
-  {
-    "id": 1756,
-    "problem_id": 1713,
-    "problem": "line C D, line A D, line B E D, line B A, line B C, line A E C, line C D, line A D, line B E D, line B A, line B C, line A E C\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1713.jpg"
-  },
-  {
-    "id": 1757,
-    "problem_id": 1714,
-    "problem": "line C D, line A D, line B E D, line B A, line B C, line A E C, line C D, line A D, line B E D, line B A, line B C, line A E C\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1714.jpg"
-  },
-  {
-    "id": 1758,
-    "problem_id": 1715,
-    "problem": "line A O D, line A B C, line O B, \\odot O lieson D C A, line A O D, line A B C, line O B, \\odot O lieson D C A\nFind the exact circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1715.jpg"
-  },
-  {
-    "id": 1759,
-    "problem_id": 1716,
-    "problem": "line A O D, line A B C, line O B, \\odot O lieson D C A, line A O D, line A B C, line O B, \\odot O lieson D C A\nFind the exact circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1716.jpg"
-  },
-  {
-    "id": 1760,
-    "problem_id": 1717,
-    "problem": "line A O D, line A B C, line O B, \\odot O lieson D C A, line A O D, line A B C, line O B, \\odot O lieson D C A\nFind the exact circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1717.jpg"
-  },
-  {
-    "id": 1761,
-    "problem_id": 1718,
-    "problem": "line A O D, line A B C, line O B, \\odot O lieson D C A, line A O D, line A B C, line O B, \\odot O lieson D C A\nFind the exact circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1718.jpg"
-  },
-  {
-    "id": 1762,
-    "problem_id": 1719,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1719.jpg"
-  },
-  {
-    "id": 1763,
-    "problem_id": 1720,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1720.jpg"
-  },
-  {
-    "id": 1764,
-    "problem_id": 1721,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1721.jpg"
-  },
-  {
-    "id": 1765,
-    "problem_id": 1722,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1722.jpg"
-  },
-  {
-    "id": 1766,
-    "problem_id": 1723,
-    "problem": "line M A P, line M N, line P N, line L P, line L M, line L A N, line M A P, line M N, line P N, line L P, line L M, line L A N\nQuadrilateral LMNP is a parallelogram. Find d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1723.jpg"
-  },
-  {
-    "id": 1767,
-    "problem_id": 1724,
-    "problem": "line M A P, line M N, line P N, line L P, line L M, line L A N, line M A P, line M N, line P N, line L P, line L M, line L A N\nQuadrilateral LMNP is a parallelogram. Find d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1724.jpg"
-  },
-  {
-    "id": 1768,
-    "problem_id": 1725,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1725.jpg"
-  },
-  {
-    "id": 1769,
-    "problem_id": 1726,
-    "problem": "line G A E B, line D E F, line B C H, \\odot I lieson A F B D, line G A E B, line D E F, line B C H, \\odot I lieson A F B D\nFind m \\widehat FA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1726.jpg"
-  },
-  {
-    "id": 1770,
-    "problem_id": 1727,
-    "problem": "line A B, line D E F, line A D, line B F, line C E, line A B, line D E F, line A D, line B F, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1727.jpg"
-  },
-  {
-    "id": 1771,
-    "problem_id": 1728,
-    "problem": "line A B, line D E F, line A D, line B F, line C E, line A B, line D E F, line A D, line B F, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1728.jpg"
-  },
-  {
-    "id": 1772,
-    "problem_id": 1729,
-    "problem": "line A B, line D E F, line A D, line B F, line C E, line A B, line D E F, line A D, line B F, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1729.jpg"
-  },
-  {
-    "id": 1773,
-    "problem_id": 1730,
-    "problem": "line A B, line D E F, line A D, line B F, line C E, line A B, line D E F, line A D, line B F, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1730.jpg"
-  },
-  {
-    "id": 1774,
-    "problem_id": 1731,
-    "problem": "line B A, line A C, line B D, line D C, line A D, line B A, line A C, line B D, line D C, line A D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1731.jpg"
-  },
-  {
-    "id": 1775,
-    "problem_id": 1732,
-    "problem": "line B A, line A C, line B D, line D C, line A D, line B A, line A C, line B D, line D C, line A D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1732.jpg"
-  },
-  {
-    "id": 1776,
-    "problem_id": 1733,
-    "problem": "line B A, line A C, line B D, line D C, line A D, line B A, line A C, line B D, line D C, line A D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1733.jpg"
-  },
-  {
-    "id": 1777,
-    "problem_id": 1734,
-    "problem": "line B A, line A C, line B D, line D C, line A D, line B A, line A C, line B D, line D C, line A D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1734.jpg"
-  },
-  {
-    "id": 1778,
-    "problem_id": 1735,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1735.jpg"
-  },
-  {
-    "id": 1779,
-    "problem_id": 1736,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1736.jpg"
-  },
-  {
-    "id": 1780,
-    "problem_id": 1737,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1737.jpg"
-  },
-  {
-    "id": 1781,
-    "problem_id": 1738,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1738.jpg"
-  },
-  {
-    "id": 1782,
-    "problem_id": 1739,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1739.jpg"
-  },
-  {
-    "id": 1783,
-    "problem_id": 1740,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1740.jpg"
-  },
-  {
-    "id": 1784,
-    "problem_id": 1741,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nWhat is the length of JL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1741.jpg"
-  },
-  {
-    "id": 1785,
-    "problem_id": 1742,
-    "problem": "line L H M, line K J L, line K P M, line P H, line J H, line J P, line L H M, line K J L, line K P M, line P H, line J H, line J P\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1742.jpg"
-  },
-  {
-    "id": 1786,
-    "problem_id": 1743,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1743.jpg"
-  },
-  {
-    "id": 1787,
-    "problem_id": 1744,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1744.jpg"
-  },
-  {
-    "id": 1788,
-    "problem_id": 1745,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1745.jpg"
-  },
-  {
-    "id": 1789,
-    "problem_id": 1746,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1746.jpg"
-  },
-  {
-    "id": 1790,
-    "problem_id": 1747,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1747.jpg"
-  },
-  {
-    "id": 1791,
-    "problem_id": 1748,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1748.jpg"
-  },
-  {
-    "id": 1792,
-    "problem_id": 1749,
-    "problem": "line H G, line E F, line E H, line F G, line H G, line E F, line E H, line F G\nEFGH is a rhombus. Find m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1749.jpg"
-  },
-  {
-    "id": 1793,
-    "problem_id": 1750,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1750.jpg"
-  },
-  {
-    "id": 1794,
-    "problem_id": 1751,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1751.jpg"
-  },
-  {
-    "id": 1795,
-    "problem_id": 1752,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1752.jpg"
-  },
-  {
-    "id": 1796,
-    "problem_id": 1753,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1753.jpg"
-  },
-  {
-    "id": 1797,
-    "problem_id": 1754,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1754.jpg"
-  },
-  {
-    "id": 1798,
-    "problem_id": 1755,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1755.jpg"
-  },
-  {
-    "id": 1799,
-    "problem_id": 1756,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1756.jpg"
-  },
-  {
-    "id": 1800,
-    "problem_id": 1757,
-    "problem": "line A B, line B C, \\odot B lieson A C, line A B, line B C, \\odot B lieson A C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1757.jpg"
-  },
-  {
-    "id": 1801,
-    "problem_id": 1758,
-    "problem": "line A B, line B C, \\odot B lieson A C, line A B, line B C, \\odot B lieson A C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1758.jpg"
-  },
-  {
-    "id": 1802,
-    "problem_id": 1759,
-    "problem": "line A B, line B C, \\odot B lieson A C, line A B, line B C, \\odot B lieson A C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1759.jpg"
-  },
-  {
-    "id": 1803,
-    "problem_id": 1760,
-    "problem": "line A B, line B C, \\odot B lieson A C, line A B, line B C, \\odot B lieson A C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1760.jpg"
-  },
-  {
-    "id": 1804,
-    "problem_id": 1761,
-    "problem": "line A B, line B C, \\odot B lieson A C, line A B, line B C, \\odot B lieson A C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1761.jpg"
-  },
-  {
-    "id": 1805,
-    "problem_id": 1762,
-    "problem": "line A D, line C D, \\odot B lieson C D A, line A D, line C D, \\odot B lieson C D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1762.jpg"
-  },
-  {
-    "id": 1806,
-    "problem_id": 1763,
-    "problem": "line A D, line C D, \\odot B lieson C D A, line A D, line C D, \\odot B lieson C D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1763.jpg"
-  },
-  {
-    "id": 1807,
-    "problem_id": 1764,
-    "problem": "line A D, line C D, \\odot B lieson C D A, line A D, line C D, \\odot B lieson C D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1764.jpg"
-  },
-  {
-    "id": 1808,
-    "problem_id": 1765,
-    "problem": "line D C, line E C, line B C, line A B, line A E, line D C, line E C, line B C, line A B, line A E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1765.jpg"
-  },
-  {
-    "id": 1809,
-    "problem_id": 1766,
-    "problem": "line H K, line K J, line H J, line H K, line K J, line H J\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1766.jpg"
-  },
-  {
-    "id": 1810,
-    "problem_id": 1767,
-    "problem": "line H K, line K J, line H J, line H K, line K J, line H J\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1767.jpg"
-  },
-  {
-    "id": 1811,
-    "problem_id": 1768,
-    "problem": "line H K, line K J, line H J, line H K, line K J, line H J\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1768.jpg"
-  },
-  {
-    "id": 1812,
-    "problem_id": 1769,
-    "problem": "line H K, line K J, line H J, line H K, line K J, line H J\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1769.jpg"
-  },
-  {
-    "id": 1813,
-    "problem_id": 1770,
-    "problem": "line H K, line K J, line H J, line H K, line K J, line H J\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1770.jpg"
-  },
-  {
-    "id": 1814,
-    "problem_id": 1771,
-    "problem": "line H K, line K J, line H J, line H K, line K J, line H J\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1771.jpg"
-  },
-  {
-    "id": 1815,
-    "problem_id": 1772,
-    "problem": "line R V, line S W V, line R W T, line T V, line S R, line S T, line R V, line S W V, line R W T, line T V, line S R, line S T\nRW = 17.7, and SV = 23.3. Find VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1772.jpg"
-  },
-  {
-    "id": 1816,
-    "problem_id": 1773,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1773.jpg"
-  },
-  {
-    "id": 1817,
-    "problem_id": 1774,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1774.jpg"
-  },
-  {
-    "id": 1818,
-    "problem_id": 1775,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1775.jpg"
-  },
-  {
-    "id": 1819,
-    "problem_id": 1776,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1776.jpg"
-  },
-  {
-    "id": 1820,
-    "problem_id": 1777,
-    "problem": "line Q T R, line P T S, \\odot P lieson R S Q, line Q T R, line P T S, \\odot P lieson R S Q\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1777.jpg"
-  },
-  {
-    "id": 1821,
-    "problem_id": 1778,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1778.jpg"
-  },
-  {
-    "id": 1822,
-    "problem_id": 1779,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1779.jpg"
-  },
-  {
-    "id": 1823,
-    "problem_id": 1780,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1780.jpg"
-  },
-  {
-    "id": 1824,
-    "problem_id": 1781,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1781.jpg"
-  },
-  {
-    "id": 1825,
-    "problem_id": 1782,
-    "problem": "line A C, line A E, line C D E, line C B, line B D, line A C, line A E, line C D E, line C B, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1782.jpg"
-  },
-  {
-    "id": 1826,
-    "problem_id": 1783,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AD = EF, EF = CF, find the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1783.jpg"
-  },
-  {
-    "id": 1827,
-    "problem_id": 1784,
-    "problem": "line D E F, line C F, line A B C, line A D, line D E F, line C F, line A B C, line A D\nIf AD = EF, EF = CF, find the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1784.jpg"
-  },
-  {
-    "id": 1828,
-    "problem_id": 1785,
-    "problem": "line A B, line D B, line D E, line B E, \\odot C lieson A D E B, line A B, line D B, line D E, line B E, \\odot C lieson A D E B\nFind the value of variable c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1785.jpg"
-  },
-  {
-    "id": 1829,
-    "problem_id": 1786,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1786.jpg"
-  },
-  {
-    "id": 1830,
-    "problem_id": 1787,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1787.jpg"
-  },
-  {
-    "id": 1831,
-    "problem_id": 1788,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1788.jpg"
-  },
-  {
-    "id": 1832,
-    "problem_id": 1789,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1789.jpg"
-  },
-  {
-    "id": 1833,
-    "problem_id": 1790,
-    "problem": "line A N, line M A, \\odot A lieson N M, line A N, line M A, \\odot A lieson N M\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1790.jpg"
-  },
-  {
-    "id": 1834,
-    "problem_id": 1791,
-    "problem": "line A N, line M A, \\odot A lieson N M, line A N, line M A, \\odot A lieson N M\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1791.jpg"
-  },
-  {
-    "id": 1835,
-    "problem_id": 1792,
-    "problem": "line A N, line M A, \\odot A lieson N M, line A N, line M A, \\odot A lieson N M\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1792.jpg"
-  },
-  {
-    "id": 1836,
-    "problem_id": 1793,
-    "problem": "line A N, line M A, \\odot A lieson N M, line A N, line M A, \\odot A lieson N M\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1793.jpg"
-  },
-  {
-    "id": 1837,
-    "problem_id": 1794,
-    "problem": "line A N, line M A, \\odot A lieson N M, line A N, line M A, \\odot A lieson N M\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1794.jpg"
-  },
-  {
-    "id": 1838,
-    "problem_id": 1795,
-    "problem": "line A N, line M A, \\odot A lieson N M, line A N, line M A, \\odot A lieson N M\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1795.jpg"
-  },
-  {
-    "id": 1839,
-    "problem_id": 1796,
-    "problem": "line S U, line U T, line S T, line R U, line R S, line S U, line U T, line S T, line R U, line R S\nFind ST in rectangle RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1796.jpg"
-  },
-  {
-    "id": 1840,
-    "problem_id": 1797,
-    "problem": "line S U, line U T, line S T, line R U, line R S, line S U, line U T, line S T, line R U, line R S\nFind ST in rectangle RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1797.jpg"
-  },
-  {
-    "id": 1841,
-    "problem_id": 1798,
-    "problem": "line S U, line U T, line S T, line R U, line R S, line S U, line U T, line S T, line R U, line R S\nFind ST in rectangle RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1798.jpg"
-  },
-  {
-    "id": 1842,
-    "problem_id": 1799,
-    "problem": "line S U, line U T, line S T, line R U, line R S, line S U, line U T, line S T, line R U, line R S\nFind ST in rectangle RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1799.jpg"
-  },
-  {
-    "id": 1843,
-    "problem_id": 1800,
-    "problem": "line A B, line D C B, \\odot E lieson A C D, line A B, line D C B, \\odot E lieson A C D\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1800.jpg"
-  },
-  {
-    "id": 1844,
-    "problem_id": 1801,
-    "problem": "line P M, line N M, line P N, line P M, line N M, line P N\nFind PN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1801.jpg"
-  },
-  {
-    "id": 1845,
-    "problem_id": 1802,
-    "problem": "line P M, line N M, line P N, line P M, line N M, line P N\nFind PN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1802.jpg"
-  },
-  {
-    "id": 1846,
-    "problem_id": 1803,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1803.jpg"
-  },
-  {
-    "id": 1847,
-    "problem_id": 1804,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1804.jpg"
-  },
-  {
-    "id": 1848,
-    "problem_id": 1805,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1805.jpg"
-  },
-  {
-    "id": 1849,
-    "problem_id": 1806,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1806.jpg"
-  },
-  {
-    "id": 1850,
-    "problem_id": 1807,
-    "problem": "line A F E, line E D, line C D, line F B C, line F D, line A B, line A F E, line E D, line C D, line F B C, line F D, line A B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1807.jpg"
-  },
-  {
-    "id": 1851,
-    "problem_id": 1808,
-    "problem": "line A F E, line E D, line C D, line F B C, line F D, line A B, line A F E, line E D, line C D, line F B C, line F D, line A B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1808.jpg"
-  },
-  {
-    "id": 1852,
-    "problem_id": 1809,
-    "problem": "line A F E, line E D, line C D, line F B C, line F D, line A B, line A F E, line E D, line C D, line F B C, line F D, line A B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1809.jpg"
-  },
-  {
-    "id": 1853,
-    "problem_id": 1810,
-    "problem": "line A F E, line E D, line C D, line F B C, line F D, line A B, line A F E, line E D, line C D, line F B C, line F D, line A B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1810.jpg"
-  },
-  {
-    "id": 1854,
-    "problem_id": 1811,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find the length of AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1811.jpg"
-  },
-  {
-    "id": 1855,
-    "problem_id": 1812,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find the length of AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1812.jpg"
-  },
-  {
-    "id": 1856,
-    "problem_id": 1813,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOB = 4x-2, m \\angle BOC = 5x+10, m \\angle COD = 3x-8. Find m \\angle DOE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1813.jpg"
-  },
-  {
-    "id": 1857,
-    "problem_id": 1814,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOB = 4x-2, m \\angle BOC = 5x+10, m \\angle COD = 3x-8. Find m \\angle DOE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1814.jpg"
-  },
-  {
-    "id": 1858,
-    "problem_id": 1815,
-    "problem": "line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E, line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E\nFind the area of a regular hexagon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1815.jpg"
-  },
-  {
-    "id": 1859,
-    "problem_id": 1816,
-    "problem": "line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E, line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E\nFind the area of a regular hexagon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1816.jpg"
-  },
-  {
-    "id": 1860,
-    "problem_id": 1817,
-    "problem": "line W X, line X Y, line Y Z, line W X, line X Y, line Y Z\nIf XY = WX, YZ = WX, find XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1817.jpg"
-  },
-  {
-    "id": 1861,
-    "problem_id": 1818,
-    "problem": "line W X, line X Y, line Y Z, line W X, line X Y, line Y Z\nIf XY = WX, YZ = WX, find XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1818.jpg"
-  },
-  {
-    "id": 1862,
-    "problem_id": 1819,
-    "problem": "line W X, line X Y, line Y Z, line W X, line X Y, line Y Z\nIf XY = WX, YZ = WX, find XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1819.jpg"
-  },
-  {
-    "id": 1863,
-    "problem_id": 1820,
-    "problem": "line F G H, line C E H, line A D F, line A B C, \\odot H lieson G E, \\odot C lieson B E, \\odot A lieson D B, \\odot F lieson D G, line F G H, line C E H, line A D F, line A B C, \\odot H lieson G E, \\odot C lieson B E, \\odot A lieson D B, \\odot F lieson D G\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1820.jpg"
-  },
-  {
-    "id": 1864,
-    "problem_id": 1821,
-    "problem": "line F G H, line C E H, line A D F, line A B C, \\odot H lieson G E, \\odot C lieson B E, \\odot A lieson D B, \\odot F lieson D G, line F G H, line C E H, line A D F, line A B C, \\odot H lieson G E, \\odot C lieson B E, \\odot A lieson D B, \\odot F lieson D G\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1821.jpg"
-  },
-  {
-    "id": 1865,
-    "problem_id": 1822,
-    "problem": "line H C N, line M N, line M H, line M C, line A B M, line S B E, \\odot M lieson S H N E A, line H C N, line M N, line M H, line M C, line A B M, line S B E, \\odot M lieson S H N E A\nFind m \\angle MNH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1822.jpg"
-  },
-  {
-    "id": 1866,
-    "problem_id": 1823,
-    "problem": "line A C, line C D, line A B D, line C B, line A C, line C D, line A B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1823.jpg"
-  },
-  {
-    "id": 1867,
-    "problem_id": 1824,
-    "problem": "line A C, line C D, line A B D, line C B, line A C, line C D, line A B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1824.jpg"
-  },
-  {
-    "id": 1868,
-    "problem_id": 1825,
-    "problem": "line A C, line C D, line A B D, line C B, line A C, line C D, line A B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1825.jpg"
-  },
-  {
-    "id": 1869,
-    "problem_id": 1826,
-    "problem": "line A C, line C D, line A B D, line C B, line A C, line C D, line A B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1826.jpg"
-  },
-  {
-    "id": 1870,
-    "problem_id": 1827,
-    "problem": "line E F, line C D, line B D F, line A C E, line A B, line E F, line C D, line B D F, line A C E, line A B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1827.jpg"
-  },
-  {
-    "id": 1872,
-    "problem_id": 1828,
-    "problem": "line E F, line C D, line B D F, line A C E, line A B, line E F, line C D, line B D F, line A C E, line A B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1828.jpg"
-  },
-  {
-    "id": 1873,
-    "problem_id": 1829,
-    "problem": "line C D B, line A D E, line C D B, line A D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1829.jpg"
-  },
-  {
-    "id": 1874,
-    "problem_id": 1830,
-    "problem": "line C D B, line A D E, line C D B, line A D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1830.jpg"
-  },
-  {
-    "id": 1875,
-    "problem_id": 1831,
-    "problem": "line A B, line D B, line D C A, \\odot C lieson A B D, line A B, line D B, line D C A, \\odot C lieson A B D\nThe triangle is inscribed into the circle. Find the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1831.jpg"
-  },
-  {
-    "id": 1876,
-    "problem_id": 1832,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nWhat is the area of the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1832.jpg"
-  },
-  {
-    "id": 1877,
-    "problem_id": 1833,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nWhat is the area of the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1833.jpg"
-  },
-  {
-    "id": 1878,
-    "problem_id": 1834,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nWhat is the area of the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1834.jpg"
-  },
-  {
-    "id": 1879,
-    "problem_id": 1835,
-    "problem": "line D B, line C B, line A B, line D A, line D C, line D B, line C B, line A B, line D A, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1835.jpg"
-  },
-  {
-    "id": 1880,
-    "problem_id": 1836,
-    "problem": "line D B, line C B, line A B, line D A, line D C, line D B, line C B, line A B, line D A, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1836.jpg"
-  },
-  {
-    "id": 1881,
-    "problem_id": 1837,
-    "problem": "line D B, line C B, line A B, line D A, line D C, line D B, line C B, line A B, line D A, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1837.jpg"
-  },
-  {
-    "id": 1882,
-    "problem_id": 1838,
-    "problem": "line D B, line C B, line A B, line D A, line D C, line D B, line C B, line A B, line D A, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1838.jpg"
-  },
-  {
-    "id": 1883,
-    "problem_id": 1839,
-    "problem": "line D B, line C B, line A B, line D A, line D C, line D B, line C B, line A B, line D A, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1839.jpg"
-  },
-  {
-    "id": 1884,
-    "problem_id": 1840,
-    "problem": "line M C F N, line H D E F O, line I A D J, line G A B C P, line K B E L, line M C F N, line H D E F O, line I A D J, line G A B C P, line K B E L\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1840.jpg"
-  },
-  {
-    "id": 1885,
-    "problem_id": 1841,
-    "problem": "line M C F N, line H D E F O, line I A D J, line G A B C P, line K B E L, line M C F N, line H D E F O, line I A D J, line G A B C P, line K B E L\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1841.jpg"
-  },
-  {
-    "id": 1886,
-    "problem_id": 1842,
-    "problem": "line M C F N, line H D E F O, line I A D J, line G A B C P, line K B E L, line M C F N, line H D E F O, line I A D J, line G A B C P, line K B E L\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1842.jpg"
-  },
-  {
-    "id": 1887,
-    "problem_id": 1843,
-    "problem": "line B A, \\odot B lieson P Q A, line B A, \\odot B lieson P Q A\nWhat is the length of \\widehat QP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1843.jpg"
-  },
-  {
-    "id": 1888,
-    "problem_id": 1844,
-    "problem": "line B A, \\odot B lieson P Q A, line B A, \\odot B lieson P Q A\nWhat is the length of \\widehat QP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1844.jpg"
-  },
-  {
-    "id": 1889,
-    "problem_id": 1845,
-    "problem": "line B A, \\odot B lieson P Q A, line B A, \\odot B lieson P Q A\nWhat is the length of \\widehat QP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1845.jpg"
-  },
-  {
-    "id": 1890,
-    "problem_id": 1846,
-    "problem": "line A E, line B A, line B D, \\odot C lieson E D, line A E, line B A, line B D, \\odot C lieson E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1846.jpg"
-  },
-  {
-    "id": 1891,
-    "problem_id": 1847,
-    "problem": "line A E, line B A, line B D, \\odot C lieson E D, line A E, line B A, line B D, \\odot C lieson E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1847.jpg"
-  },
-  {
-    "id": 1892,
-    "problem_id": 1848,
-    "problem": "line A E, line B A, line B D, \\odot C lieson E D, line A E, line B A, line B D, \\odot C lieson E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1848.jpg"
-  },
-  {
-    "id": 1893,
-    "problem_id": 1849,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1849.jpg"
-  },
-  {
-    "id": 1894,
-    "problem_id": 1850,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1850.jpg"
-  },
-  {
-    "id": 1895,
-    "problem_id": 1851,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1851.jpg"
-  },
-  {
-    "id": 1896,
-    "problem_id": 1852,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1852.jpg"
-  },
-  {
-    "id": 1897,
-    "problem_id": 1853,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1853.jpg"
-  },
-  {
-    "id": 1898,
-    "problem_id": 1854,
-    "problem": "line K R, line M N, line J T, line K M J, line R N T, line K R, line M N, line J T, line K M J, line R N T\nFind KR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1854.jpg"
-  },
-  {
-    "id": 1899,
-    "problem_id": 1855,
-    "problem": "line K R, line M N, line J T, line K M J, line R N T, line K R, line M N, line J T, line K M J, line R N T\nFind KR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1855.jpg"
-  },
-  {
-    "id": 1900,
-    "problem_id": 1856,
-    "problem": "line K R, line M N, line J T, line K M J, line R N T, line K R, line M N, line J T, line K M J, line R N T\nFind KR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1856.jpg"
-  },
-  {
-    "id": 1901,
-    "problem_id": 1857,
-    "problem": "line K R, line M N, line J T, line K M J, line R N T, line K R, line M N, line J T, line K M J, line R N T\nFind KR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1857.jpg"
-  },
-  {
-    "id": 1902,
-    "problem_id": 1858,
-    "problem": "line K R, line M N, line J T, line K M J, line R N T, line K R, line M N, line J T, line K M J, line R N T\nFind KR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1858.jpg"
-  },
-  {
-    "id": 1903,
-    "problem_id": 1859,
-    "problem": "line X Z V, line U V, line X Y U, line Y Z, line X Z V, line U V, line X Y U, line Y Z\nFind the length of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1859.jpg"
-  },
-  {
-    "id": 1904,
-    "problem_id": 1860,
-    "problem": "line X Z V, line U V, line X Y U, line Y Z, line X Z V, line U V, line X Y U, line Y Z\nFind the length of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1860.jpg"
-  },
-  {
-    "id": 1905,
-    "problem_id": 1861,
-    "problem": "line X Z V, line U V, line X Y U, line Y Z, line X Z V, line U V, line X Y U, line Y Z\nFind the length of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1861.jpg"
-  },
-  {
-    "id": 1906,
-    "problem_id": 1862,
-    "problem": "line X Z V, line U V, line X Y U, line Y Z, line X Z V, line U V, line X Y U, line Y Z\nFind the length of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1862.jpg"
-  },
-  {
-    "id": 1907,
-    "problem_id": 1863,
-    "problem": "line R V, line V U T, line R S T, line S U, line R V, line V U T, line R S T, line S U\nFind the length of SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1863.jpg"
-  },
-  {
-    "id": 1908,
-    "problem_id": 1864,
-    "problem": "line R V, line V U T, line R S T, line S U, line R V, line V U T, line R S T, line S U\nFind the length of SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1864.jpg"
-  },
-  {
-    "id": 1909,
-    "problem_id": 1865,
-    "problem": "line C A, line B A, line C B, \\odot B lieson C A, line C A, line B A, line C B, \\odot B lieson C A\nFind the circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1865.jpg"
-  },
-  {
-    "id": 1910,
-    "problem_id": 1866,
-    "problem": "line C A, line B A, line C B, \\odot B lieson C A, line C A, line B A, line C B, \\odot B lieson C A\nFind the circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1866.jpg"
-  },
-  {
-    "id": 1911,
-    "problem_id": 1867,
-    "problem": "line C A, line B A, line C B, \\odot B lieson C A, line C A, line B A, line C B, \\odot B lieson C A\nFind the circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1867.jpg"
-  },
-  {
-    "id": 1912,
-    "problem_id": 1868,
-    "problem": "line A B, line A C, line C D, line A D, line A B, line A C, line C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1868.jpg"
-  },
-  {
-    "id": 1913,
-    "problem_id": 1869,
-    "problem": "line A B, line A C, line C D, line A D, line A B, line A C, line C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1869.jpg"
-  },
-  {
-    "id": 1914,
-    "problem_id": 1870,
-    "problem": "line A B, line A C, line C D, line A D, line A B, line A C, line C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1870.jpg"
-  },
-  {
-    "id": 1915,
-    "problem_id": 1871,
-    "problem": "line A B, line A C, line C D, line A D, line A B, line A C, line C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1871.jpg"
-  },
-  {
-    "id": 1916,
-    "problem_id": 1872,
-    "problem": "line A B, line A C, line C D, line A D, line A B, line A C, line C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1872.jpg"
-  },
-  {
-    "id": 1917,
-    "problem_id": 1873,
-    "problem": "line A B, line A C, line C D, line A D, line A B, line A C, line C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1873.jpg"
-  },
-  {
-    "id": 1918,
-    "problem_id": 1874,
-    "problem": "line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F, line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1874.jpg"
-  },
-  {
-    "id": 1919,
-    "problem_id": 1875,
-    "problem": "line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F, line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1875.jpg"
-  },
-  {
-    "id": 1920,
-    "problem_id": 1876,
-    "problem": "line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F, line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1876.jpg"
-  },
-  {
-    "id": 1921,
-    "problem_id": 1877,
-    "problem": "line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F, line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1877.jpg"
-  },
-  {
-    "id": 1922,
-    "problem_id": 1878,
-    "problem": "line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F, line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1878.jpg"
-  },
-  {
-    "id": 1923,
-    "problem_id": 1879,
-    "problem": "line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F, line C B, line A D C, line A B, line D B, line E G H, line E F, line F H, line G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1879.jpg"
-  },
-  {
-    "id": 1924,
-    "problem_id": 1880,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle RQP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1880.jpg"
-  },
-  {
-    "id": 1925,
-    "problem_id": 1881,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle RQP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1881.jpg"
-  },
-  {
-    "id": 1926,
-    "problem_id": 1882,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle RQP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1882.jpg"
-  },
-  {
-    "id": 1927,
-    "problem_id": 1883,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle RQP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1883.jpg"
-  },
-  {
-    "id": 1928,
-    "problem_id": 1884,
-    "problem": "line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G, line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1884.jpg"
-  },
-  {
-    "id": 1929,
-    "problem_id": 1885,
-    "problem": "line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G, line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1885.jpg"
-  },
-  {
-    "id": 1930,
-    "problem_id": 1886,
-    "problem": "line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G, line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1886.jpg"
-  },
-  {
-    "id": 1931,
-    "problem_id": 1887,
-    "problem": "line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G, line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1887.jpg"
-  },
-  {
-    "id": 1932,
-    "problem_id": 1888,
-    "problem": "line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G, line A B, line A C, line C F, line B E, line F G H, line E H, line D F, line D G\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1888.jpg"
-  },
-  {
-    "id": 1933,
-    "problem_id": 1889,
-    "problem": "line H G, line E H, line E F, line G F, line H G, line E H, line E F, line G F\nEFGH is a kite. What is m \\angle G?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1889.jpg"
-  },
-  {
-    "id": 1934,
-    "problem_id": 1890,
-    "problem": "line H G, line E H, line E F, line G F, line H G, line E H, line E F, line G F\nEFGH is a kite. What is m \\angle G?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1890.jpg"
-  },
-  {
-    "id": 1935,
-    "problem_id": 1891,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1891.jpg"
-  },
-  {
-    "id": 1936,
-    "problem_id": 1892,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1892.jpg"
-  },
-  {
-    "id": 1937,
-    "problem_id": 1893,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1893.jpg"
-  },
-  {
-    "id": 1938,
-    "problem_id": 1894,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1894.jpg"
-  },
-  {
-    "id": 1939,
-    "problem_id": 1895,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1895.jpg"
-  },
-  {
-    "id": 1940,
-    "problem_id": 1896,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1896.jpg"
-  },
-  {
-    "id": 1941,
-    "problem_id": 1897,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1897.jpg"
-  },
-  {
-    "id": 1942,
-    "problem_id": 1898,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1898.jpg"
-  },
-  {
-    "id": 1943,
-    "problem_id": 1899,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1899.jpg"
-  },
-  {
-    "id": 1944,
-    "problem_id": 1900,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1900.jpg"
-  },
-  {
-    "id": 1945,
-    "problem_id": 1901,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1901.jpg"
-  },
-  {
-    "id": 1946,
-    "problem_id": 1902,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1902.jpg"
-  },
-  {
-    "id": 1947,
-    "problem_id": 1903,
-    "problem": "line F E D C, line B D H, line A E G, line F E D C, line B D H, line A E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1903.jpg"
-  },
-  {
-    "id": 1948,
-    "problem_id": 1904,
-    "problem": "line F E D C, line B D H, line A E G, line F E D C, line B D H, line A E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1904.jpg"
-  },
-  {
-    "id": 1949,
-    "problem_id": 1905,
-    "problem": "line A B C, line A D, line D C, \\odot B lieson A C D, line A B C, line A D, line D C, \\odot B lieson A C D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1905.jpg"
-  },
-  {
-    "id": 1950,
-    "problem_id": 1906,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1906.jpg"
-  },
-  {
-    "id": 1951,
-    "problem_id": 1907,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1907.jpg"
-  },
-  {
-    "id": 1952,
-    "problem_id": 1908,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1908.jpg"
-  },
-  {
-    "id": 1953,
-    "problem_id": 1909,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1909.jpg"
-  },
-  {
-    "id": 1954,
-    "problem_id": 1910,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1910.jpg"
-  },
-  {
-    "id": 1955,
-    "problem_id": 1911,
-    "problem": "line A C, line D B C, line D A, line A B, line A C, line D B C, line D A, line A B\nWhat is w?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1911.jpg"
-  },
-  {
-    "id": 1956,
-    "problem_id": 1912,
-    "problem": "line A C, line D B C, line D A, line A B, line A C, line D B C, line D A, line A B\nWhat is w?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1912.jpg"
-  },
-  {
-    "id": 1957,
-    "problem_id": 1913,
-    "problem": "line A C, line D B C, line D A, line A B, line A C, line D B C, line D A, line A B\nWhat is w?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1913.jpg"
-  },
-  {
-    "id": 1958,
-    "problem_id": 1914,
-    "problem": "line A C, line D B C, line D A, line A B, line A C, line D B C, line D A, line A B\nWhat is w?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1914.jpg"
-  },
-  {
-    "id": 1959,
-    "problem_id": 1915,
-    "problem": "line A C, line A B, line C B, line A C, line A B, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1915.jpg"
-  },
-  {
-    "id": 1960,
-    "problem_id": 1916,
-    "problem": "line A C, line A B, line C B, line A C, line A B, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1916.jpg"
-  },
-  {
-    "id": 1961,
-    "problem_id": 1917,
-    "problem": "line A C, line A B, line C B, line A C, line A B, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1917.jpg"
-  },
-  {
-    "id": 1962,
-    "problem_id": 1918,
-    "problem": "line A C, line A B, line C B, line A C, line A B, line C B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1918.jpg"
-  },
-  {
-    "id": 1963,
-    "problem_id": 1919,
-    "problem": "line L M J, line H M K, \\odot A lieson H L K J, line L M J, line H M K, \\odot A lieson H L K J\nFind m \\angle JMK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1919.jpg"
-  },
-  {
-    "id": 1964,
-    "problem_id": 1920,
-    "problem": "line Q R, line S R, line S Q, line Q R, line S R, line S Q\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1920.jpg"
-  },
-  {
-    "id": 1965,
-    "problem_id": 1921,
-    "problem": "line Q R, line S R, line S Q, line Q R, line S R, line S Q\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1921.jpg"
-  },
-  {
-    "id": 1966,
-    "problem_id": 1922,
-    "problem": "line Q R, line S R, line S Q, line Q R, line S R, line S Q\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1922.jpg"
-  },
-  {
-    "id": 1967,
-    "problem_id": 1923,
-    "problem": "line P M, line A Q M, \\odot B lieson P R M, line P M, line A Q M, \\odot B lieson P R M\nFind m \\widehat PRM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1923.jpg"
-  },
-  {
-    "id": 1968,
-    "problem_id": 1924,
-    "problem": "line A C E, line B C D, line C F, line A C E, line B C D, line C F\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1924.jpg"
-  },
-  {
-    "id": 1969,
-    "problem_id": 1925,
-    "problem": "line A C E, line B C D, line C F, line A C E, line B C D, line C F\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1925.jpg"
-  },
-  {
-    "id": 1970,
-    "problem_id": 1926,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find JF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1926.jpg"
-  },
-  {
-    "id": 1971,
-    "problem_id": 1927,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find JF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1927.jpg"
-  },
-  {
-    "id": 1972,
-    "problem_id": 1928,
-    "problem": "line A X Z, line Y X, \\odot X lieson A Y Z, line A X Z, line Y X, \\odot X lieson A Y Z\nFind the length of \\widehat ZY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1928.jpg"
-  },
-  {
-    "id": 1973,
-    "problem_id": 1929,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1929.jpg"
-  },
-  {
-    "id": 1974,
-    "problem_id": 1930,
-    "problem": "line D A, line D C B, line B E, line D E, \\odot C lieson D E B A, line D A, line D C B, line B E, line D E, \\odot C lieson D E B A\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1930.jpg"
-  },
-  {
-    "id": 1975,
-    "problem_id": 1931,
-    "problem": "line E D, line A E B, line B C, line A D, line D C, line E D, line A E B, line B C, line A D, line D C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1931.jpg"
-  },
-  {
-    "id": 1976,
-    "problem_id": 1932,
-    "problem": "line E D, line A E B, line B C, line A D, line D C, line E D, line A E B, line B C, line A D, line D C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1932.jpg"
-  },
-  {
-    "id": 1977,
-    "problem_id": 1933,
-    "problem": "line E D, line A E B, line B C, line A D, line D C, line E D, line A E B, line B C, line A D, line D C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1933.jpg"
-  },
-  {
-    "id": 1978,
-    "problem_id": 1934,
-    "problem": "line E D, line A E B, line B C, line A D, line D C, line E D, line A E B, line B C, line A D, line D C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1934.jpg"
-  },
-  {
-    "id": 1979,
-    "problem_id": 1935,
-    "problem": "line M N, line M P, line N P, line J L, line K L, line J K, line M N, line M P, line N P, line J L, line K L, line J K\n\\triangle JKL \\sim \\triangle MNP. Find NP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1935.jpg"
-  },
-  {
-    "id": 1980,
-    "problem_id": 1936,
-    "problem": "line M N, line M P, line N P, line J L, line K L, line J K, line M N, line M P, line N P, line J L, line K L, line J K\n\\triangle JKL \\sim \\triangle MNP. Find NP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1936.jpg"
-  },
-  {
-    "id": 1981,
-    "problem_id": 1937,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 9 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1937.jpg"
-  },
-  {
-    "id": 1982,
-    "problem_id": 1938,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 9 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1938.jpg"
-  },
-  {
-    "id": 1983,
-    "problem_id": 1939,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 9 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1939.jpg"
-  },
-  {
-    "id": 1984,
-    "problem_id": 1940,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 9 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1940.jpg"
-  },
-  {
-    "id": 1985,
-    "problem_id": 1941,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 9 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1941.jpg"
-  },
-  {
-    "id": 1986,
-    "problem_id": 1942,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind x. Perimeter = 54 feet.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1942.jpg"
-  },
-  {
-    "id": 1987,
-    "problem_id": 1943,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind x. Perimeter = 54 feet.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1943.jpg"
-  },
-  {
-    "id": 1988,
-    "problem_id": 1944,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nSolve for the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1944.jpg"
-  },
-  {
-    "id": 1989,
-    "problem_id": 1945,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nSolve for the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1945.jpg"
-  },
-  {
-    "id": 1990,
-    "problem_id": 1946,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nSolve for the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1946.jpg"
-  },
-  {
-    "id": 1991,
-    "problem_id": 1947,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nSolve for the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1947.jpg"
-  },
-  {
-    "id": 1992,
-    "problem_id": 1948,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat QRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1948.jpg"
-  },
-  {
-    "id": 1993,
-    "problem_id": 1949,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat QRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1949.jpg"
-  },
-  {
-    "id": 1994,
-    "problem_id": 1950,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat QRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1950.jpg"
-  },
-  {
-    "id": 1995,
-    "problem_id": 1951,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat QRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1951.jpg"
-  },
-  {
-    "id": 1996,
-    "problem_id": 1952,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1952.jpg"
-  },
-  {
-    "id": 1997,
-    "problem_id": 1953,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1953.jpg"
-  },
-  {
-    "id": 1998,
-    "problem_id": 1954,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1954.jpg"
-  },
-  {
-    "id": 1999,
-    "problem_id": 1955,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1955.jpg"
-  },
-  {
-    "id": 2000,
-    "problem_id": 1956,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1956.jpg"
-  },
-  {
-    "id": 2001,
-    "problem_id": 1957,
-    "problem": "line D C B, line A C E, line A D, line A B, line D E, line B E, line D C B, line A C E, line A D, line A B, line D E, line B E\nFor what value of x is the rectangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1957.jpg"
-  },
-  {
-    "id": 2002,
-    "problem_id": 1958,
-    "problem": "line D C B, line A C E, line A D, line A B, line D E, line B E, line D C B, line A C E, line A D, line A B, line D E, line B E\nFor what value of x is the rectangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1958.jpg"
-  },
-  {
-    "id": 2003,
-    "problem_id": 1959,
-    "problem": "line D C B, line A C E, line A D, line A B, line D E, line B E, line D C B, line A C E, line A D, line A B, line D E, line B E\nFor what value of x is the rectangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1959.jpg"
-  },
-  {
-    "id": 2004,
-    "problem_id": 1960,
-    "problem": "line D C B, line A C E, line A D, line A B, line D E, line B E, line D C B, line A C E, line A D, line A B, line D E, line B E\nFor what value of x is the rectangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1960.jpg"
-  },
-  {
-    "id": 2005,
-    "problem_id": 1961,
-    "problem": "line D C B, line A C E, line A D, line A B, line D E, line B E, line D C B, line A C E, line A D, line A B, line D E, line B E\nFor what value of x is the rectangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1961.jpg"
-  },
-  {
-    "id": 2006,
-    "problem_id": 1962,
-    "problem": "line E R B, line C D A B, \\odot F lieson D R A, line E R B, line C D A B, \\odot F lieson D R A\nFind the measure of \\widehat DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1962.jpg"
-  },
-  {
-    "id": 2007,
-    "problem_id": 1963,
-    "problem": "line E R B, line C D A B, \\odot F lieson D R A, line E R B, line C D A B, \\odot F lieson D R A\nFind the measure of \\widehat DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1963.jpg"
-  },
-  {
-    "id": 2008,
-    "problem_id": 1964,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PV in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1964.jpg"
-  },
-  {
-    "id": 2009,
-    "problem_id": 1965,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PV in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1965.jpg"
-  },
-  {
-    "id": 2010,
-    "problem_id": 1966,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind PV in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1966.jpg"
-  },
-  {
-    "id": 2011,
-    "problem_id": 1967,
-    "problem": "line W Z, line W X, line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y\nWXYZ is a parallelogram. Solve for YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1967.jpg"
-  },
-  {
-    "id": 2012,
-    "problem_id": 1968,
-    "problem": "line W Z, line W X, line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y\nWXYZ is a parallelogram. Solve for YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1968.jpg"
-  },
-  {
-    "id": 2013,
-    "problem_id": 1969,
-    "problem": "line J K L, line J K L\nIn the diagram, KL = 120. What is JK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1969.jpg"
-  },
-  {
-    "id": 2014,
-    "problem_id": 1970,
-    "problem": "line E B C, line A C, line C D F, \\odot G lieson A C B, line E B C, line A C, line C D F, \\odot G lieson A C B\nFind m \\widehat ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1970.jpg"
-  },
-  {
-    "id": 2015,
-    "problem_id": 1971,
-    "problem": "line B A, line D C, line B D E, line A C, line E C, line B A, line D C, line B D E, line A C, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1971.jpg"
-  },
-  {
-    "id": 2016,
-    "problem_id": 1972,
-    "problem": "line B A, line D C, line B D E, line A C, line E C, line B A, line D C, line B D E, line A C, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1972.jpg"
-  },
-  {
-    "id": 2018,
-    "problem_id": 1973,
-    "problem": "line B A, line D C, line B D E, line A C, line E C, line B A, line D C, line B D E, line A C, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1973.jpg"
-  },
-  {
-    "id": 2019,
-    "problem_id": 1974,
-    "problem": "line B A, line D C, line B D E, line A C, line E C, line B A, line D C, line B D E, line A C, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1974.jpg"
-  },
-  {
-    "id": 2020,
-    "problem_id": 1975,
-    "problem": "line B A, line D C, line B D E, line A C, line E C, line B A, line D C, line B D E, line A C, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1975.jpg"
-  },
-  {
-    "id": 2021,
-    "problem_id": 1976,
-    "problem": "line A D I, line B F H, line E F G, line C D E, line A D I, line B F H, line E F G, line C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1976.jpg"
-  },
-  {
-    "id": 2022,
-    "problem_id": 1977,
-    "problem": "line A D I, line B F H, line E F G, line C D E, line A D I, line B F H, line E F G, line C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1977.jpg"
-  },
-  {
-    "id": 2023,
-    "problem_id": 1978,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the length of ZV?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1978.jpg"
-  },
-  {
-    "id": 2024,
-    "problem_id": 1979,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the length of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1979.jpg"
-  },
-  {
-    "id": 2025,
-    "problem_id": 1980,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the length of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1980.jpg"
-  },
-  {
-    "id": 2026,
-    "problem_id": 1981,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the length of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1981.jpg"
-  },
-  {
-    "id": 2027,
-    "problem_id": 1982,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the length of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1982.jpg"
-  },
-  {
-    "id": 2028,
-    "problem_id": 1983,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the length of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1983.jpg"
-  },
-  {
-    "id": 2029,
-    "problem_id": 1984,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the length of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1984.jpg"
-  },
-  {
-    "id": 2030,
-    "problem_id": 1985,
-    "problem": "line I E P, line I N, \\odot A lieson N E P, line I E P, line I N, \\odot A lieson N E P\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1985.jpg"
-  },
-  {
-    "id": 2031,
-    "problem_id": 1986,
-    "problem": "line A C, line B T C, line B A, \\odot T lieson B A C, line A C, line B T C, line B A, \\odot T lieson B A C\nWhat is the diameter of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1986.jpg"
-  },
-  {
-    "id": 2032,
-    "problem_id": 1987,
-    "problem": "line A C, line B T C, line B A, \\odot T lieson B A C, line A C, line B T C, line B A, \\odot T lieson B A C\nWhat is the diameter of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1987.jpg"
-  },
-  {
-    "id": 2033,
-    "problem_id": 1988,
-    "problem": "line A C, line B T C, line B A, \\odot T lieson B A C, line A C, line B T C, line B A, \\odot T lieson B A C\nWhat is the diameter of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1988.jpg"
-  },
-  {
-    "id": 2034,
-    "problem_id": 1989,
-    "problem": "line A C, line B T C, line B A, \\odot T lieson B A C, line A C, line B T C, line B A, \\odot T lieson B A C\nWhat is the diameter of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1989.jpg"
-  },
-  {
-    "id": 2035,
-    "problem_id": 1990,
-    "problem": "line A C, line B T C, line B A, \\odot T lieson B A C, line A C, line B T C, line B A, \\odot T lieson B A C\nWhat is the diameter of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1990.jpg"
-  },
-  {
-    "id": 2036,
-    "problem_id": 1991,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable a in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1991.jpg"
-  },
-  {
-    "id": 2037,
-    "problem_id": 1992,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable a in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1992.jpg"
-  },
-  {
-    "id": 2038,
-    "problem_id": 1993,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1993.jpg"
-  },
-  {
-    "id": 2039,
-    "problem_id": 1994,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1994.jpg"
-  },
-  {
-    "id": 2041,
-    "problem_id": 1995,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1995.jpg"
-  },
-  {
-    "id": 2042,
-    "problem_id": 1996,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1996.jpg"
-  },
-  {
-    "id": 2043,
-    "problem_id": 1997,
-    "problem": "line B C E, line D E, line D C A, \\odot F lieson B D E A, line B C E, line D E, line D C A, \\odot F lieson B D E A\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1997.jpg"
-  },
-  {
-    "id": 2044,
-    "problem_id": 1998,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nWhat is the length of AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1998.jpg"
-  },
-  {
-    "id": 2045,
-    "problem_id": 1999,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nWhat is the length of AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/1999.jpg"
-  },
-  {
-    "id": 2046,
-    "problem_id": 2000,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nWhat is the length of AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2000.jpg"
-  },
-  {
-    "id": 2047,
-    "problem_id": 2001,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nWhat is the length of AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2001.jpg"
-  },
-  {
-    "id": 2048,
-    "problem_id": 2002,
-    "problem": "line B C, line A B, \\odot B lieson A C, line B C, line A B, \\odot B lieson A C\nIf area of sector ABC is 9\\pi. Find the area of \\odot B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2002.jpg"
-  },
-  {
-    "id": 2049,
-    "problem_id": 2003,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle ADB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2003.jpg"
-  },
-  {
-    "id": 2050,
-    "problem_id": 2004,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle ADB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2004.jpg"
-  },
-  {
-    "id": 2051,
-    "problem_id": 2005,
-    "problem": "line P G, line P H, \\odot P lieson G H, line P G, line P H, \\odot P lieson G H\nWhat is the length of \\widehat GH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2005.jpg"
-  },
-  {
-    "id": 2052,
-    "problem_id": 2006,
-    "problem": "line P G, line P H, \\odot P lieson G H, line P G, line P H, \\odot P lieson G H\nWhat is the length of \\widehat GH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2006.jpg"
-  },
-  {
-    "id": 2053,
-    "problem_id": 2007,
-    "problem": "line P G, line P H, \\odot P lieson G H, line P G, line P H, \\odot P lieson G H\nWhat is the length of \\widehat GH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2007.jpg"
-  },
-  {
-    "id": 2054,
-    "problem_id": 2008,
-    "problem": "line A B C, line E C, line D E, line D A, line D B, line A B C, line E C, line D E, line D A, line D B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2008.jpg"
-  },
-  {
-    "id": 2055,
-    "problem_id": 2009,
-    "problem": "line A B C, line E C, line D E, line D A, line D B, line A B C, line E C, line D E, line D A, line D B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2009.jpg"
-  },
-  {
-    "id": 2056,
-    "problem_id": 2010,
-    "problem": "line A B C, line E C, line D E, line D A, line D B, line A B C, line E C, line D E, line D A, line D B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2010.jpg"
-  },
-  {
-    "id": 2059,
-    "problem_id": 2011,
-    "problem": "line X Y, line Z Y, line X Z, line X Y, line Z Y, line X Z\nWhat is the value of \\sin Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2011.jpg"
-  },
-  {
-    "id": 2060,
-    "problem_id": 2012,
-    "problem": "line J H K, line J H K\nIf JK = 48, find the length of HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2012.jpg"
-  },
-  {
-    "id": 2061,
-    "problem_id": 2013,
-    "problem": "line J H K, line J H K\nIf JK = 48, find the length of HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2013.jpg"
-  },
-  {
-    "id": 2062,
-    "problem_id": 2014,
-    "problem": "line J H K, line J H K\nIf JK = 48, find the length of HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2014.jpg"
-  },
-  {
-    "id": 2063,
-    "problem_id": 2015,
-    "problem": "line J H K, line J H K\nIf JK = 48, find the length of HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2015.jpg"
-  },
-  {
-    "id": 2064,
-    "problem_id": 2016,
-    "problem": "line B C D, line C A, \\odot C lieson B D A, line B C D, line C A, \\odot C lieson B D A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2016.jpg"
-  },
-  {
-    "id": 2065,
-    "problem_id": 2017,
-    "problem": "line Q A S, line P S, line P A R, line Q R, \\odot B lieson P S R Q, line Q A S, line P S, line P A R, line Q R, \\odot B lieson P S R Q\nIf m \\angle 1 = x, m \\angle 2 = 2x-13. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2017.jpg"
-  },
-  {
-    "id": 2066,
-    "problem_id": 2018,
-    "problem": "line Q R, line Q S, line R S, line Q R, line Q S, line R S\nFind the length of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2018.jpg"
-  },
-  {
-    "id": 2067,
-    "problem_id": 2019,
-    "problem": "line Q R, line Q S, line R S, line Q R, line Q S, line R S\nFind the length of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2019.jpg"
-  },
-  {
-    "id": 2068,
-    "problem_id": 2020,
-    "problem": "line Q R, line Q S, line R S, line Q R, line Q S, line R S\nFind the length of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2020.jpg"
-  },
-  {
-    "id": 2069,
-    "problem_id": 2021,
-    "problem": "line H G, line F G, line F H, line H G, line F G, line F H\n\\triangle FGH is an equilateral triangle. Find FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2021.jpg"
-  },
-  {
-    "id": 2070,
-    "problem_id": 2022,
-    "problem": "line H G, line F G, line F H, line H G, line F G, line F H\n\\triangle FGH is an equilateral triangle. Find FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2022.jpg"
-  },
-  {
-    "id": 2071,
-    "problem_id": 2023,
-    "problem": "line H G, line F G, line F H, line H G, line F G, line F H\n\\triangle FGH is an equilateral triangle. Find FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2023.jpg"
-  },
-  {
-    "id": 2072,
-    "problem_id": 2024,
-    "problem": "line H G, line F G, line F H, line H G, line F G, line F H\n\\triangle FGH is an equilateral triangle. Find FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2024.jpg"
-  },
-  {
-    "id": 2073,
-    "problem_id": 2025,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle TQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2025.jpg"
-  },
-  {
-    "id": 2074,
-    "problem_id": 2026,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle TQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2026.jpg"
-  },
-  {
-    "id": 2075,
-    "problem_id": 2027,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle TQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2027.jpg"
-  },
-  {
-    "id": 2076,
-    "problem_id": 2028,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle TQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2028.jpg"
-  },
-  {
-    "id": 2077,
-    "problem_id": 2029,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle TQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2029.jpg"
-  },
-  {
-    "id": 2078,
-    "problem_id": 2030,
-    "problem": "line C S R, line R Q B, line R T A, line S Q, line Q T, line C S R, line R Q B, line R T A, line S Q, line Q T\nFind m \\angle TQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2030.jpg"
-  },
-  {
-    "id": 2079,
-    "problem_id": 2031,
-    "problem": "line B D A, line C A, line B C, line C D, line B D A, line C A, line B C, line C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2031.jpg"
-  },
-  {
-    "id": 2080,
-    "problem_id": 2032,
-    "problem": "line B D A, line C A, line B C, line C D, line B D A, line C A, line B C, line C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2032.jpg"
-  },
-  {
-    "id": 2081,
-    "problem_id": 2033,
-    "problem": "line B D A, line C A, line B C, line C D, line B D A, line C A, line B C, line C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2033.jpg"
-  },
-  {
-    "id": 2082,
-    "problem_id": 2034,
-    "problem": "line B D A, line C A, line B C, line C D, line B D A, line C A, line B C, line C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2034.jpg"
-  },
-  {
-    "id": 2083,
-    "problem_id": 2035,
-    "problem": "line F A H, line G A J, line F J, line G H, line H J, line G F, line F A H, line G A J, line F J, line G H, line H J, line G F\nGJ = 4x-1, and FH = 9x-15. Find FH so that FGHJ is isosceles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2035.jpg"
-  },
-  {
-    "id": 2084,
-    "problem_id": 2036,
-    "problem": "line F A H, line G A J, line F J, line G H, line H J, line G F, line F A H, line G A J, line F J, line G H, line H J, line G F\nGJ = 4x-1, and FH = 9x-15. Find FH so that FGHJ is isosceles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2036.jpg"
-  },
-  {
-    "id": 2085,
-    "problem_id": 2037,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2037.jpg"
-  },
-  {
-    "id": 2086,
-    "problem_id": 2038,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2038.jpg"
-  },
-  {
-    "id": 2087,
-    "problem_id": 2039,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2039.jpg"
-  },
-  {
-    "id": 2088,
-    "problem_id": 2040,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2040.jpg"
-  },
-  {
-    "id": 2089,
-    "problem_id": 2041,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2041.jpg"
-  },
-  {
-    "id": 2090,
-    "problem_id": 2042,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2042.jpg"
-  },
-  {
-    "id": 2091,
-    "problem_id": 2043,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nGiven that m \\angle 7 = 38, find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2043.jpg"
-  },
-  {
-    "id": 2092,
-    "problem_id": 2044,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nGiven that m \\angle 7 = 38, find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2044.jpg"
-  },
-  {
-    "id": 2093,
-    "problem_id": 2045,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nGiven that m \\angle 7 = 38, find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2045.jpg"
-  },
-  {
-    "id": 2094,
-    "problem_id": 2046,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nGiven that m \\angle 7 = 38, find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2046.jpg"
-  },
-  {
-    "id": 2095,
-    "problem_id": 2047,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is DE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2047.jpg"
-  },
-  {
-    "id": 2096,
-    "problem_id": 2048,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is DE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2048.jpg"
-  },
-  {
-    "id": 2097,
-    "problem_id": 2049,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is DE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2049.jpg"
-  },
-  {
-    "id": 2098,
-    "problem_id": 2050,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the value of h for the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2050.jpg"
-  },
-  {
-    "id": 2099,
-    "problem_id": 2051,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2051.jpg"
-  },
-  {
-    "id": 2100,
-    "problem_id": 2052,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2052.jpg"
-  },
-  {
-    "id": 2101,
-    "problem_id": 2053,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2053.jpg"
-  },
-  {
-    "id": 2102,
-    "problem_id": 2054,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2054.jpg"
-  },
-  {
-    "id": 2103,
-    "problem_id": 2055,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2055.jpg"
-  },
-  {
-    "id": 2104,
-    "problem_id": 2056,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2056.jpg"
-  },
-  {
-    "id": 2105,
-    "problem_id": 2057,
-    "problem": "line E F, line F G, line E G, line E F, line F G, line E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2057.jpg"
-  },
-  {
-    "id": 2106,
-    "problem_id": 2058,
-    "problem": "line E F, line F G, line E G, line E F, line F G, line E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2058.jpg"
-  },
-  {
-    "id": 2107,
-    "problem_id": 2059,
-    "problem": "line E F, line F G, line E G, line E F, line F G, line E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2059.jpg"
-  },
-  {
-    "id": 2108,
-    "problem_id": 2060,
-    "problem": "line E F, line F G, line E G, line E F, line F G, line E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2060.jpg"
-  },
-  {
-    "id": 2109,
-    "problem_id": 2061,
-    "problem": "line E F, line F G, line E G, line E F, line F G, line E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2061.jpg"
-  },
-  {
-    "id": 2110,
-    "problem_id": 2062,
-    "problem": "line E F, line F G, line E G, line E F, line F G, line E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2062.jpg"
-  },
-  {
-    "id": 2111,
-    "problem_id": 2063,
-    "problem": "line D C B, line A C E, line D C B, line A C E\nm \\angle 13 = 2x+94, m \\angle 14 = 7x+49, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2063.jpg"
-  },
-  {
-    "id": 2112,
-    "problem_id": 2064,
-    "problem": "line D C B, line A C E, line D C B, line A C E\nm \\angle 13 = 2x+94, m \\angle 14 = 7x+49, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2064.jpg"
-  },
-  {
-    "id": 2113,
-    "problem_id": 2065,
-    "problem": "line D C B, line A C E, line D C B, line A C E\nm \\angle 13 = 2x+94, m \\angle 14 = 7x+49, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2065.jpg"
-  },
-  {
-    "id": 2114,
-    "problem_id": 2066,
-    "problem": "line A I K, line B H G, line C E F, line J I H E D, line A I K, line B H G, line C E F, line J I H E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2066.jpg"
-  },
-  {
-    "id": 2115,
-    "problem_id": 2067,
-    "problem": "line A I K, line B H G, line C E F, line J I H E D, line A I K, line B H G, line C E F, line J I H E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2067.jpg"
-  },
-  {
-    "id": 2116,
-    "problem_id": 2068,
-    "problem": "line A I K, line B H G, line C E F, line J I H E D, line A I K, line B H G, line C E F, line J I H E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2068.jpg"
-  },
-  {
-    "id": 2117,
-    "problem_id": 2069,
-    "problem": "line A I K, line B H G, line C E F, line J I H E D, line A I K, line B H G, line C E F, line J I H E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2069.jpg"
-  },
-  {
-    "id": 2118,
-    "problem_id": 2070,
-    "problem": "line A I K, line B H G, line C E F, line J I H E D, line A I K, line B H G, line C E F, line J I H E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2070.jpg"
-  },
-  {
-    "id": 2119,
-    "problem_id": 2071,
-    "problem": "line A I K, line B H G, line C E F, line J I H E D, line A I K, line B H G, line C E F, line J I H E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2071.jpg"
-  },
-  {
-    "id": 2120,
-    "problem_id": 2072,
-    "problem": "line H G, line F G, line F E, line E D, line C D, line C B, line A B, line H A, line H G, line F G, line F E, line E D, line C D, line C B, line A B, line H A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2072.jpg"
-  },
-  {
-    "id": 2121,
-    "problem_id": 2073,
-    "problem": "line H G, line F G, line F E, line E D, line C D, line C B, line A B, line H A, line H G, line F G, line F E, line E D, line C D, line C B, line A B, line H A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2073.jpg"
-  },
-  {
-    "id": 2122,
-    "problem_id": 2074,
-    "problem": "line H G, line F G, line F E, line E D, line C D, line C B, line A B, line H A, line H G, line F G, line F E, line E D, line C D, line C B, line A B, line H A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2074.jpg"
-  },
-  {
-    "id": 2123,
-    "problem_id": 2075,
-    "problem": "line A B C D, line E B, line E C, line A B C D, line E B, line E C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2075.jpg"
-  },
-  {
-    "id": 2124,
-    "problem_id": 2076,
-    "problem": "line A B C D, line E B, line E C, line A B C D, line E B, line E C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2076.jpg"
-  },
-  {
-    "id": 2125,
-    "problem_id": 2077,
-    "problem": "line A B C D, line E B, line E C, line A B C D, line E B, line E C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2077.jpg"
-  },
-  {
-    "id": 2126,
-    "problem_id": 2078,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of the segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2078.jpg"
-  },
-  {
-    "id": 2127,
-    "problem_id": 2079,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of the segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2079.jpg"
-  },
-  {
-    "id": 2128,
-    "problem_id": 2080,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of the segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2080.jpg"
-  },
-  {
-    "id": 2129,
-    "problem_id": 2081,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram PQRS to find m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2081.jpg"
-  },
-  {
-    "id": 2130,
-    "problem_id": 2082,
-    "problem": "line J F G A, line I E H B, line K F E D, line L G H C, line J F G A, line I E H B, line K F E D, line L G H C\nIf m \\angle 1 = 3x+40, m \\angle 2 = 2(y-10), and m \\angle 3 = 2x+70, find m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2082.jpg"
-  },
-  {
-    "id": 2131,
-    "problem_id": 2083,
-    "problem": "line J F G A, line I E H B, line K F E D, line L G H C, line J F G A, line I E H B, line K F E D, line L G H C\nIf m \\angle 1 = 3x+40, m \\angle 2 = 2(y-10), and m \\angle 3 = 2x+70, find m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2083.jpg"
-  },
-  {
-    "id": 2132,
-    "problem_id": 2084,
-    "problem": "line J F G A, line I E H B, line K F E D, line L G H C, line J F G A, line I E H B, line K F E D, line L G H C\nIf m \\angle 1 = 3x+40, m \\angle 2 = 2(y-10), and m \\angle 3 = 2x+70, find m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2084.jpg"
-  },
-  {
-    "id": 2133,
-    "problem_id": 2085,
-    "problem": "line J F G A, line I E H B, line K F E D, line L G H C, line J F G A, line I E H B, line K F E D, line L G H C\nIf m \\angle 1 = 3x+40, m \\angle 2 = 2(y-10), and m \\angle 3 = 2x+70, find m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2085.jpg"
-  },
-  {
-    "id": 2134,
-    "problem_id": 2086,
-    "problem": "line J F G A, line I E H B, line K F E D, line L G H C, line J F G A, line I E H B, line K F E D, line L G H C\nIf m \\angle 1 = 3x+40, m \\angle 2 = 2(y-10), and m \\angle 3 = 2x+70, find m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2086.jpg"
-  },
-  {
-    "id": 2135,
-    "problem_id": 2087,
-    "problem": "line D F, line E D, line E F, line D F, line E D, line E F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2087.jpg"
-  },
-  {
-    "id": 2136,
-    "problem_id": 2088,
-    "problem": "line D F, line E D, line E F, line D F, line E D, line E F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2088.jpg"
-  },
-  {
-    "id": 2137,
-    "problem_id": 2089,
-    "problem": "line D F, line E D, line E F, line D F, line E D, line E F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2089.jpg"
-  },
-  {
-    "id": 2138,
-    "problem_id": 2090,
-    "problem": "line B D, line A C, line C D, line A B, line B D, line A C, line C D, line A B\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2090.jpg"
-  },
-  {
-    "id": 2139,
-    "problem_id": 2091,
-    "problem": "line B D, line A C, line C D, line A B, line B D, line A C, line C D, line A B\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2091.jpg"
-  },
-  {
-    "id": 2140,
-    "problem_id": 2092,
-    "problem": "line B D, line A C, line C D, line A B, line B D, line A C, line C D, line A B\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2092.jpg"
-  },
-  {
-    "id": 2141,
-    "problem_id": 2093,
-    "problem": "line C D B, line A D E, line E B, line A B, line C A, line C E, line C D B, line A D E, line E B, line A B, line C A, line C E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2093.jpg"
-  },
-  {
-    "id": 2142,
-    "problem_id": 2094,
-    "problem": "line C D B, line A D E, line E B, line A B, line C A, line C E, line C D B, line A D E, line E B, line A B, line C A, line C E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2094.jpg"
-  },
-  {
-    "id": 2143,
-    "problem_id": 2095,
-    "problem": "line C D B, line A D E, line E B, line A B, line C A, line C E, line C D B, line A D E, line E B, line A B, line C A, line C E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2095.jpg"
-  },
-  {
-    "id": 2144,
-    "problem_id": 2096,
-    "problem": "line C D B, line A D E, line E B, line A B, line C A, line C E, line C D B, line A D E, line E B, line A B, line C A, line C E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2096.jpg"
-  },
-  {
-    "id": 2145,
-    "problem_id": 2097,
-    "problem": "line C D, line E F, line A B, line A E C, line B F D, line C D, line E F, line A B, line A E C, line B F D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2097.jpg"
-  },
-  {
-    "id": 2146,
-    "problem_id": 2098,
-    "problem": "line C D, line E F, line A B, line A E C, line B F D, line C D, line E F, line A B, line A E C, line B F D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2098.jpg"
-  },
-  {
-    "id": 2147,
-    "problem_id": 2099,
-    "problem": "line L Q, line M P, line M L, line P Q, line L Q, line M P, line M L, line P Q\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2099.jpg"
-  },
-  {
-    "id": 2148,
-    "problem_id": 2100,
-    "problem": "line L Q, line M P, line M L, line P Q, line L Q, line M P, line M L, line P Q\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2100.jpg"
-  },
-  {
-    "id": 2149,
-    "problem_id": 2101,
-    "problem": "line A B C, line A D E, \\odot F lieson B D E C, line A B C, line A D E, \\odot F lieson B D E C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2101.jpg"
-  },
-  {
-    "id": 2150,
-    "problem_id": 2102,
-    "problem": "line F A, line F E, line E D, line D C, line A C, line B A, \\odot B lieson E F A C D, line F A, line F E, line E D, line D C, line A C, line B A, \\odot B lieson E F A C D\nFind the area of the regular polygon formed by the circle and regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2102.jpg"
-  },
-  {
-    "id": 2151,
-    "problem_id": 2103,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2103.jpg"
-  },
-  {
-    "id": 2152,
-    "problem_id": 2104,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2104.jpg"
-  },
-  {
-    "id": 2153,
-    "problem_id": 2105,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2105.jpg"
-  },
-  {
-    "id": 2154,
-    "problem_id": 2106,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2106.jpg"
-  },
-  {
-    "id": 2155,
-    "problem_id": 2107,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2107.jpg"
-  },
-  {
-    "id": 2156,
-    "problem_id": 2108,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2108.jpg"
-  },
-  {
-    "id": 2157,
-    "problem_id": 2109,
-    "problem": "line O Q' Q C, line F G J L N C, line Q' J H E, line A E K C, line B D H I M C, line D E, line G D, line G Q', line L I, line Q N M K, line L Q, line I K, line O Q' Q C, line F G J L N C, line Q' J H E, line A E K C, line B D H I M C, line D E, line G D, line G Q', line L I, line Q N M K, line L Q, line I K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2109.jpg"
-  },
-  {
-    "id": 2158,
-    "problem_id": 2110,
-    "problem": "line O Q' Q C, line F G J L N C, line Q' J H E, line A E K C, line B D H I M C, line D E, line G D, line G Q', line L I, line Q N M K, line L Q, line I K, line O Q' Q C, line F G J L N C, line Q' J H E, line A E K C, line B D H I M C, line D E, line G D, line G Q', line L I, line Q N M K, line L Q, line I K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2110.jpg"
-  },
-  {
-    "id": 2159,
-    "problem_id": 2111,
-    "problem": "line O Q' Q C, line F G J L N C, line Q' J H E, line A E K C, line B D H I M C, line D E, line G D, line G Q', line L I, line Q N M K, line L Q, line I K, line O Q' Q C, line F G J L N C, line Q' J H E, line A E K C, line B D H I M C, line D E, line G D, line G Q', line L I, line Q N M K, line L Q, line I K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2111.jpg"
-  },
-  {
-    "id": 2160,
-    "problem_id": 2112,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2112.jpg"
-  },
-  {
-    "id": 2161,
-    "problem_id": 2113,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2113.jpg"
-  },
-  {
-    "id": 2162,
-    "problem_id": 2114,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2114.jpg"
-  },
-  {
-    "id": 2163,
-    "problem_id": 2115,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2115.jpg"
-  },
-  {
-    "id": 2164,
-    "problem_id": 2116,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2116.jpg"
-  },
-  {
-    "id": 2165,
-    "problem_id": 2117,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2117.jpg"
-  },
-  {
-    "id": 2166,
-    "problem_id": 2118,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nSolve for the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2118.jpg"
-  },
-  {
-    "id": 2167,
-    "problem_id": 2119,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nSolve for the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2119.jpg"
-  },
-  {
-    "id": 2168,
-    "problem_id": 2120,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nSolve for the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2120.jpg"
-  },
-  {
-    "id": 2169,
-    "problem_id": 2121,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nSolve for the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2121.jpg"
-  },
-  {
-    "id": 2170,
-    "problem_id": 2122,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2122.jpg"
-  },
-  {
-    "id": 2171,
-    "problem_id": 2123,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2123.jpg"
-  },
-  {
-    "id": 2172,
-    "problem_id": 2124,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2124.jpg"
-  },
-  {
-    "id": 2173,
-    "problem_id": 2125,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2125.jpg"
-  },
-  {
-    "id": 2174,
-    "problem_id": 2126,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2126.jpg"
-  },
-  {
-    "id": 2175,
-    "problem_id": 2127,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2127.jpg"
-  },
-  {
-    "id": 2176,
-    "problem_id": 2128,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2128.jpg"
-  },
-  {
-    "id": 2177,
-    "problem_id": 2129,
-    "problem": "line A D, line A B, line B C D, line A C, line A D, line A B, line B C D, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2129.jpg"
-  },
-  {
-    "id": 2178,
-    "problem_id": 2130,
-    "problem": "line D B A, line A C, line B C, line D C, line D B A, line A C, line B C, line D C\nIf y = 18, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2130.jpg"
-  },
-  {
-    "id": 2179,
-    "problem_id": 2131,
-    "problem": "line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson , line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson \nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2131.jpg"
-  },
-  {
-    "id": 2180,
-    "problem_id": 2132,
-    "problem": "line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson , line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson \nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2132.jpg"
-  },
-  {
-    "id": 2181,
-    "problem_id": 2133,
-    "problem": "line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson , line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson \nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2133.jpg"
-  },
-  {
-    "id": 2182,
-    "problem_id": 2134,
-    "problem": "line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson , line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson \nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2134.jpg"
-  },
-  {
-    "id": 2183,
-    "problem_id": 2135,
-    "problem": "line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson , line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson \nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2135.jpg"
-  },
-  {
-    "id": 2184,
-    "problem_id": 2136,
-    "problem": "line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson , line A C, line B C, \\odot C0 lieson A B, \\odot C1 lieson \nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2136.jpg"
-  },
-  {
-    "id": 2185,
-    "problem_id": 2137,
-    "problem": "line G A H, line G P B, line G C J, line C P H, line A P J, line H B J, line G A H, line G P B, line G C J, line C P H, line A P J, line H B J\nPA = 2.9, and HC = 10.8. Solve for the length of HP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2137.jpg"
-  },
-  {
-    "id": 2186,
-    "problem_id": 2138,
-    "problem": "line G A H, line G P B, line G C J, line C P H, line A P J, line H B J, line G A H, line G P B, line G C J, line C P H, line A P J, line H B J\nPA = 2.9, and HC = 10.8. Solve for the length of HP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2138.jpg"
-  },
-  {
-    "id": 2187,
-    "problem_id": 2139,
-    "problem": "line G A H, line G P B, line G C J, line C P H, line A P J, line H B J, line G A H, line G P B, line G C J, line C P H, line A P J, line H B J\nPA = 2.9, and HC = 10.8. Solve for the length of HP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2139.jpg"
-  },
-  {
-    "id": 2188,
-    "problem_id": 2140,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2140.jpg"
-  },
-  {
-    "id": 2189,
-    "problem_id": 2141,
-    "problem": "line A B, line D C B, line E D, line E A, line A C, line A B, line D C B, line E D, line E A, line A C\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2141.jpg"
-  },
-  {
-    "id": 2190,
-    "problem_id": 2142,
-    "problem": "line V T S, line Q R S, line Q V, line R T, line V T S, line Q R S, line Q V, line R T\nFind VS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2142.jpg"
-  },
-  {
-    "id": 2191,
-    "problem_id": 2143,
-    "problem": "line V T S, line Q R S, line Q V, line R T, line V T S, line Q R S, line Q V, line R T\nFind VS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2143.jpg"
-  },
-  {
-    "id": 2192,
-    "problem_id": 2144,
-    "problem": "line V T S, line Q R S, line Q V, line R T, line V T S, line Q R S, line Q V, line R T\nFind VS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2144.jpg"
-  },
-  {
-    "id": 2193,
-    "problem_id": 2145,
-    "problem": "line B A, line C B, line C A, line B A, line C B, line C A\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2145.jpg"
-  },
-  {
-    "id": 2194,
-    "problem_id": 2146,
-    "problem": "line B A, line C B, line C A, line B A, line C B, line C A\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2146.jpg"
-  },
-  {
-    "id": 2195,
-    "problem_id": 2147,
-    "problem": "line B A, line C B, line C A, line B A, line C B, line C A\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2147.jpg"
-  },
-  {
-    "id": 2196,
-    "problem_id": 2148,
-    "problem": "line B A, line C B, line C A, line B A, line C B, line C A\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2148.jpg"
-  },
-  {
-    "id": 2197,
-    "problem_id": 2149,
-    "problem": "line B A, line C B, line C A, line B A, line C B, line C A\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2149.jpg"
-  },
-  {
-    "id": 2198,
-    "problem_id": 2150,
-    "problem": "line P N, line P M, line N M, line P N, line P M, line N M\nDetermine \\cos M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2150.jpg"
-  },
-  {
-    "id": 2199,
-    "problem_id": 2151,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the measurement of WV?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2151.jpg"
-  },
-  {
-    "id": 2200,
-    "problem_id": 2152,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the measurement of WV?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2152.jpg"
-  },
-  {
-    "id": 2201,
-    "problem_id": 2153,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the measurement of WV?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2153.jpg"
-  },
-  {
-    "id": 2202,
-    "problem_id": 2154,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. What is the measurement of WV?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2154.jpg"
-  },
-  {
-    "id": 2203,
-    "problem_id": 2155,
-    "problem": "line A F C, line C B, line A B, line D C, line D A, line D F B, line A F C, line C B, line A B, line D C, line D A, line D F B\nUse parallelogram ABCD to find CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2155.jpg"
-  },
-  {
-    "id": 2204,
-    "problem_id": 2156,
-    "problem": "line A F C, line C B, line A B, line D C, line D A, line D F B, line A F C, line C B, line A B, line D C, line D A, line D F B\nUse parallelogram ABCD to find CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2156.jpg"
-  },
-  {
-    "id": 2205,
-    "problem_id": 2157,
-    "problem": "line G A B C, line F E D C, \\odot H lieson E A B D, line G A B C, line F E D C, \\odot H lieson E A B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2157.jpg"
-  },
-  {
-    "id": 2206,
-    "problem_id": 2158,
-    "problem": "line G A B C, line F E D C, \\odot H lieson E A B D, line G A B C, line F E D C, \\odot H lieson E A B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2158.jpg"
-  },
-  {
-    "id": 2207,
-    "problem_id": 2159,
-    "problem": "line G A B C, line F E D C, \\odot H lieson E A B D, line G A B C, line F E D C, \\odot H lieson E A B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2159.jpg"
-  },
-  {
-    "id": 2208,
-    "problem_id": 2160,
-    "problem": "line P Q R, line P Q R\nQ is between P and R. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2160.jpg"
-  },
-  {
-    "id": 2209,
-    "problem_id": 2161,
-    "problem": "line P Q R, line P Q R\nQ is between P and R. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2161.jpg"
-  },
-  {
-    "id": 2210,
-    "problem_id": 2162,
-    "problem": "line P Q R, line P Q R\nQ is between P and R. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2162.jpg"
-  },
-  {
-    "id": 2211,
-    "problem_id": 2163,
-    "problem": "line P Q R, line P Q R\nQ is between P and R. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2163.jpg"
-  },
-  {
-    "id": 2212,
-    "problem_id": 2164,
-    "problem": "line C D, line A C, line A B, line B D, line C D, line A C, line A B, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2164.jpg"
-  },
-  {
-    "id": 2213,
-    "problem_id": 2165,
-    "problem": "line C D, line A C, line A B, line B D, line C D, line A C, line A B, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2165.jpg"
-  },
-  {
-    "id": 2214,
-    "problem_id": 2166,
-    "problem": "line C D, line A C, line A B, line B D, line C D, line A C, line A B, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2166.jpg"
-  },
-  {
-    "id": 2215,
-    "problem_id": 2167,
-    "problem": "line C D, line A C, line A B, line B D, line C D, line A C, line A B, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2167.jpg"
-  },
-  {
-    "id": 2216,
-    "problem_id": 2168,
-    "problem": "line C D, line A C, line A B, line B D, line C D, line A C, line A B, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2168.jpg"
-  },
-  {
-    "id": 2217,
-    "problem_id": 2169,
-    "problem": "line W A X, line V X, \\odot A lieson V W X, line W A X, line V X, \\odot A lieson V W X\nFind m \\widehat VX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2169.jpg"
-  },
-  {
-    "id": 2218,
-    "problem_id": 2170,
-    "problem": "line A C, line A B D, line C D, \\odot A lieson C B, line A C, line A B D, line C D, \\odot A lieson C B\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2170.jpg"
-  },
-  {
-    "id": 2219,
-    "problem_id": 2171,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2171.jpg"
-  },
-  {
-    "id": 2220,
-    "problem_id": 2172,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2172.jpg"
-  },
-  {
-    "id": 2221,
-    "problem_id": 2173,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2173.jpg"
-  },
-  {
-    "id": 2222,
-    "problem_id": 2174,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2174.jpg"
-  },
-  {
-    "id": 2223,
-    "problem_id": 2175,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2175.jpg"
-  },
-  {
-    "id": 2224,
-    "problem_id": 2176,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2176.jpg"
-  },
-  {
-    "id": 2225,
-    "problem_id": 2177,
-    "problem": "line A D, line B E D, line A B, line B C, line D C, line A E C, line A D, line B E D, line A B, line B C, line D C, line A E C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2177.jpg"
-  },
-  {
-    "id": 2226,
-    "problem_id": 2178,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2178.jpg"
-  },
-  {
-    "id": 2227,
-    "problem_id": 2179,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2179.jpg"
-  },
-  {
-    "id": 2228,
-    "problem_id": 2180,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2180.jpg"
-  },
-  {
-    "id": 2229,
-    "problem_id": 2181,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2181.jpg"
-  },
-  {
-    "id": 2230,
-    "problem_id": 2182,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2182.jpg"
-  },
-  {
-    "id": 2231,
-    "problem_id": 2183,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable n in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2183.jpg"
-  },
-  {
-    "id": 2233,
-    "problem_id": 2184,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable n in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2184.jpg"
-  },
-  {
-    "id": 2234,
-    "problem_id": 2185,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2185.jpg"
-  },
-  {
-    "id": 2235,
-    "problem_id": 2186,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2186.jpg"
-  },
-  {
-    "id": 2236,
-    "problem_id": 2187,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2187.jpg"
-  },
-  {
-    "id": 2237,
-    "problem_id": 2188,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2188.jpg"
-  },
-  {
-    "id": 2238,
-    "problem_id": 2189,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2189.jpg"
-  },
-  {
-    "id": 2239,
-    "problem_id": 2190,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2190.jpg"
-  },
-  {
-    "id": 2240,
-    "problem_id": 2191,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2191.jpg"
-  },
-  {
-    "id": 2241,
-    "problem_id": 2192,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2192.jpg"
-  },
-  {
-    "id": 2242,
-    "problem_id": 2193,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2193.jpg"
-  },
-  {
-    "id": 2243,
-    "problem_id": 2194,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2194.jpg"
-  },
-  {
-    "id": 2244,
-    "problem_id": 2195,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2195.jpg"
-  },
-  {
-    "id": 2245,
-    "problem_id": 2196,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2196.jpg"
-  },
-  {
-    "id": 2246,
-    "problem_id": 2197,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2197.jpg"
-  },
-  {
-    "id": 2247,
-    "problem_id": 2198,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2198.jpg"
-  },
-  {
-    "id": 2248,
-    "problem_id": 2199,
-    "problem": "line A B, line B E, line E F G, line H G, line C H, line A C, line D F, line A B, line B E, line E F G, line H G, line C H, line A C, line D F\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2199.jpg"
-  },
-  {
-    "id": 2249,
-    "problem_id": 2200,
-    "problem": "line A B, line D C A, line C B, line A B, line D C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2200.jpg"
-  },
-  {
-    "id": 2250,
-    "problem_id": 2201,
-    "problem": "line A B, line D C A, line C B, line A B, line D C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2201.jpg"
-  },
-  {
-    "id": 2251,
-    "problem_id": 2202,
-    "problem": "line B C, line E D C, line A E, line A B, line B E, line B D, line B C, line E D C, line A E, line A B, line B E, line B D\nm \\angle DBE = 50. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2202.jpg"
-  },
-  {
-    "id": 2252,
-    "problem_id": 2203,
-    "problem": "line B C, line E D C, line A E, line A B, line B E, line B D, line B C, line E D C, line A E, line A B, line B E, line B D\nm \\angle DBE = 50. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2203.jpg"
-  },
-  {
-    "id": 2253,
-    "problem_id": 2204,
-    "problem": "line B C, line E D C, line A E, line A B, line B E, line B D, line B C, line E D C, line A E, line A B, line B E, line B D\nm \\angle DBE = 50. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2204.jpg"
-  },
-  {
-    "id": 2254,
-    "problem_id": 2205,
-    "problem": "line B C, line E D C, line A E, line A B, line B E, line B D, line B C, line E D C, line A E, line A B, line B E, line B D\nm \\angle DBE = 50. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2205.jpg"
-  },
-  {
-    "id": 2255,
-    "problem_id": 2206,
-    "problem": "line B C, line E D C, line A E, line A B, line B E, line B D, line B C, line E D C, line A E, line A B, line B E, line B D\nm \\angle DBE = 50. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2206.jpg"
-  },
-  {
-    "id": 2256,
-    "problem_id": 2207,
-    "problem": "line B C, line E D C, line A E, line A B, line B E, line B D, line B C, line E D C, line A E, line A B, line B E, line B D\nm \\angle DBE = 50. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2207.jpg"
-  },
-  {
-    "id": 2257,
-    "problem_id": 2208,
-    "problem": "line L J N, line J M, line K P, \\odot J lieson K L M N P, line L J N, line J M, line K P, \\odot J lieson K L M N P\nIf JM = 12.4, what is LN?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2208.jpg"
-  },
-  {
-    "id": 2258,
-    "problem_id": 2209,
-    "problem": "line S B, line S A, line S T, line A T B, line S B, line S A, line S T, line A T B\nWhat is the area of \\triangle SAB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2209.jpg"
-  },
-  {
-    "id": 2259,
-    "problem_id": 2210,
-    "problem": "line S B, line S A, line S T, line A T B, line S B, line S A, line S T, line A T B\nWhat is the area of \\triangle SAB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2210.jpg"
-  },
-  {
-    "id": 2260,
-    "problem_id": 2211,
-    "problem": "line S B, line S A, line S T, line A T B, line S B, line S A, line S T, line A T B\nWhat is the area of \\triangle SAB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2211.jpg"
-  },
-  {
-    "id": 2261,
-    "problem_id": 2212,
-    "problem": "line S B, line S A, line S T, line A T B, line S B, line S A, line S T, line A T B\nWhat is the area of \\triangle SAB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2212.jpg"
-  },
-  {
-    "id": 2262,
-    "problem_id": 2213,
-    "problem": "line S B, line S A, line S T, line A T B, line S B, line S A, line S T, line A T B\nWhat is the area of \\triangle SAB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2213.jpg"
-  },
-  {
-    "id": 2263,
-    "problem_id": 2214,
-    "problem": "line S B, line S A, line S T, line A T B, line S B, line S A, line S T, line A T B\nWhat is the area of \\triangle SAB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2214.jpg"
-  },
-  {
-    "id": 2264,
-    "problem_id": 2215,
-    "problem": "line I G F, line A E F, line A B C, line H G E B D, line I G F, line A E F, line A B C, line H G E B D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2215.jpg"
-  },
-  {
-    "id": 2265,
-    "problem_id": 2216,
-    "problem": "line I G F, line A E F, line A B C, line H G E B D, line I G F, line A E F, line A B C, line H G E B D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2216.jpg"
-  },
-  {
-    "id": 2266,
-    "problem_id": 2217,
-    "problem": "line I G F, line A E F, line A B C, line H G E B D, line I G F, line A E F, line A B C, line H G E B D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2217.jpg"
-  },
-  {
-    "id": 2267,
-    "problem_id": 2218,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line E C A, line B A, line A D, line E D, line B E, line B C D, line E C A\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2218.jpg"
-  },
-  {
-    "id": 2268,
-    "problem_id": 2219,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line E C A, line B A, line A D, line E D, line B E, line B C D, line E C A\nWhat is the perimeter of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2219.jpg"
-  },
-  {
-    "id": 2269,
-    "problem_id": 2220,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2220.jpg"
-  },
-  {
-    "id": 2270,
-    "problem_id": 2221,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2221.jpg"
-  },
-  {
-    "id": 2271,
-    "problem_id": 2222,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2222.jpg"
-  },
-  {
-    "id": 2272,
-    "problem_id": 2223,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2223.jpg"
-  },
-  {
-    "id": 2273,
-    "problem_id": 2224,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2224.jpg"
-  },
-  {
-    "id": 2274,
-    "problem_id": 2225,
-    "problem": "line A D, line B D, line C D, line C B A, line A D, line B D, line C D, line C B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2225.jpg"
-  },
-  {
-    "id": 2275,
-    "problem_id": 2226,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2226.jpg"
-  },
-  {
-    "id": 2276,
-    "problem_id": 2227,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2227.jpg"
-  },
-  {
-    "id": 2277,
-    "problem_id": 2228,
-    "problem": "line G J, line H G, line K J, line H K, line G J, line H G, line K J, line H K\nFind the measure of \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2228.jpg"
-  },
-  {
-    "id": 2278,
-    "problem_id": 2229,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2229.jpg"
-  },
-  {
-    "id": 2279,
-    "problem_id": 2230,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2230.jpg"
-  },
-  {
-    "id": 2280,
-    "problem_id": 2231,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2231.jpg"
-  },
-  {
-    "id": 2281,
-    "problem_id": 2232,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2232.jpg"
-  },
-  {
-    "id": 2282,
-    "problem_id": 2233,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2233.jpg"
-  },
-  {
-    "id": 2283,
-    "problem_id": 2234,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2234.jpg"
-  },
-  {
-    "id": 2284,
-    "problem_id": 2235,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind the length of FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2235.jpg"
-  },
-  {
-    "id": 2285,
-    "problem_id": 2236,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2236.jpg"
-  },
-  {
-    "id": 2286,
-    "problem_id": 2237,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2237.jpg"
-  },
-  {
-    "id": 2287,
-    "problem_id": 2238,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2238.jpg"
-  },
-  {
-    "id": 2288,
-    "problem_id": 2239,
-    "problem": "line Z Y, line Z X, line Y N X, line Z N, line Z Y, line Z X, line Y N X, line Z N\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2239.jpg"
-  },
-  {
-    "id": 2289,
-    "problem_id": 2240,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2240.jpg"
-  },
-  {
-    "id": 2290,
-    "problem_id": 2241,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2241.jpg"
-  },
-  {
-    "id": 2291,
-    "problem_id": 2242,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2242.jpg"
-  },
-  {
-    "id": 2292,
-    "problem_id": 2243,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2243.jpg"
-  },
-  {
-    "id": 2293,
-    "problem_id": 2244,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2244.jpg"
-  },
-  {
-    "id": 2294,
-    "problem_id": 2245,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2245.jpg"
-  },
-  {
-    "id": 2295,
-    "problem_id": 2246,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2246.jpg"
-  },
-  {
-    "id": 2296,
-    "problem_id": 2247,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2247.jpg"
-  },
-  {
-    "id": 2297,
-    "problem_id": 2248,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2248.jpg"
-  },
-  {
-    "id": 2298,
-    "problem_id": 2249,
-    "problem": "line C A, line A D, line E D, line C E, \\odot B lieson C E D A, line C A, line A D, line E D, line C E, \\odot B lieson C E D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2249.jpg"
-  },
-  {
-    "id": 2299,
-    "problem_id": 2250,
-    "problem": "line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C, line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2250.jpg"
-  },
-  {
-    "id": 2300,
-    "problem_id": 2251,
-    "problem": "line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C, line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2251.jpg"
-  },
-  {
-    "id": 2301,
-    "problem_id": 2252,
-    "problem": "line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C, line A C B, line A E H, line H J I, line B G I, line F D B, \\odot F0 lieson A H I B, \\odot F1 lieson E J G D C\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2252.jpg"
-  },
-  {
-    "id": 2302,
-    "problem_id": 2253,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2253.jpg"
-  },
-  {
-    "id": 2303,
-    "problem_id": 2254,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2254.jpg"
-  },
-  {
-    "id": 2304,
-    "problem_id": 2255,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2255.jpg"
-  },
-  {
-    "id": 2305,
-    "problem_id": 2256,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2256.jpg"
-  },
-  {
-    "id": 2306,
-    "problem_id": 2257,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2257.jpg"
-  },
-  {
-    "id": 2307,
-    "problem_id": 2258,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2258.jpg"
-  },
-  {
-    "id": 2308,
-    "problem_id": 2259,
-    "problem": "line X Y, line W Y, line X W, line X Y, line W Y, line X W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2259.jpg"
-  },
-  {
-    "id": 2309,
-    "problem_id": 2260,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2260.jpg"
-  },
-  {
-    "id": 2310,
-    "problem_id": 2261,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2261.jpg"
-  },
-  {
-    "id": 2311,
-    "problem_id": 2262,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2262.jpg"
-  },
-  {
-    "id": 2312,
-    "problem_id": 2263,
-    "problem": "line S P Q, line T P, line P R, \\odot P lieson T S R Q, line S P Q, line T P, line P R, \\odot P lieson T S R Q\nSolve for m \\widehat RQT in \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2263.jpg"
-  },
-  {
-    "id": 2313,
-    "problem_id": 2264,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2264.jpg"
-  },
-  {
-    "id": 2314,
-    "problem_id": 2265,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2265.jpg"
-  },
-  {
-    "id": 2315,
-    "problem_id": 2266,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2266.jpg"
-  },
-  {
-    "id": 2316,
-    "problem_id": 2267,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2267.jpg"
-  },
-  {
-    "id": 2318,
-    "problem_id": 2268,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the value of variable q in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2268.jpg"
-  },
-  {
-    "id": 2319,
-    "problem_id": 2269,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nFind the value of variable q in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2269.jpg"
-  },
-  {
-    "id": 2320,
-    "problem_id": 2270,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2270.jpg"
-  },
-  {
-    "id": 2321,
-    "problem_id": 2271,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2271.jpg"
-  },
-  {
-    "id": 2322,
-    "problem_id": 2272,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2272.jpg"
-  },
-  {
-    "id": 2323,
-    "problem_id": 2273,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2273.jpg"
-  },
-  {
-    "id": 2324,
-    "problem_id": 2274,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2274.jpg"
-  },
-  {
-    "id": 2325,
-    "problem_id": 2275,
-    "problem": "line A C, line B C D, line C E, line A C, line B C D, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2275.jpg"
-  },
-  {
-    "id": 2326,
-    "problem_id": 2276,
-    "problem": "line A C, line B C D, line C E, line A C, line B C D, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2276.jpg"
-  },
-  {
-    "id": 2327,
-    "problem_id": 2277,
-    "problem": "line A C, line B C D, line C E, line A C, line B C D, line C E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2277.jpg"
-  },
-  {
-    "id": 2328,
-    "problem_id": 2278,
-    "problem": "line K A M, line L M, line N M, line K L, line L A N, line K N, line K A M, line L M, line N M, line K L, line L A N, line K N\nQuadrilateral KLMN is a kite. What is m \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2278.jpg"
-  },
-  {
-    "id": 2329,
-    "problem_id": 2279,
-    "problem": "line A B C, line D B, line D C, line A B C, line D B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2279.jpg"
-  },
-  {
-    "id": 2330,
-    "problem_id": 2280,
-    "problem": "line A B C, line D B, line D C, line A B C, line D B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2280.jpg"
-  },
-  {
-    "id": 2331,
-    "problem_id": 2281,
-    "problem": "line A B C, line D B, line D C, line A B C, line D B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2281.jpg"
-  },
-  {
-    "id": 2332,
-    "problem_id": 2282,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If CF = 4x+1 and DF = x+13, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2282.jpg"
-  },
-  {
-    "id": 2333,
-    "problem_id": 2283,
-    "problem": "line D C, line B C, line A B, line A D, line D F B, line A F C, line D C, line B C, line A B, line A D, line D F B, line A F C\nABCD is a rectangle. If CF = 4x+1 and DF = x+13, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2283.jpg"
-  },
-  {
-    "id": 2334,
-    "problem_id": 2284,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2284.jpg"
-  },
-  {
-    "id": 2335,
-    "problem_id": 2285,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2285.jpg"
-  },
-  {
-    "id": 2336,
-    "problem_id": 2286,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2286.jpg"
-  },
-  {
-    "id": 2337,
-    "problem_id": 2287,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2287.jpg"
-  },
-  {
-    "id": 2338,
-    "problem_id": 2288,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2288.jpg"
-  },
-  {
-    "id": 2339,
-    "problem_id": 2289,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2289.jpg"
-  },
-  {
-    "id": 2340,
-    "problem_id": 2290,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2290.jpg"
-  },
-  {
-    "id": 2341,
-    "problem_id": 2291,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2291.jpg"
-  },
-  {
-    "id": 2342,
-    "problem_id": 2292,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2292.jpg"
-  },
-  {
-    "id": 2343,
-    "problem_id": 2293,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2293.jpg"
-  },
-  {
-    "id": 2344,
-    "problem_id": 2294,
-    "problem": "line A C F H, line E F G, line B C D, line A C F H, line E F G, line B C D\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2294.jpg"
-  },
-  {
-    "id": 2345,
-    "problem_id": 2295,
-    "problem": "line D B A, line A C, line B C, line D C, line D B A, line A C, line B C, line D C\nIf x = 14, find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2295.jpg"
-  },
-  {
-    "id": 2346,
-    "problem_id": 2296,
-    "problem": "line S R, line T R, line T S, line S R, line T R, line T S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2296.jpg"
-  },
-  {
-    "id": 2347,
-    "problem_id": 2297,
-    "problem": "line S R, line T R, line T S, line S R, line T R, line T S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2297.jpg"
-  },
-  {
-    "id": 2348,
-    "problem_id": 2298,
-    "problem": "line S R, line T R, line T S, line S R, line T R, line T S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2298.jpg"
-  },
-  {
-    "id": 2349,
-    "problem_id": 2299,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2299.jpg"
-  },
-  {
-    "id": 2350,
-    "problem_id": 2300,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2300.jpg"
-  },
-  {
-    "id": 2351,
-    "problem_id": 2301,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2301.jpg"
-  },
-  {
-    "id": 2352,
-    "problem_id": 2302,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2302.jpg"
-  },
-  {
-    "id": 2353,
-    "problem_id": 2303,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2303.jpg"
-  },
-  {
-    "id": 2354,
-    "problem_id": 2304,
-    "problem": "line C B A, line D C, line D B, line C B A, line D C, line D B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2304.jpg"
-  },
-  {
-    "id": 2355,
-    "problem_id": 2305,
-    "problem": "line C B A, line D C, line D B, line C B A, line D C, line D B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2305.jpg"
-  },
-  {
-    "id": 2356,
-    "problem_id": 2306,
-    "problem": "line I E Y B D H, line G X Y Z K, line F A B C J, line I E Y B D H, line G X Y Z K, line F A B C J\nFind m \\angle CBY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2306.jpg"
-  },
-  {
-    "id": 2357,
-    "problem_id": 2307,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2307.jpg"
-  },
-  {
-    "id": 2358,
-    "problem_id": 2308,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2308.jpg"
-  },
-  {
-    "id": 2360,
-    "problem_id": 2309,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2309.jpg"
-  },
-  {
-    "id": 2361,
-    "problem_id": 2310,
-    "problem": "line C B, line F E, line D A, line B E A, line C F D, line C B, line F E, line D A, line B E A, line C F D\nIn trapezoid ABCE, what is the length sum of BC and DA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2310.jpg"
-  },
-  {
-    "id": 2362,
-    "problem_id": 2311,
-    "problem": "line B C, line B D, line A C, line B A, line D C, line B C, line B D, line A C, line B A, line D C\nFind the value of a that would make the quadrilateral a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2311.jpg"
-  },
-  {
-    "id": 2363,
-    "problem_id": 2312,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle JKL of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2312.jpg"
-  },
-  {
-    "id": 2364,
-    "problem_id": 2313,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle JKL of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2313.jpg"
-  },
-  {
-    "id": 2365,
-    "problem_id": 2314,
-    "problem": "line K L, line L M, line J M, line J K, line K L, line L M, line J M, line J K\nFind the measurement of \\angle JKL of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2314.jpg"
-  },
-  {
-    "id": 2367,
-    "problem_id": 2315,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2315.jpg"
-  },
-  {
-    "id": 2368,
-    "problem_id": 2316,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2316.jpg"
-  },
-  {
-    "id": 2369,
-    "problem_id": 2317,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2317.jpg"
-  },
-  {
-    "id": 2370,
-    "problem_id": 2318,
-    "problem": "line A B, line C A D, line D E F, line C G F, \\odot B lieson A E G, line A B, line C A D, line D E F, line C G F, \\odot B lieson A E G\nFind the area of the circle. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2318.jpg"
-  },
-  {
-    "id": 2371,
-    "problem_id": 2319,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2319.jpg"
-  },
-  {
-    "id": 2372,
-    "problem_id": 2320,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2320.jpg"
-  },
-  {
-    "id": 2373,
-    "problem_id": 2321,
-    "problem": "line A D, line D E, line B E, line A B, line A C E, line B C D, line A D, line D E, line B E, line A B, line A C E, line B C D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2321.jpg"
-  },
-  {
-    "id": 2374,
-    "problem_id": 2322,
-    "problem": "line A D, line D E, line B E, line A B, line A C E, line B C D, line A D, line D E, line B E, line A B, line A C E, line B C D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2322.jpg"
-  },
-  {
-    "id": 2375,
-    "problem_id": 2323,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2323.jpg"
-  },
-  {
-    "id": 2376,
-    "problem_id": 2324,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2324.jpg"
-  },
-  {
-    "id": 2377,
-    "problem_id": 2325,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2325.jpg"
-  },
-  {
-    "id": 2378,
-    "problem_id": 2326,
-    "problem": "line B A, line C D, \\odot E lieson B C D A, line B A, line C D, \\odot E lieson B C D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2326.jpg"
-  },
-  {
-    "id": 2379,
-    "problem_id": 2327,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2327.jpg"
-  },
-  {
-    "id": 2380,
-    "problem_id": 2328,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2328.jpg"
-  },
-  {
-    "id": 2381,
-    "problem_id": 2329,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2329.jpg"
-  },
-  {
-    "id": 2382,
-    "problem_id": 2330,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2330.jpg"
-  },
-  {
-    "id": 2383,
-    "problem_id": 2331,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2331.jpg"
-  },
-  {
-    "id": 2384,
-    "problem_id": 2332,
-    "problem": "line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C, line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C\nFind the area of the regular polygon. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2332.jpg"
-  },
-  {
-    "id": 2385,
-    "problem_id": 2333,
-    "problem": "line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C, line B A, line B C, line C D, line D E, line F E, line A F, line G E, \\odot G lieson B A F E D C\nFind the area of the regular polygon. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2333.jpg"
-  },
-  {
-    "id": 2386,
-    "problem_id": 2334,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2334.jpg"
-  },
-  {
-    "id": 2387,
-    "problem_id": 2335,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2335.jpg"
-  },
-  {
-    "id": 2388,
-    "problem_id": 2336,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2336.jpg"
-  },
-  {
-    "id": 2389,
-    "problem_id": 2337,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2337.jpg"
-  },
-  {
-    "id": 2390,
-    "problem_id": 2338,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nSolve for the measure of \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2338.jpg"
-  },
-  {
-    "id": 2391,
-    "problem_id": 2339,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2339.jpg"
-  },
-  {
-    "id": 2392,
-    "problem_id": 2340,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2340.jpg"
-  },
-  {
-    "id": 2393,
-    "problem_id": 2341,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2341.jpg"
-  },
-  {
-    "id": 2394,
-    "problem_id": 2342,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2342.jpg"
-  },
-  {
-    "id": 2395,
-    "problem_id": 2343,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2343.jpg"
-  },
-  {
-    "id": 2396,
-    "problem_id": 2344,
-    "problem": "line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2344.jpg"
-  },
-  {
-    "id": 2397,
-    "problem_id": 2345,
-    "problem": "line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2345.jpg"
-  },
-  {
-    "id": 2398,
-    "problem_id": 2346,
-    "problem": "line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2346.jpg"
-  },
-  {
-    "id": 2399,
-    "problem_id": 2347,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2347.jpg"
-  },
-  {
-    "id": 2400,
-    "problem_id": 2348,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2348.jpg"
-  },
-  {
-    "id": 2401,
-    "problem_id": 2349,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2349.jpg"
-  },
-  {
-    "id": 2402,
-    "problem_id": 2350,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2350.jpg"
-  },
-  {
-    "id": 2403,
-    "problem_id": 2351,
-    "problem": "line A C, line C E, line A E, line A B, line B C D, line E D, line A C, line C E, line A E, line A B, line B C D, line E D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2351.jpg"
-  },
-  {
-    "id": 2404,
-    "problem_id": 2352,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat BAD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2352.jpg"
-  },
-  {
-    "id": 2405,
-    "problem_id": 2353,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2353.jpg"
-  },
-  {
-    "id": 2406,
-    "problem_id": 2354,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2354.jpg"
-  },
-  {
-    "id": 2407,
-    "problem_id": 2355,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2355.jpg"
-  },
-  {
-    "id": 2408,
-    "problem_id": 2356,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2356.jpg"
-  },
-  {
-    "id": 2409,
-    "problem_id": 2357,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2357.jpg"
-  },
-  {
-    "id": 2410,
-    "problem_id": 2358,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2358.jpg"
-  },
-  {
-    "id": 2411,
-    "problem_id": 2359,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2359.jpg"
-  },
-  {
-    "id": 2412,
-    "problem_id": 2360,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2360.jpg"
-  },
-  {
-    "id": 2413,
-    "problem_id": 2361,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2361.jpg"
-  },
-  {
-    "id": 2414,
-    "problem_id": 2362,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2362.jpg"
-  },
-  {
-    "id": 2415,
-    "problem_id": 2363,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2363.jpg"
-  },
-  {
-    "id": 2416,
-    "problem_id": 2364,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2364.jpg"
-  },
-  {
-    "id": 2417,
-    "problem_id": 2365,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2365.jpg"
-  },
-  {
-    "id": 2418,
-    "problem_id": 2366,
-    "problem": "line K L, line J L, line J K, line T S, line S R, line T R, line K L, line J L, line J K, line T S, line S R, line T R\nFind SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2366.jpg"
-  },
-  {
-    "id": 2419,
-    "problem_id": 2367,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2367.jpg"
-  },
-  {
-    "id": 2420,
-    "problem_id": 2368,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2368.jpg"
-  },
-  {
-    "id": 2421,
-    "problem_id": 2369,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2369.jpg"
-  },
-  {
-    "id": 2422,
-    "problem_id": 2370,
-    "problem": "line A C D, line B C, line B A, line B D, line A C D, line B C, line B A, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2370.jpg"
-  },
-  {
-    "id": 2423,
-    "problem_id": 2371,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2371.jpg"
-  },
-  {
-    "id": 2424,
-    "problem_id": 2372,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2372.jpg"
-  },
-  {
-    "id": 2425,
-    "problem_id": 2373,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2373.jpg"
-  },
-  {
-    "id": 2426,
-    "problem_id": 2374,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2374.jpg"
-  },
-  {
-    "id": 2427,
-    "problem_id": 2375,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2375.jpg"
-  },
-  {
-    "id": 2428,
-    "problem_id": 2376,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2376.jpg"
-  },
-  {
-    "id": 2429,
-    "problem_id": 2377,
-    "problem": "line A B, line C B, line D B, line A D C, line A B, line C B, line D B, line A D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2377.jpg"
-  },
-  {
-    "id": 2430,
-    "problem_id": 2378,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nFind the measure of \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2378.jpg"
-  },
-  {
-    "id": 2431,
-    "problem_id": 2379,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2379.jpg"
-  },
-  {
-    "id": 2432,
-    "problem_id": 2380,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2380.jpg"
-  },
-  {
-    "id": 2433,
-    "problem_id": 2381,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2381.jpg"
-  },
-  {
-    "id": 2434,
-    "problem_id": 2382,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2382.jpg"
-  },
-  {
-    "id": 2435,
-    "problem_id": 2383,
-    "problem": "line A D, line A B C, line C E, line D E, line B D, line A D, line A B C, line C E, line D E, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2383.jpg"
-  },
-  {
-    "id": 2436,
-    "problem_id": 2384,
-    "problem": "line A D, line A B C, line C E, line D E, line B D, line A D, line A B C, line C E, line D E, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2384.jpg"
-  },
-  {
-    "id": 2437,
-    "problem_id": 2385,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2385.jpg"
-  },
-  {
-    "id": 2438,
-    "problem_id": 2386,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2386.jpg"
-  },
-  {
-    "id": 2439,
-    "problem_id": 2387,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2387.jpg"
-  },
-  {
-    "id": 2440,
-    "problem_id": 2388,
-    "problem": "line E D, line D C, line A B C, line E B, line E A, line E D, line D C, line A B C, line E B, line E A\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2388.jpg"
-  },
-  {
-    "id": 2441,
-    "problem_id": 2389,
-    "problem": "line E D, line D C, line A B C, line E B, line E A, line E D, line D C, line A B C, line E B, line E A\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2389.jpg"
-  },
-  {
-    "id": 2442,
-    "problem_id": 2390,
-    "problem": "line E D, line D C, line A B C, line E B, line E A, line E D, line D C, line A B C, line E B, line E A\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2390.jpg"
-  },
-  {
-    "id": 2443,
-    "problem_id": 2391,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2391.jpg"
-  },
-  {
-    "id": 2444,
-    "problem_id": 2392,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2392.jpg"
-  },
-  {
-    "id": 2445,
-    "problem_id": 2393,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2393.jpg"
-  },
-  {
-    "id": 2446,
-    "problem_id": 2394,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2394.jpg"
-  },
-  {
-    "id": 2447,
-    "problem_id": 2395,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2395.jpg"
-  },
-  {
-    "id": 2448,
-    "problem_id": 2396,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2396.jpg"
-  },
-  {
-    "id": 2449,
-    "problem_id": 2397,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2397.jpg"
-  },
-  {
-    "id": 2450,
-    "problem_id": 2398,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 9?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2398.jpg"
-  },
-  {
-    "id": 2451,
-    "problem_id": 2399,
-    "problem": "line D E F, line H G F, line D J G, line E J H, \\odot A lieson D H G E, line D E F, line H G F, line D J G, line E J H, \\odot A lieson D H G E\nFind m \\widehat DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2399.jpg"
-  },
-  {
-    "id": 2452,
-    "problem_id": 2400,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2400.jpg"
-  },
-  {
-    "id": 2453,
-    "problem_id": 2401,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2401.jpg"
-  },
-  {
-    "id": 2454,
-    "problem_id": 2402,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2402.jpg"
-  },
-  {
-    "id": 2455,
-    "problem_id": 2403,
-    "problem": "line A B C, line A D, line D C, line D B, line A B C, line A D, line D C, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2403.jpg"
-  },
-  {
-    "id": 2456,
-    "problem_id": 2404,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2404.jpg"
-  },
-  {
-    "id": 2457,
-    "problem_id": 2405,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2405.jpg"
-  },
-  {
-    "id": 2458,
-    "problem_id": 2406,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Solve for the length of PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2406.jpg"
-  },
-  {
-    "id": 2459,
-    "problem_id": 2407,
-    "problem": "line L M, line K M, line L K, line L M, line K M, line L K\nExpress the ratio of \\sin M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2407.jpg"
-  },
-  {
-    "id": 2460,
-    "problem_id": 2408,
-    "problem": "line L M, line K M, line L K, line L M, line K M, line L K\nExpress the ratio of \\sin M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2408.jpg"
-  },
-  {
-    "id": 2461,
-    "problem_id": 2409,
-    "problem": "line L M, line K M, line L K, line L M, line K M, line L K\nExpress the ratio of \\sin M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2409.jpg"
-  },
-  {
-    "id": 2462,
-    "problem_id": 2410,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2410.jpg"
-  },
-  {
-    "id": 2463,
-    "problem_id": 2411,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2411.jpg"
-  },
-  {
-    "id": 2464,
-    "problem_id": 2412,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2412.jpg"
-  },
-  {
-    "id": 2465,
-    "problem_id": 2413,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2413.jpg"
-  },
-  {
-    "id": 2466,
-    "problem_id": 2414,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2414.jpg"
-  },
-  {
-    "id": 2467,
-    "problem_id": 2415,
-    "problem": "line A D, line D C, line B C, line A B, line A E C, line B E D, line A D, line D C, line B C, line A B, line A E C, line B E D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2415.jpg"
-  },
-  {
-    "id": 2468,
-    "problem_id": 2416,
-    "problem": "line D C, line D B, line D A, line A B, line B C, \\odot B lieson D A C, line D C, line D B, line D A, line A B, line B C, \\odot B lieson D A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2416.jpg"
-  },
-  {
-    "id": 2469,
-    "problem_id": 2417,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2417.jpg"
-  },
-  {
-    "id": 2470,
-    "problem_id": 2418,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2418.jpg"
-  },
-  {
-    "id": 2471,
-    "problem_id": 2419,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2419.jpg"
-  },
-  {
-    "id": 2472,
-    "problem_id": 2420,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2420.jpg"
-  },
-  {
-    "id": 2473,
-    "problem_id": 2421,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2421.jpg"
-  },
-  {
-    "id": 2474,
-    "problem_id": 2422,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2422.jpg"
-  },
-  {
-    "id": 2475,
-    "problem_id": 2423,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2423.jpg"
-  },
-  {
-    "id": 2476,
-    "problem_id": 2424,
-    "problem": "line A B, line C B, line D B, line E A, line E D C, line A B, line C B, line D B, line E A, line E D C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2424.jpg"
-  },
-  {
-    "id": 2477,
-    "problem_id": 2425,
-    "problem": "line A B, line C B, line D B, line E A, line E D C, line A B, line C B, line D B, line E A, line E D C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2425.jpg"
-  },
-  {
-    "id": 2478,
-    "problem_id": 2426,
-    "problem": "line A B, line C B, line D B, line E A, line E D C, line A B, line C B, line D B, line E A, line E D C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2426.jpg"
-  },
-  {
-    "id": 2479,
-    "problem_id": 2427,
-    "problem": "line A B, line C B, line D B, line E A, line E D C, line A B, line C B, line D B, line E A, line E D C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2427.jpg"
-  },
-  {
-    "id": 2480,
-    "problem_id": 2428,
-    "problem": "line M N R, line M N R\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2428.jpg"
-  },
-  {
-    "id": 2481,
-    "problem_id": 2429,
-    "problem": "line M N R, line M N R\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2429.jpg"
-  },
-  {
-    "id": 2482,
-    "problem_id": 2430,
-    "problem": "line M N R, line M N R\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2430.jpg"
-  },
-  {
-    "id": 2483,
-    "problem_id": 2431,
-    "problem": "line M N R, line M N R\nFind MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2431.jpg"
-  },
-  {
-    "id": 2484,
-    "problem_id": 2432,
-    "problem": "line A B C, line D C, line D B, line E D, line E A, line A B C, line D C, line D B, line E D, line E A\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2432.jpg"
-  },
-  {
-    "id": 2485,
-    "problem_id": 2433,
-    "problem": "line A B C, line D C, line D B, line E D, line E A, line A B C, line D C, line D B, line E D, line E A\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2433.jpg"
-  },
-  {
-    "id": 2486,
-    "problem_id": 2434,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2434.jpg"
-  },
-  {
-    "id": 2487,
-    "problem_id": 2435,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2435.jpg"
-  },
-  {
-    "id": 2488,
-    "problem_id": 2436,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2436.jpg"
-  },
-  {
-    "id": 2489,
-    "problem_id": 2437,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2437.jpg"
-  },
-  {
-    "id": 2490,
-    "problem_id": 2438,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2438.jpg"
-  },
-  {
-    "id": 2491,
-    "problem_id": 2439,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2439.jpg"
-  },
-  {
-    "id": 2492,
-    "problem_id": 2440,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2440.jpg"
-  },
-  {
-    "id": 2493,
-    "problem_id": 2441,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2441.jpg"
-  },
-  {
-    "id": 2494,
-    "problem_id": 2442,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2442.jpg"
-  },
-  {
-    "id": 2495,
-    "problem_id": 2443,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2443.jpg"
-  },
-  {
-    "id": 2496,
-    "problem_id": 2444,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2444.jpg"
-  },
-  {
-    "id": 2497,
-    "problem_id": 2445,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2445.jpg"
-  },
-  {
-    "id": 2498,
-    "problem_id": 2446,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2446.jpg"
-  },
-  {
-    "id": 2499,
-    "problem_id": 2447,
-    "problem": "line D C G E, line D A B, line F G B, line F E, \\odot H lieson A C F E B, line D C G E, line D A B, line F G B, line F E, \\odot H lieson A C F E B\nFind m \\angle EDB if m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2447.jpg"
-  },
-  {
-    "id": 2500,
-    "problem_id": 2448,
-    "problem": "line D C G E, line D A B, line F G B, line F E, \\odot H lieson A C F E B, line D C G E, line D A B, line F G B, line F E, \\odot H lieson A C F E B\nFind m \\angle EDB if m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2448.jpg"
-  },
-  {
-    "id": 2501,
-    "problem_id": 2449,
-    "problem": "line D C G E, line D A B, line F G B, line F E, \\odot H lieson A C F E B, line D C G E, line D A B, line F G B, line F E, \\odot H lieson A C F E B\nFind m \\angle EDB if m \\widehat FE = 118, m \\widehat AB = 108, m \\angle EGB = 52, and m \\angle EFB = 30.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2449.jpg"
-  },
-  {
-    "id": 2502,
-    "problem_id": 2450,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2450.jpg"
-  },
-  {
-    "id": 2503,
-    "problem_id": 2451,
-    "problem": "line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F, line A G, line B H, line C D, line G H, line C E, line D F, line A B, line E F\nPolygon CDFE \\sim polygon HGAB. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2451.jpg"
-  },
-  {
-    "id": 2504,
-    "problem_id": 2452,
-    "problem": "line T W, line U V, line V W, line U T, line T W, line U V, line V W, line U T\nTUVW is a parallelogram. Solve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2452.jpg"
-  },
-  {
-    "id": 2505,
-    "problem_id": 2453,
-    "problem": "line T W, line U V, line V W, line U T, line T W, line U V, line V W, line U T\nTUVW is a parallelogram. Solve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2453.jpg"
-  },
-  {
-    "id": 2506,
-    "problem_id": 2454,
-    "problem": "line T W, line U V, line V W, line U T, line T W, line U V, line V W, line U T\nTUVW is a parallelogram. Solve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2454.jpg"
-  },
-  {
-    "id": 2507,
-    "problem_id": 2455,
-    "problem": "line T W, line U V, line V W, line U T, line T W, line U V, line V W, line U T\nTUVW is a parallelogram. Solve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2455.jpg"
-  },
-  {
-    "id": 2508,
-    "problem_id": 2456,
-    "problem": "line T W, line U V, line V W, line U T, line T W, line U V, line V W, line U T\nTUVW is a parallelogram. Solve for a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2456.jpg"
-  },
-  {
-    "id": 2509,
-    "problem_id": 2457,
-    "problem": "line Z Y, line X Y, line W X, line W Z, line Z Y, line X Y, line W X, line W Z\nUse parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2457.jpg"
-  },
-  {
-    "id": 2510,
-    "problem_id": 2458,
-    "problem": "line Z Y, line X Y, line W X, line W Z, line Z Y, line X Y, line W X, line W Z\nUse parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2458.jpg"
-  },
-  {
-    "id": 2511,
-    "problem_id": 2459,
-    "problem": "line Z Y, line X Y, line W X, line W Z, line Z Y, line X Y, line W X, line W Z\nUse parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2459.jpg"
-  },
-  {
-    "id": 2512,
-    "problem_id": 2460,
-    "problem": "line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D, line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D\nQuadrilateral ABGF \\sim quadrilateral CDHE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2460.jpg"
-  },
-  {
-    "id": 2513,
-    "problem_id": 2461,
-    "problem": "line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D, line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D\nQuadrilateral ABGF \\sim quadrilateral CDHE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2461.jpg"
-  },
-  {
-    "id": 2514,
-    "problem_id": 2462,
-    "problem": "line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D, line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D\nQuadrilateral ABGF \\sim quadrilateral CDHE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2462.jpg"
-  },
-  {
-    "id": 2515,
-    "problem_id": 2463,
-    "problem": "line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D, line F G, line B G, line E H, line A B, line D H, line A F, line C E, line C D\nQuadrilateral ABGF \\sim quadrilateral CDHE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2463.jpg"
-  },
-  {
-    "id": 2516,
-    "problem_id": 2464,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2464.jpg"
-  },
-  {
-    "id": 2517,
-    "problem_id": 2465,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2465.jpg"
-  },
-  {
-    "id": 2518,
-    "problem_id": 2466,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2466.jpg"
-  },
-  {
-    "id": 2519,
-    "problem_id": 2467,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2467.jpg"
-  },
-  {
-    "id": 2520,
-    "problem_id": 2468,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2468.jpg"
-  },
-  {
-    "id": 2521,
-    "problem_id": 2469,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2469.jpg"
-  },
-  {
-    "id": 2522,
-    "problem_id": 2470,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2470.jpg"
-  },
-  {
-    "id": 2523,
-    "problem_id": 2471,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2471.jpg"
-  },
-  {
-    "id": 2524,
-    "problem_id": 2472,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2472.jpg"
-  },
-  {
-    "id": 2525,
-    "problem_id": 2473,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2473.jpg"
-  },
-  {
-    "id": 2526,
-    "problem_id": 2474,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2474.jpg"
-  },
-  {
-    "id": 2527,
-    "problem_id": 2475,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2475.jpg"
-  },
-  {
-    "id": 2528,
-    "problem_id": 2476,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2476.jpg"
-  },
-  {
-    "id": 2529,
-    "problem_id": 2477,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2477.jpg"
-  },
-  {
-    "id": 2530,
-    "problem_id": 2478,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2478.jpg"
-  },
-  {
-    "id": 2532,
-    "problem_id": 2479,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2479.jpg"
-  },
-  {
-    "id": 2533,
-    "problem_id": 2480,
-    "problem": "line W A Y, line X Y, line X W, line X A, line W A Y, line X Y, line X W, line X A\nTriangle WXY has an area of 248 square inches. Find the length of the base.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2480.jpg"
-  },
-  {
-    "id": 2534,
-    "problem_id": 2481,
-    "problem": "line W A Y, line X Y, line X W, line X A, line W A Y, line X Y, line X W, line X A\nTriangle WXY has an area of 248 square inches. Find the length of the base.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2481.jpg"
-  },
-  {
-    "id": 2535,
-    "problem_id": 2482,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2482.jpg"
-  },
-  {
-    "id": 2536,
-    "problem_id": 2483,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2483.jpg"
-  },
-  {
-    "id": 2537,
-    "problem_id": 2484,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2484.jpg"
-  },
-  {
-    "id": 2538,
-    "problem_id": 2485,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2485.jpg"
-  },
-  {
-    "id": 2539,
-    "problem_id": 2486,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2486.jpg"
-  },
-  {
-    "id": 2540,
-    "problem_id": 2487,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2487.jpg"
-  },
-  {
-    "id": 2541,
-    "problem_id": 2488,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2488.jpg"
-  },
-  {
-    "id": 2542,
-    "problem_id": 2489,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2489.jpg"
-  },
-  {
-    "id": 2543,
-    "problem_id": 2490,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of HB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2490.jpg"
-  },
-  {
-    "id": 2544,
-    "problem_id": 2491,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of HB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2491.jpg"
-  },
-  {
-    "id": 2545,
-    "problem_id": 2492,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of HB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2492.jpg"
-  },
-  {
-    "id": 2546,
-    "problem_id": 2493,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of HB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2493.jpg"
-  },
-  {
-    "id": 2547,
-    "problem_id": 2494,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of HB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2494.jpg"
-  },
-  {
-    "id": 2548,
-    "problem_id": 2495,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2495.jpg"
-  },
-  {
-    "id": 2549,
-    "problem_id": 2496,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2496.jpg"
-  },
-  {
-    "id": 2550,
-    "problem_id": 2497,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2497.jpg"
-  },
-  {
-    "id": 2551,
-    "problem_id": 2498,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2498.jpg"
-  },
-  {
-    "id": 2552,
-    "problem_id": 2499,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2499.jpg"
-  },
-  {
-    "id": 2553,
-    "problem_id": 2500,
-    "problem": "line Q R, line R S, line Q S, line Q R, line R S, line Q S\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2500.jpg"
-  },
-  {
-    "id": 2554,
-    "problem_id": 2501,
-    "problem": "line Q R, line R S, line Q S, line Q R, line R S, line Q S\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2501.jpg"
-  },
-  {
-    "id": 2555,
-    "problem_id": 2502,
-    "problem": "line Q R, line R S, line Q S, line Q R, line R S, line Q S\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2502.jpg"
-  },
-  {
-    "id": 2556,
-    "problem_id": 2503,
-    "problem": "line Q R, line R S, line Q S, line Q R, line R S, line Q S\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2503.jpg"
-  },
-  {
-    "id": 2557,
-    "problem_id": 2504,
-    "problem": "line Q R, line R S, line Q S, line Q R, line R S, line Q S\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2504.jpg"
-  },
-  {
-    "id": 2558,
-    "problem_id": 2505,
-    "problem": "line Q R, line R S, line Q S, line Q R, line R S, line Q S\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2505.jpg"
-  },
-  {
-    "id": 2559,
-    "problem_id": 2506,
-    "problem": "line D A, line A B, line C B, line D C, line D A, line A B, line C B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2506.jpg"
-  },
-  {
-    "id": 2560,
-    "problem_id": 2507,
-    "problem": "line D A, line A B, line C B, line D C, line D A, line A B, line C B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2507.jpg"
-  },
-  {
-    "id": 2561,
-    "problem_id": 2508,
-    "problem": "line D A, line A B, line C B, line D C, line D A, line A B, line C B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2508.jpg"
-  },
-  {
-    "id": 2562,
-    "problem_id": 2509,
-    "problem": "line D A, line A B, line C B, line D C, line D A, line A B, line C B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2509.jpg"
-  },
-  {
-    "id": 2563,
-    "problem_id": 2510,
-    "problem": "line D A, line A B, line C B, line D C, line D A, line A B, line C B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2510.jpg"
-  },
-  {
-    "id": 2564,
-    "problem_id": 2511,
-    "problem": "line D A, line A B, line C B, line D C, line D A, line A B, line C B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2511.jpg"
-  },
-  {
-    "id": 2565,
-    "problem_id": 2512,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nExpress the ratio of \\cos C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2512.jpg"
-  },
-  {
-    "id": 2566,
-    "problem_id": 2513,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nExpress the ratio of \\cos C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2513.jpg"
-  },
-  {
-    "id": 2567,
-    "problem_id": 2514,
-    "problem": "line H X Z C, line F W X E, line B Y Z D, line G W Y A, line H X Z C, line F W X E, line B Y Z D, line G W Y A\nm \\angle 1 = 53. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2514.jpg"
-  },
-  {
-    "id": 2568,
-    "problem_id": 2515,
-    "problem": "line H X Z C, line F W X E, line B Y Z D, line G W Y A, line H X Z C, line F W X E, line B Y Z D, line G W Y A\nm \\angle 1 = 53. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2515.jpg"
-  },
-  {
-    "id": 2570,
-    "problem_id": 2516,
-    "problem": "line A C D, line A C D\nC is the midpoint of DA, what is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2516.jpg"
-  },
-  {
-    "id": 2571,
-    "problem_id": 2517,
-    "problem": "line A C D, line A C D\nC is the midpoint of DA, what is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2517.jpg"
-  },
-  {
-    "id": 2572,
-    "problem_id": 2518,
-    "problem": "line A C, line A B, line C D B, \\odot C lieson A D, line A C, line A B, line C D B, \\odot C lieson A D\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2518.jpg"
-  },
-  {
-    "id": 2573,
-    "problem_id": 2519,
-    "problem": "line S T, line R A S, \\odot A lieson S T R, line S T, line R A S, \\odot A lieson S T R\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2519.jpg"
-  },
-  {
-    "id": 2574,
-    "problem_id": 2520,
-    "problem": "line A B C, line D B, line D C, line D A, line A B C, line D B, line D C, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2520.jpg"
-  },
-  {
-    "id": 2575,
-    "problem_id": 2521,
-    "problem": "line A B C, line D B, line D C, line D A, line A B C, line D B, line D C, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2521.jpg"
-  },
-  {
-    "id": 2576,
-    "problem_id": 2522,
-    "problem": "line A B, line B C, \\odot D lieson A B C, line A B, line B C, \\odot D lieson A B C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2522.jpg"
-  },
-  {
-    "id": 2577,
-    "problem_id": 2523,
-    "problem": "line A B, line B C, \\odot D lieson A B C, line A B, line B C, \\odot D lieson A B C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2523.jpg"
-  },
-  {
-    "id": 2578,
-    "problem_id": 2524,
-    "problem": "line A B, line B C, \\odot D lieson A B C, line A B, line B C, \\odot D lieson A B C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2524.jpg"
-  },
-  {
-    "id": 2579,
-    "problem_id": 2525,
-    "problem": "line A B, line B C, \\odot D lieson A B C, line A B, line B C, \\odot D lieson A B C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2525.jpg"
-  },
-  {
-    "id": 2580,
-    "problem_id": 2526,
-    "problem": "line A B, line B C, \\odot D lieson A B C, line A B, line B C, \\odot D lieson A B C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2526.jpg"
-  },
-  {
-    "id": 2581,
-    "problem_id": 2527,
-    "problem": "line A B, line B C, \\odot D lieson A B C, line A B, line B C, \\odot D lieson A B C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2527.jpg"
-  },
-  {
-    "id": 2582,
-    "problem_id": 2528,
-    "problem": "line A E G F, line C D F, line J E B, line H F, \\odot I lieson A B C D G H J, line A E G F, line C D F, line J E B, line H F, \\odot I lieson A B C D G H J\nFind the length of segment FH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2528.jpg"
-  },
-  {
-    "id": 2583,
-    "problem_id": 2529,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2529.jpg"
-  },
-  {
-    "id": 2584,
-    "problem_id": 2530,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2530.jpg"
-  },
-  {
-    "id": 2585,
-    "problem_id": 2531,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2531.jpg"
-  },
-  {
-    "id": 2586,
-    "problem_id": 2532,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2532.jpg"
-  },
-  {
-    "id": 2587,
-    "problem_id": 2533,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2533.jpg"
-  },
-  {
-    "id": 2588,
-    "problem_id": 2534,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2534.jpg"
-  },
-  {
-    "id": 2589,
-    "problem_id": 2535,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2535.jpg"
-  },
-  {
-    "id": 2590,
-    "problem_id": 2536,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2536.jpg"
-  },
-  {
-    "id": 2591,
-    "problem_id": 2537,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2537.jpg"
-  },
-  {
-    "id": 2592,
-    "problem_id": 2538,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2538.jpg"
-  },
-  {
-    "id": 2593,
-    "problem_id": 2539,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2539.jpg"
-  },
-  {
-    "id": 2594,
-    "problem_id": 2540,
-    "problem": "line P L, line M P, line M L, line P L, line M P, line M L\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2540.jpg"
-  },
-  {
-    "id": 2595,
-    "problem_id": 2541,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2541.jpg"
-  },
-  {
-    "id": 2596,
-    "problem_id": 2542,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2542.jpg"
-  },
-  {
-    "id": 2597,
-    "problem_id": 2543,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2543.jpg"
-  },
-  {
-    "id": 2598,
-    "problem_id": 2544,
-    "problem": "line W Y, line X Y, line W X, line W Y, line X Y, line W X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2544.jpg"
-  },
-  {
-    "id": 2599,
-    "problem_id": 2545,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nWhat is the area of the circle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2545.jpg"
-  },
-  {
-    "id": 2600,
-    "problem_id": 2546,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nWhat is the area of the circle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2546.jpg"
-  },
-  {
-    "id": 2601,
-    "problem_id": 2547,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nWhat is the area of the circle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2547.jpg"
-  },
-  {
-    "id": 2602,
-    "problem_id": 2548,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2548.jpg"
-  },
-  {
-    "id": 2603,
-    "problem_id": 2549,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2549.jpg"
-  },
-  {
-    "id": 2604,
-    "problem_id": 2550,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2550.jpg"
-  },
-  {
-    "id": 2606,
-    "problem_id": 2551,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2551.jpg"
-  },
-  {
-    "id": 2607,
-    "problem_id": 2552,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2552.jpg"
-  },
-  {
-    "id": 2608,
-    "problem_id": 2553,
-    "problem": "line G D J, line H J, line H D, line H G, line G D J, line H J, line H D, line H G\nFind DH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2553.jpg"
-  },
-  {
-    "id": 2609,
-    "problem_id": 2554,
-    "problem": "line G D J, line H J, line H D, line H G, line G D J, line H J, line H D, line H G\nFind DH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2554.jpg"
-  },
-  {
-    "id": 2610,
-    "problem_id": 2555,
-    "problem": "line G D J, line H J, line H D, line H G, line G D J, line H J, line H D, line H G\nFind DH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2555.jpg"
-  },
-  {
-    "id": 2611,
-    "problem_id": 2556,
-    "problem": "line G D J, line H J, line H D, line H G, line G D J, line H J, line H D, line H G\nFind DH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2556.jpg"
-  },
-  {
-    "id": 2612,
-    "problem_id": 2557,
-    "problem": "line A B, line B D, line C D, line A C, \\odot E lieson A C D B, line A B, line B D, line C D, line A C, \\odot E lieson A C D B\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2557.jpg"
-  },
-  {
-    "id": 2613,
-    "problem_id": 2558,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2558.jpg"
-  },
-  {
-    "id": 2614,
-    "problem_id": 2559,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2559.jpg"
-  },
-  {
-    "id": 2615,
-    "problem_id": 2560,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2560.jpg"
-  },
-  {
-    "id": 2616,
-    "problem_id": 2561,
-    "problem": "line M R K, line J R L, line J M, line J K, line K L, line M L, line M R K, line J R L, line J M, line J K, line K L, line M L\nUse parallelogram JKLM to find m \\angle JML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2561.jpg"
-  },
-  {
-    "id": 2617,
-    "problem_id": 2562,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2562.jpg"
-  },
-  {
-    "id": 2618,
-    "problem_id": 2563,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2563.jpg"
-  },
-  {
-    "id": 2619,
-    "problem_id": 2564,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2564.jpg"
-  },
-  {
-    "id": 2620,
-    "problem_id": 2565,
-    "problem": "line B A, line A C, line C E, line D E, line B D, line B A, line A C, line C E, line D E, line B D\nFind the area of the figure. Perimeter = 60 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2565.jpg"
-  },
-  {
-    "id": 2621,
-    "problem_id": 2566,
-    "problem": "line B A, line A C, line C E, line D E, line B D, line B A, line A C, line C E, line D E, line B D\nFind the area of the figure. Perimeter = 60 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2566.jpg"
-  },
-  {
-    "id": 2622,
-    "problem_id": 2567,
-    "problem": "line B A, line A C, line C E, line D E, line B D, line B A, line A C, line C E, line D E, line B D\nFind the area of the figure. Perimeter = 60 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2567.jpg"
-  },
-  {
-    "id": 2623,
-    "problem_id": 2568,
-    "problem": "line B A, line A C, line C E, line D E, line B D, line B A, line A C, line C E, line D E, line B D\nFind the area of the figure. Perimeter = 60 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2568.jpg"
-  },
-  {
-    "id": 2624,
-    "problem_id": 2569,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2569.jpg"
-  },
-  {
-    "id": 2625,
-    "problem_id": 2570,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2570.jpg"
-  },
-  {
-    "id": 2626,
-    "problem_id": 2571,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2571.jpg"
-  },
-  {
-    "id": 2627,
-    "problem_id": 2572,
-    "problem": "line W V, line T U, \\odot A lieson T W V U, line W V, line T U, \\odot A lieson T W V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2572.jpg"
-  },
-  {
-    "id": 2628,
-    "problem_id": 2573,
-    "problem": "line W V, line T U, \\odot A lieson T W V U, line W V, line T U, \\odot A lieson T W V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2573.jpg"
-  },
-  {
-    "id": 2629,
-    "problem_id": 2574,
-    "problem": "line W V, line T U, \\odot A lieson T W V U, line W V, line T U, \\odot A lieson T W V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2574.jpg"
-  },
-  {
-    "id": 2630,
-    "problem_id": 2575,
-    "problem": "line W V, line T U, \\odot A lieson T W V U, line W V, line T U, \\odot A lieson T W V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2575.jpg"
-  },
-  {
-    "id": 2631,
-    "problem_id": 2576,
-    "problem": "line W V, line T U, \\odot A lieson T W V U, line W V, line T U, \\odot A lieson T W V U\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2576.jpg"
-  },
-  {
-    "id": 2632,
-    "problem_id": 2577,
-    "problem": "line A B C, line C D, line A D, \\odot B lieson A D C, line A B C, line C D, line A D, \\odot B lieson A D C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2577.jpg"
-  },
-  {
-    "id": 2633,
-    "problem_id": 2578,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2578.jpg"
-  },
-  {
-    "id": 2634,
-    "problem_id": 2579,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2579.jpg"
-  },
-  {
-    "id": 2635,
-    "problem_id": 2580,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2580.jpg"
-  },
-  {
-    "id": 2636,
-    "problem_id": 2581,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2581.jpg"
-  },
-  {
-    "id": 2637,
-    "problem_id": 2582,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2582.jpg"
-  },
-  {
-    "id": 2638,
-    "problem_id": 2583,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2583.jpg"
-  },
-  {
-    "id": 2639,
-    "problem_id": 2584,
-    "problem": "line s lieson G F E, line q lieson B C F H, line r lieson A C D, line s lieson G F E, line q lieson B C F H, line r lieson A C D\nIf m \\angle 4 = 2x-17 and m \\angle 1 = 85, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2584.jpg"
-  },
-  {
-    "id": 2640,
-    "problem_id": 2585,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2585.jpg"
-  },
-  {
-    "id": 2641,
-    "problem_id": 2586,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2586.jpg"
-  },
-  {
-    "id": 2642,
-    "problem_id": 2587,
-    "problem": "line A D, line B C, line C D, line B A, line A D, line B C, line C D, line B A\nDetermine the value of variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2587.jpg"
-  },
-  {
-    "id": 2643,
-    "problem_id": 2588,
-    "problem": "line A D, line B C, line C D, line B A, line A D, line B C, line C D, line B A\nDetermine the value of variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2588.jpg"
-  },
-  {
-    "id": 2644,
-    "problem_id": 2589,
-    "problem": "line A D, line B C, line C D, line B A, line A D, line B C, line C D, line B A\nDetermine the value of variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2589.jpg"
-  },
-  {
-    "id": 2645,
-    "problem_id": 2590,
-    "problem": "line A D, line B C, line C D, line B A, line A D, line B C, line C D, line B A\nDetermine the value of variable x for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2590.jpg"
-  },
-  {
-    "id": 2646,
-    "problem_id": 2591,
-    "problem": "line D C, line B C, line A B, line A D, line F E, line E H, line G H, line F G, line D C, line B C, line A B, line A D, line F E, line E H, line G H, line F G\nEach pair of polygons is similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2591.jpg"
-  },
-  {
-    "id": 2647,
-    "problem_id": 2592,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nFind h in the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2592.jpg"
-  },
-  {
-    "id": 2648,
-    "problem_id": 2593,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nFind h in the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2593.jpg"
-  },
-  {
-    "id": 2649,
-    "problem_id": 2594,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nFind h in the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2594.jpg"
-  },
-  {
-    "id": 2650,
-    "problem_id": 2595,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nFind h in the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2595.jpg"
-  },
-  {
-    "id": 2651,
-    "problem_id": 2596,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nFind h in the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2596.jpg"
-  },
-  {
-    "id": 2652,
-    "problem_id": 2597,
-    "problem": "line D A, line A B C, line D C, line D B, line D A, line A B C, line D C, line D B\nFind h in the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2597.jpg"
-  },
-  {
-    "id": 2653,
-    "problem_id": 2598,
-    "problem": "line A C, line A B, line D C, line B C, line A D, line A C, line A B, line D C, line B C, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2598.jpg"
-  },
-  {
-    "id": 2654,
-    "problem_id": 2599,
-    "problem": "line A C, line A B, line D C, line B C, line A D, line A C, line A B, line D C, line B C, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2599.jpg"
-  },
-  {
-    "id": 2655,
-    "problem_id": 2600,
-    "problem": "line A C, line A B, line D C, line B C, line A D, line A C, line A B, line D C, line B C, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2600.jpg"
-  },
-  {
-    "id": 2656,
-    "problem_id": 2601,
-    "problem": "line A C, line A B, line D C, line B C, line A D, line A C, line A B, line D C, line B C, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2601.jpg"
-  },
-  {
-    "id": 2657,
-    "problem_id": 2602,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2602.jpg"
-  },
-  {
-    "id": 2658,
-    "problem_id": 2603,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2603.jpg"
-  },
-  {
-    "id": 2659,
-    "problem_id": 2604,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2604.jpg"
-  },
-  {
-    "id": 2660,
-    "problem_id": 2605,
-    "problem": "line C A, line B C, line B A, \\odot B lieson C A, line C A, line B C, line B A, \\odot B lieson C A\nFind the measure of \\angle BCA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2605.jpg"
-  },
-  {
-    "id": 2661,
-    "problem_id": 2606,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nm \\angle B = 76. The measure of \\angle A is half the measure of \\angle B. What is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2606.jpg"
-  },
-  {
-    "id": 2662,
-    "problem_id": 2607,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nm \\angle B = 76. The measure of \\angle A is half the measure of \\angle B. What is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2607.jpg"
-  },
-  {
-    "id": 2663,
-    "problem_id": 2608,
-    "problem": "line B E D, line C D, line A D, line C E A, line B A, line B C, line B E D, line C D, line A D, line C E A, line B A, line B C\nWhat is the length of BA in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2608.jpg"
-  },
-  {
-    "id": 2664,
-    "problem_id": 2609,
-    "problem": "line B E D, line C D, line A D, line C E A, line B A, line B C, line B E D, line C D, line A D, line C E A, line B A, line B C\nWhat is the length of BA in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2609.jpg"
-  },
-  {
-    "id": 2665,
-    "problem_id": 2610,
-    "problem": "line B E D, line C D, line A D, line C E A, line B A, line B C, line B E D, line C D, line A D, line C E A, line B A, line B C\nWhat is the length of BA in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2610.jpg"
-  },
-  {
-    "id": 2666,
-    "problem_id": 2611,
-    "problem": "line Q S T, line R T, \\odot Q lieson S R, line Q S T, line R T, \\odot Q lieson S R\nAssume the segments that appear to be tangent are tangent. Find the length of QT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2611.jpg"
-  },
-  {
-    "id": 2667,
-    "problem_id": 2612,
-    "problem": "line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B, line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2612.jpg"
-  },
-  {
-    "id": 2668,
-    "problem_id": 2613,
-    "problem": "line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B, line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2613.jpg"
-  },
-  {
-    "id": 2669,
-    "problem_id": 2614,
-    "problem": "line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B, line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2614.jpg"
-  },
-  {
-    "id": 2670,
-    "problem_id": 2615,
-    "problem": "line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B, line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2615.jpg"
-  },
-  {
-    "id": 2671,
-    "problem_id": 2616,
-    "problem": "line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B, line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2616.jpg"
-  },
-  {
-    "id": 2672,
-    "problem_id": 2617,
-    "problem": "line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B, line C D, line A B, line B D, line A C, \\odot E lieson C A, \\odot F lieson D B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2617.jpg"
-  },
-  {
-    "id": 2673,
-    "problem_id": 2618,
-    "problem": "line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D, line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D\nFind the measure of \\angle 4 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2618.jpg"
-  },
-  {
-    "id": 2674,
-    "problem_id": 2619,
-    "problem": "line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D, line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D\nFind the measure of \\angle 4 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2619.jpg"
-  },
-  {
-    "id": 2675,
-    "problem_id": 2620,
-    "problem": "line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D, line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D\nFind the measure of \\angle 4 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2620.jpg"
-  },
-  {
-    "id": 2676,
-    "problem_id": 2621,
-    "problem": "line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D, line A B, line B F, line E D F, line A E, line A C F, line E C B, line C D\nFind the measure of \\angle 4 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2621.jpg"
-  },
-  {
-    "id": 2677,
-    "problem_id": 2622,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2622.jpg"
-  },
-  {
-    "id": 2678,
-    "problem_id": 2623,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2623.jpg"
-  },
-  {
-    "id": 2679,
-    "problem_id": 2624,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2624.jpg"
-  },
-  {
-    "id": 2680,
-    "problem_id": 2625,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2625.jpg"
-  },
-  {
-    "id": 2681,
-    "problem_id": 2626,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2626.jpg"
-  },
-  {
-    "id": 2682,
-    "problem_id": 2627,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nFind the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2627.jpg"
-  },
-  {
-    "id": 2683,
-    "problem_id": 2628,
-    "problem": "line D E B, line A E C, line D A, line A B, line B C, line D C, line D E B, line A E C, line D A, line A B, line B C, line D C\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2628.jpg"
-  },
-  {
-    "id": 2684,
-    "problem_id": 2629,
-    "problem": "line D E B, line A E C, line D A, line A B, line B C, line D C, line D E B, line A E C, line D A, line A B, line B C, line D C\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2629.jpg"
-  },
-  {
-    "id": 2685,
-    "problem_id": 2630,
-    "problem": "line D E B, line A E C, line D A, line A B, line B C, line D C, line D E B, line A E C, line D A, line A B, line B C, line D C\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2630.jpg"
-  },
-  {
-    "id": 2686,
-    "problem_id": 2631,
-    "problem": "line D E B, line A E C, line D A, line A B, line B C, line D C, line D E B, line A E C, line D A, line A B, line B C, line D C\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2631.jpg"
-  },
-  {
-    "id": 2687,
-    "problem_id": 2632,
-    "problem": "line D E B, line A E C, line D A, line A B, line B C, line D C, line D E B, line A E C, line D A, line A B, line B C, line D C\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2632.jpg"
-  },
-  {
-    "id": 2688,
-    "problem_id": 2633,
-    "problem": "line D E B, line A E C, line D A, line A B, line B C, line D C, line D E B, line A E C, line D A, line A B, line B C, line D C\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2633.jpg"
-  },
-  {
-    "id": 2689,
-    "problem_id": 2634,
-    "problem": "line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G, line F A H, line G A J, line H J, line G H, \\odot B lieson F J H G\nm \\widehat GH = 78. Find m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2634.jpg"
-  },
-  {
-    "id": 2690,
-    "problem_id": 2635,
-    "problem": "line A B, line A D, line A C, \\odot R lieson B C, \\odot Q lieson D C, line A B, line A D, line A C, \\odot R lieson B C, \\odot Q lieson D C\nFind x. Assume that segments that appear tangent to circles are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2635.jpg"
-  },
-  {
-    "id": 2691,
-    "problem_id": 2636,
-    "problem": "line X V Y, line X T, line Z V T W, \\odot T lieson X W Y Z, line X V Y, line X T, line Z V T W, \\odot T lieson X W Y Z\nIn \\odot T, ZV = 1, and TW = 13. Find m \\widehat XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2636.jpg"
-  },
-  {
-    "id": 2692,
-    "problem_id": 2637,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind m \\angle BFD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2637.jpg"
-  },
-  {
-    "id": 2693,
-    "problem_id": 2638,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind m \\angle BFD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2638.jpg"
-  },
-  {
-    "id": 2694,
-    "problem_id": 2639,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind m \\angle BFD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2639.jpg"
-  },
-  {
-    "id": 2695,
-    "problem_id": 2640,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind m \\angle BFD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2640.jpg"
-  },
-  {
-    "id": 2696,
-    "problem_id": 2641,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind m \\angle BFD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2641.jpg"
-  },
-  {
-    "id": 2697,
-    "problem_id": 2642,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2642.jpg"
-  },
-  {
-    "id": 2698,
-    "problem_id": 2643,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2643.jpg"
-  },
-  {
-    "id": 2699,
-    "problem_id": 2644,
-    "problem": "line A B, line A C, line B D, line C D, line A B, line A C, line B D, line C D\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2644.jpg"
-  },
-  {
-    "id": 2700,
-    "problem_id": 2645,
-    "problem": "line A B, \\odot A lieson E B F, line A B, \\odot A lieson E B F\nFind the length of \\widehat FE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2645.jpg"
-  },
-  {
-    "id": 2701,
-    "problem_id": 2646,
-    "problem": "line A B, \\odot A lieson E B F, line A B, \\odot A lieson E B F\nFind the length of \\widehat FE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2646.jpg"
-  },
-  {
-    "id": 2702,
-    "problem_id": 2647,
-    "problem": "line A B, \\odot A lieson E B F, line A B, \\odot A lieson E B F\nFind the length of \\widehat FE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2647.jpg"
-  },
-  {
-    "id": 2703,
-    "problem_id": 2648,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2648.jpg"
-  },
-  {
-    "id": 2704,
-    "problem_id": 2649,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2649.jpg"
-  },
-  {
-    "id": 2705,
-    "problem_id": 2650,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2650.jpg"
-  },
-  {
-    "id": 2706,
-    "problem_id": 2651,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2651.jpg"
-  },
-  {
-    "id": 2707,
-    "problem_id": 2652,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2652.jpg"
-  },
-  {
-    "id": 2708,
-    "problem_id": 2653,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2653.jpg"
-  },
-  {
-    "id": 2709,
-    "problem_id": 2654,
-    "problem": "line D C A, line D E, line A B E, line C B, line D C A, line D E, line A B E, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2654.jpg"
-  },
-  {
-    "id": 2710,
-    "problem_id": 2655,
-    "problem": "line D C A, line D E, line A B E, line C B, line D C A, line D E, line A B E, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2655.jpg"
-  },
-  {
-    "id": 2711,
-    "problem_id": 2656,
-    "problem": "line D C A, line D E, line A B E, line C B, line D C A, line D E, line A B E, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2656.jpg"
-  },
-  {
-    "id": 2712,
-    "problem_id": 2657,
-    "problem": "line D C A, line D E, line A B E, line C B, line D C A, line D E, line A B E, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2657.jpg"
-  },
-  {
-    "id": 2713,
-    "problem_id": 2658,
-    "problem": "line F G, line G H, \\odot G lieson H F, line F G, line G H, \\odot G lieson H F\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2658.jpg"
-  },
-  {
-    "id": 2714,
-    "problem_id": 2659,
-    "problem": "line F G, line G H, \\odot G lieson H F, line F G, line G H, \\odot G lieson H F\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2659.jpg"
-  },
-  {
-    "id": 2715,
-    "problem_id": 2660,
-    "problem": "line Z W, line Z Y, line X Y, line W X, line M Q, line N M, line N P, line Q P, line Z W, line Z Y, line X Y, line W X, line M Q, line N M, line N P, line Q P\nIf MNPQ \\sim XYZW, find the perimeter of MNPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2660.jpg"
-  },
-  {
-    "id": 2716,
-    "problem_id": 2661,
-    "problem": "line Z W, line Z Y, line X Y, line W X, line M Q, line N M, line N P, line Q P, line Z W, line Z Y, line X Y, line W X, line M Q, line N M, line N P, line Q P\nIf MNPQ \\sim XYZW, find the perimeter of MNPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2661.jpg"
-  },
-  {
-    "id": 2717,
-    "problem_id": 2662,
-    "problem": "line Z W, line Z Y, line X Y, line W X, line M Q, line N M, line N P, line Q P, line Z W, line Z Y, line X Y, line W X, line M Q, line N M, line N P, line Q P\nIf MNPQ \\sim XYZW, find the perimeter of MNPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2662.jpg"
-  },
-  {
-    "id": 2718,
-    "problem_id": 2663,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line E C A, line B A, line A D, line E D, line B E, line B C D, line E C A\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2663.jpg"
-  },
-  {
-    "id": 2719,
-    "problem_id": 2664,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line E C A, line B A, line A D, line E D, line B E, line B C D, line E C A\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2664.jpg"
-  },
-  {
-    "id": 2720,
-    "problem_id": 2665,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line E C A, line B A, line A D, line E D, line B E, line B C D, line E C A\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2665.jpg"
-  },
-  {
-    "id": 2721,
-    "problem_id": 2666,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line E C A, line B A, line A D, line E D, line B E, line B C D, line E C A\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2666.jpg"
-  },
-  {
-    "id": 2722,
-    "problem_id": 2667,
-    "problem": "line A B, line C B, \\odot B lieson C A, line A B, line C B, \\odot B lieson C A\nFind the length of \\widehat AC shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2667.jpg"
-  },
-  {
-    "id": 2723,
-    "problem_id": 2668,
-    "problem": "line B C D E F, line A C H, line A D G, line B H, line E G, line B C D E F, line A C H, line A D G, line B H, line E G\nFind the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2668.jpg"
-  },
-  {
-    "id": 2724,
-    "problem_id": 2669,
-    "problem": "line B G, line B F, line A D, line G H, line D E, line A C, line F H, line C E, line B G, line B F, line A D, line G H, line D E, line A C, line F H, line C E\nPolygon BGHF \\sim polygon ADEC. Determine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2669.jpg"
-  },
-  {
-    "id": 2725,
-    "problem_id": 2670,
-    "problem": "line D C, line R S, line Q P, line A B, line A D, line B C, line S P, line R Q, line D C, line R S, line Q P, line A B, line A D, line B C, line S P, line R Q\nPolygon ABCD \\cong polygon PQRS. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2670.jpg"
-  },
-  {
-    "id": 2726,
-    "problem_id": 2671,
-    "problem": "line D C, line R S, line Q P, line A B, line A D, line B C, line S P, line R Q, line D C, line R S, line Q P, line A B, line A D, line B C, line S P, line R Q\nPolygon ABCD \\cong polygon PQRS. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2671.jpg"
-  },
-  {
-    "id": 2727,
-    "problem_id": 2672,
-    "problem": "line D A, line A B, line C B, \\odot E lieson D C, line D A, line A B, line C B, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2672.jpg"
-  },
-  {
-    "id": 2728,
-    "problem_id": 2673,
-    "problem": "line D A, line A B, line C B, \\odot E lieson D C, line D A, line A B, line C B, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2673.jpg"
-  },
-  {
-    "id": 2729,
-    "problem_id": 2674,
-    "problem": "line D A, line A B, line C B, \\odot E lieson D C, line D A, line A B, line C B, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2674.jpg"
-  },
-  {
-    "id": 2730,
-    "problem_id": 2675,
-    "problem": "line D A, line A B, line C B, \\odot E lieson D C, line D A, line A B, line C B, \\odot E lieson D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2675.jpg"
-  },
-  {
-    "id": 2731,
-    "problem_id": 2676,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2676.jpg"
-  },
-  {
-    "id": 2732,
-    "problem_id": 2677,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2677.jpg"
-  },
-  {
-    "id": 2733,
-    "problem_id": 2678,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2678.jpg"
-  },
-  {
-    "id": 2734,
-    "problem_id": 2679,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2679.jpg"
-  },
-  {
-    "id": 2735,
-    "problem_id": 2680,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2680.jpg"
-  },
-  {
-    "id": 2736,
-    "problem_id": 2681,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2681.jpg"
-  },
-  {
-    "id": 2737,
-    "problem_id": 2682,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find SL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2682.jpg"
-  },
-  {
-    "id": 2738,
-    "problem_id": 2683,
-    "problem": "line A B C, line C D, \\odot C0 lieson A, \\odot C1 lieson B D, line A B C, line C D, \\odot C0 lieson A, \\odot C1 lieson B D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2683.jpg"
-  },
-  {
-    "id": 2739,
-    "problem_id": 2684,
-    "problem": "line A B C, line C D, \\odot C0 lieson A, \\odot C1 lieson B D, line A B C, line C D, \\odot C0 lieson A, \\odot C1 lieson B D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2684.jpg"
-  },
-  {
-    "id": 2740,
-    "problem_id": 2685,
-    "problem": "line A D F G, line E F, line E D, line C D B, line C A, line A B, line A D F G, line E F, line E D, line C D B, line C A, line A B\nFind the measure of \\angle 6 if m \\angle 4 = m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2685.jpg"
-  },
-  {
-    "id": 2741,
-    "problem_id": 2686,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nWhat is \\tan B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2686.jpg"
-  },
-  {
-    "id": 2742,
-    "problem_id": 2687,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nWhat is \\tan B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2687.jpg"
-  },
-  {
-    "id": 2743,
-    "problem_id": 2688,
-    "problem": "line A B, line D C B, line A C, line E A, line E D, line A B, line D C B, line A C, line E A, line E D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2688.jpg"
-  },
-  {
-    "id": 2744,
-    "problem_id": 2689,
-    "problem": "line A B, line D C B, line A C, line E A, line E D, line A B, line D C B, line A C, line E A, line E D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2689.jpg"
-  },
-  {
-    "id": 2745,
-    "problem_id": 2690,
-    "problem": "line O A M, line L A N, line O N, line L M, line M N, line L O, line O A M, line L A N, line O N, line L M, line M N, line L O\nFind the measure of \\angle 2 in rectangle LMNO if m \\angle 5 = 38.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2690.jpg"
-  },
-  {
-    "id": 2746,
-    "problem_id": 2691,
-    "problem": "line B E, line C E, line A C, line A B, line A D E, line C D B, line B E, line C E, line A C, line A B, line A D E, line C D B\nFind the perimeter of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2691.jpg"
-  },
-  {
-    "id": 2747,
-    "problem_id": 2692,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2692.jpg"
-  },
-  {
-    "id": 2748,
-    "problem_id": 2693,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2693.jpg"
-  },
-  {
-    "id": 2749,
-    "problem_id": 2694,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2694.jpg"
-  },
-  {
-    "id": 2750,
-    "problem_id": 2695,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2695.jpg"
-  },
-  {
-    "id": 2751,
-    "problem_id": 2696,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2696.jpg"
-  },
-  {
-    "id": 2752,
-    "problem_id": 2697,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2697.jpg"
-  },
-  {
-    "id": 2753,
-    "problem_id": 2698,
-    "problem": "line l lieson A D H, line m lieson B E G, line C D E F, line l lieson A D H, line m lieson B E G, line C D E F\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2698.jpg"
-  },
-  {
-    "id": 2754,
-    "problem_id": 2699,
-    "problem": "line l lieson A D H, line m lieson B E G, line C D E F, line l lieson A D H, line m lieson B E G, line C D E F\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2699.jpg"
-  },
-  {
-    "id": 2755,
-    "problem_id": 2700,
-    "problem": "line l lieson A D H, line m lieson B E G, line C D E F, line l lieson A D H, line m lieson B E G, line C D E F\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2700.jpg"
-  },
-  {
-    "id": 2756,
-    "problem_id": 2701,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2701.jpg"
-  },
-  {
-    "id": 2757,
-    "problem_id": 2702,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2702.jpg"
-  },
-  {
-    "id": 2758,
-    "problem_id": 2703,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2703.jpg"
-  },
-  {
-    "id": 2759,
-    "problem_id": 2704,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2704.jpg"
-  },
-  {
-    "id": 2760,
-    "problem_id": 2705,
-    "problem": "line P U T, line Q S, line R Q P, line R S T, line Q U, line S U, line P U T, line Q S, line R Q P, line R S T, line Q U, line S U\nIf RQ = RS and m \\angle RQS = 75, find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2705.jpg"
-  },
-  {
-    "id": 2763,
-    "problem_id": 2706,
-    "problem": "line A D, line B A, line C D, line B C, line A D, line B A, line C D, line B C\nWhat is m \\angle 2 in the isosceles trapezoid?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2706.jpg"
-  },
-  {
-    "id": 2764,
-    "problem_id": 2707,
-    "problem": "line Y Z, line X Z, line X Y, line Y Z, line X Z, line X Y\nIn the triangle, what is the measure of \\angle Z?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2707.jpg"
-  },
-  {
-    "id": 2765,
-    "problem_id": 2708,
-    "problem": "line Y Z, line X Z, line X Y, line Y Z, line X Z, line X Y\nIn the triangle, what is the measure of \\angle Z?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2708.jpg"
-  },
-  {
-    "id": 2766,
-    "problem_id": 2709,
-    "problem": "line Y Z, line X Z, line X Y, line Y Z, line X Z, line X Y\nIn the triangle, what is the measure of \\angle Z?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2709.jpg"
-  },
-  {
-    "id": 2767,
-    "problem_id": 2710,
-    "problem": "line A B, line B C, line D C, line B D, line A D, line A B, line B C, line D C, line B D, line A D\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2710.jpg"
-  },
-  {
-    "id": 2768,
-    "problem_id": 2711,
-    "problem": "line A B, line B C, line D C, line B D, line A D, line A B, line B C, line D C, line B D, line A D\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2711.jpg"
-  },
-  {
-    "id": 2769,
-    "problem_id": 2712,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is m \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2712.jpg"
-  },
-  {
-    "id": 2770,
-    "problem_id": 2713,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is m \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2713.jpg"
-  },
-  {
-    "id": 2771,
-    "problem_id": 2714,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is m \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2714.jpg"
-  },
-  {
-    "id": 2772,
-    "problem_id": 2715,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is m \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2715.jpg"
-  },
-  {
-    "id": 2773,
-    "problem_id": 2716,
-    "problem": "line C A, line D A, \\odot A lieson C D, line C A, line D A, \\odot A lieson C D\nFind the length of \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2716.jpg"
-  },
-  {
-    "id": 2774,
-    "problem_id": 2717,
-    "problem": "line C A, line D A, \\odot A lieson C D, line C A, line D A, \\odot A lieson C D\nFind the length of \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2717.jpg"
-  },
-  {
-    "id": 2775,
-    "problem_id": 2718,
-    "problem": "line C A, line D A, \\odot A lieson C D, line C A, line D A, \\odot A lieson C D\nFind the length of \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2718.jpg"
-  },
-  {
-    "id": 2776,
-    "problem_id": 2719,
-    "problem": "line M P, line N P, line N M, line J H, line G H, line J G, line M P, line N P, line N M, line J H, line G H, line J G\nGiven m \\angle M = m \\angle G and m \\angle N = m \\angle H, find m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2719.jpg"
-  },
-  {
-    "id": 2777,
-    "problem_id": 2720,
-    "problem": "line M P, line N P, line N M, line J H, line G H, line J G, line M P, line N P, line N M, line J H, line G H, line J G\nGiven m \\angle M = m \\angle G and m \\angle N = m \\angle H, find m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2720.jpg"
-  },
-  {
-    "id": 2778,
-    "problem_id": 2721,
-    "problem": "line M P, line N P, line N M, line J H, line G H, line J G, line M P, line N P, line N M, line J H, line G H, line J G\nGiven m \\angle M = m \\angle G and m \\angle N = m \\angle H, find m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2721.jpg"
-  },
-  {
-    "id": 2779,
-    "problem_id": 2722,
-    "problem": "line M P, line N P, line N M, line J H, line G H, line J G, line M P, line N P, line N M, line J H, line G H, line J G\nGiven m \\angle M = m \\angle G and m \\angle N = m \\angle H, find m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2722.jpg"
-  },
-  {
-    "id": 2780,
-    "problem_id": 2723,
-    "problem": "line M P, line N P, line N M, line J H, line G H, line J G, line M P, line N P, line N M, line J H, line G H, line J G\nGiven m \\angle M = m \\angle G and m \\angle N = m \\angle H, find m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2723.jpg"
-  },
-  {
-    "id": 2781,
-    "problem_id": 2724,
-    "problem": "line A B C, line C D, line E D, line A E, line E B, line A B C, line C D, line E D, line A E, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2724.jpg"
-  },
-  {
-    "id": 2782,
-    "problem_id": 2725,
-    "problem": "line B C, line D C, line A D, line A B E, line B C, line D C, line A D, line A B E\nWhat is m \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2725.jpg"
-  },
-  {
-    "id": 2783,
-    "problem_id": 2726,
-    "problem": "line B C, line D C, line A D, line A B E, line B C, line D C, line A D, line A B E\nWhat is m \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2726.jpg"
-  },
-  {
-    "id": 2784,
-    "problem_id": 2727,
-    "problem": "line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R, line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R\nIn \\odot A, m \\widehat PQ = m \\widehat RS. Find m \\angle 2 if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2727.jpg"
-  },
-  {
-    "id": 2785,
-    "problem_id": 2728,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2728.jpg"
-  },
-  {
-    "id": 2786,
-    "problem_id": 2729,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2729.jpg"
-  },
-  {
-    "id": 2787,
-    "problem_id": 2730,
-    "problem": "line A B, line C A, line C B, line D B, \\odot D lieson C A B, line A B, line C A, line C B, line D B, \\odot D lieson C A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2730.jpg"
-  },
-  {
-    "id": 2788,
-    "problem_id": 2731,
-    "problem": "line A B, line C A, line C B, line D B, \\odot D lieson C A B, line A B, line C A, line C B, line D B, \\odot D lieson C A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2731.jpg"
-  },
-  {
-    "id": 2789,
-    "problem_id": 2732,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2732.jpg"
-  },
-  {
-    "id": 2790,
-    "problem_id": 2733,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2733.jpg"
-  },
-  {
-    "id": 2791,
-    "problem_id": 2734,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2734.jpg"
-  },
-  {
-    "id": 2792,
-    "problem_id": 2735,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2735.jpg"
-  },
-  {
-    "id": 2793,
-    "problem_id": 2736,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2736.jpg"
-  },
-  {
-    "id": 2794,
-    "problem_id": 2737,
-    "problem": "line T W, line V W, line U V, line U T, line T W, line V W, line U V, line U T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2737.jpg"
-  },
-  {
-    "id": 2795,
-    "problem_id": 2738,
-    "problem": "line T W, line V W, line U V, line U T, line T W, line V W, line U V, line U T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2738.jpg"
-  },
-  {
-    "id": 2796,
-    "problem_id": 2739,
-    "problem": "line T W, line V W, line U V, line U T, line T W, line V W, line U V, line U T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2739.jpg"
-  },
-  {
-    "id": 2797,
-    "problem_id": 2740,
-    "problem": "line T W, line V W, line U V, line U T, line T W, line V W, line U V, line U T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2740.jpg"
-  },
-  {
-    "id": 2798,
-    "problem_id": 2741,
-    "problem": "line T W, line V W, line U V, line U T, line T W, line V W, line U V, line U T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2741.jpg"
-  },
-  {
-    "id": 2799,
-    "problem_id": 2742,
-    "problem": "line T W, line V W, line U V, line U T, line T W, line V W, line U V, line U T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2742.jpg"
-  },
-  {
-    "id": 2800,
-    "problem_id": 2743,
-    "problem": "line Y P X, line B P A, line P C, \\odot P lieson B X A C Y, line Y P X, line B P A, line P C, \\odot P lieson B X A C Y\nFind m \\widehat CXB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2743.jpg"
-  },
-  {
-    "id": 2801,
-    "problem_id": 2744,
-    "problem": "line X M Y, line X M Y\nM is the midpoint of XY. Find the length of YX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2744.jpg"
-  },
-  {
-    "id": 2802,
-    "problem_id": 2745,
-    "problem": "line A B, \\odot B lieson A C D, line A B, \\odot B lieson A C D\nFind the diameter.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2745.jpg"
-  },
-  {
-    "id": 2803,
-    "problem_id": 2746,
-    "problem": "line A B, \\odot B lieson A C D, line A B, \\odot B lieson A C D\nFind the diameter.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2746.jpg"
-  },
-  {
-    "id": 2804,
-    "problem_id": 2747,
-    "problem": "line A B, \\odot B lieson A C D, line A B, \\odot B lieson A C D\nFind the diameter.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2747.jpg"
-  },
-  {
-    "id": 2806,
-    "problem_id": 2748,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2748.jpg"
-  },
-  {
-    "id": 2807,
-    "problem_id": 2749,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2749.jpg"
-  },
-  {
-    "id": 2808,
-    "problem_id": 2750,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2750.jpg"
-  },
-  {
-    "id": 2809,
-    "problem_id": 2751,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2751.jpg"
-  },
-  {
-    "id": 2810,
-    "problem_id": 2752,
-    "problem": "line M L K A, line N M, line N L, line M L K A, line N M, line N L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2752.jpg"
-  },
-  {
-    "id": 2811,
-    "problem_id": 2753,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2753.jpg"
-  },
-  {
-    "id": 2812,
-    "problem_id": 2754,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2754.jpg"
-  },
-  {
-    "id": 2813,
-    "problem_id": 2755,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2755.jpg"
-  },
-  {
-    "id": 2814,
-    "problem_id": 2756,
-    "problem": "line R Q S, line P S, line R P, line Q P, line R Q S, line P S, line R P, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2756.jpg"
-  },
-  {
-    "id": 2815,
-    "problem_id": 2757,
-    "problem": "line R Q S, line P S, line R P, line Q P, line R Q S, line P S, line R P, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2757.jpg"
-  },
-  {
-    "id": 2816,
-    "problem_id": 2758,
-    "problem": "line R Q S, line P S, line R P, line Q P, line R Q S, line P S, line R P, line Q P\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2758.jpg"
-  },
-  {
-    "id": 2817,
-    "problem_id": 2759,
-    "problem": "line A D E, line C D B, line C E, line A B, line C A, line E B, line A D E, line C D B, line C E, line A B, line C A, line E B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2759.jpg"
-  },
-  {
-    "id": 2818,
-    "problem_id": 2760,
-    "problem": "line A D E, line C D B, line C E, line A B, line C A, line E B, line A D E, line C D B, line C E, line A B, line C A, line E B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2760.jpg"
-  },
-  {
-    "id": 2819,
-    "problem_id": 2761,
-    "problem": "line B E C F, line A G C, line D F, line A B, line D G E, line B E C F, line A G C, line D F, line A B, line D G E\nWhat is DE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2761.jpg"
-  },
-  {
-    "id": 2820,
-    "problem_id": 2762,
-    "problem": "line B E C F, line A G C, line D F, line A B, line D G E, line B E C F, line A G C, line D F, line A B, line D G E\nWhat is DE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2762.jpg"
-  },
-  {
-    "id": 2821,
-    "problem_id": 2763,
-    "problem": "line B E C F, line A G C, line D F, line A B, line D G E, line B E C F, line A G C, line D F, line A B, line D G E\nWhat is DE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2763.jpg"
-  },
-  {
-    "id": 2822,
-    "problem_id": 2764,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2764.jpg"
-  },
-  {
-    "id": 2823,
-    "problem_id": 2765,
-    "problem": "line N P, line P Q, \\odot A lieson N Q P, line N P, line P Q, \\odot A lieson N Q P\nFind m \\widehat NQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2765.jpg"
-  },
-  {
-    "id": 2824,
-    "problem_id": 2766,
-    "problem": "line N P, line P Q, \\odot A lieson N Q P, line N P, line P Q, \\odot A lieson N Q P\nFind m \\widehat NQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2766.jpg"
-  },
-  {
-    "id": 2825,
-    "problem_id": 2767,
-    "problem": "line N P, line P Q, \\odot A lieson N Q P, line N P, line P Q, \\odot A lieson N Q P\nFind m \\widehat NQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2767.jpg"
-  },
-  {
-    "id": 2826,
-    "problem_id": 2768,
-    "problem": "line C D E, line A E, line C B A, line B D, line C D E, line A E, line C B A, line B D\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2768.jpg"
-  },
-  {
-    "id": 2827,
-    "problem_id": 2769,
-    "problem": "line C D E, line A E, line C B A, line B D, line C D E, line A E, line C B A, line B D\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2769.jpg"
-  },
-  {
-    "id": 2828,
-    "problem_id": 2770,
-    "problem": "line C D E, line A E, line C B A, line B D, line C D E, line A E, line C B A, line B D\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2770.jpg"
-  },
-  {
-    "id": 2829,
-    "problem_id": 2771,
-    "problem": "line W X A, line W Z B, line W Y C, line Z Y, line X Z, line W X A, line W Z B, line W Y C, line Z Y, line X Z\nFind XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2771.jpg"
-  },
-  {
-    "id": 2830,
-    "problem_id": 2772,
-    "problem": "line W X A, line W Z B, line W Y C, line Z Y, line X Z, line W X A, line W Z B, line W Y C, line Z Y, line X Z\nFind XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2772.jpg"
-  },
-  {
-    "id": 2831,
-    "problem_id": 2773,
-    "problem": "line W X A, line W Z B, line W Y C, line Z Y, line X Z, line W X A, line W Z B, line W Y C, line Z Y, line X Z\nFind XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2773.jpg"
-  },
-  {
-    "id": 2832,
-    "problem_id": 2774,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2774.jpg"
-  },
-  {
-    "id": 2833,
-    "problem_id": 2775,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2775.jpg"
-  },
-  {
-    "id": 2834,
-    "problem_id": 2776,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2776.jpg"
-  },
-  {
-    "id": 2835,
-    "problem_id": 2777,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2777.jpg"
-  },
-  {
-    "id": 2836,
-    "problem_id": 2778,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2778.jpg"
-  },
-  {
-    "id": 2837,
-    "problem_id": 2779,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2779.jpg"
-  },
-  {
-    "id": 2838,
-    "problem_id": 2780,
-    "problem": "line A C E, line D C B, line B E, line A B, line A D, line D E, line A C E, line D C B, line B E, line A B, line A D, line D E\nFind the perimeter of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2780.jpg"
-  },
-  {
-    "id": 2839,
-    "problem_id": 2781,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2781.jpg"
-  },
-  {
-    "id": 2840,
-    "problem_id": 2782,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2782.jpg"
-  },
-  {
-    "id": 2841,
-    "problem_id": 2783,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2783.jpg"
-  },
-  {
-    "id": 2842,
-    "problem_id": 2784,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2784.jpg"
-  },
-  {
-    "id": 2843,
-    "problem_id": 2785,
-    "problem": "line G R, line F R, line H R, line R E, \\odot R lieson F E H G, line G R, line F R, line H R, line R E, \\odot R lieson F E H G\nWhat is m \\widehat FGH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2785.jpg"
-  },
-  {
-    "id": 2844,
-    "problem_id": 2786,
-    "problem": "line G R, line F R, line H R, line R E, \\odot R lieson F E H G, line G R, line F R, line H R, line R E, \\odot R lieson F E H G\nWhat is m \\widehat FGH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2786.jpg"
-  },
-  {
-    "id": 2845,
-    "problem_id": 2787,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2787.jpg"
-  },
-  {
-    "id": 2846,
-    "problem_id": 2788,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2788.jpg"
-  },
-  {
-    "id": 2847,
-    "problem_id": 2789,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2789.jpg"
-  },
-  {
-    "id": 2848,
-    "problem_id": 2790,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2790.jpg"
-  },
-  {
-    "id": 2849,
-    "problem_id": 2791,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2791.jpg"
-  },
-  {
-    "id": 2850,
-    "problem_id": 2792,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2792.jpg"
-  },
-  {
-    "id": 2851,
-    "problem_id": 2793,
-    "problem": "line H G, line F G, \\odot A lieson F H G, line H G, line F G, \\odot A lieson F H G\nFind the measure of \\widehat FG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2793.jpg"
-  },
-  {
-    "id": 2852,
-    "problem_id": 2794,
-    "problem": "line D C B, line A C E, line A B, line B E, line A D, line D E, line D C B, line A C E, line A B, line B E, line A D, line D E\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2794.jpg"
-  },
-  {
-    "id": 2853,
-    "problem_id": 2795,
-    "problem": "line D C B, line A C E, line A B, line B E, line A D, line D E, line D C B, line A C E, line A B, line B E, line A D, line D E\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2795.jpg"
-  },
-  {
-    "id": 2854,
-    "problem_id": 2796,
-    "problem": "line D C B, line A C E, line A B, line B E, line A D, line D E, line D C B, line A C E, line A B, line B E, line A D, line D E\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2796.jpg"
-  },
-  {
-    "id": 2855,
-    "problem_id": 2797,
-    "problem": "line J B K, line H K, line H J, \\odot B lieson H J K, line J B K, line H K, line H J, \\odot B lieson H J K\nSolve for m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2797.jpg"
-  },
-  {
-    "id": 2857,
-    "problem_id": 2798,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nDetermine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2798.jpg"
-  },
-  {
-    "id": 2858,
-    "problem_id": 2799,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nDetermine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2799.jpg"
-  },
-  {
-    "id": 2859,
-    "problem_id": 2800,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nDetermine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2800.jpg"
-  },
-  {
-    "id": 2860,
-    "problem_id": 2801,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nDetermine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2801.jpg"
-  },
-  {
-    "id": 2861,
-    "problem_id": 2802,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nDetermine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2802.jpg"
-  },
-  {
-    "id": 2862,
-    "problem_id": 2803,
-    "problem": "line A T Q R B, line D S Q, line C P Q, line A T Q R B, line D S Q, line C P Q\nIf m \\angle SQT = 30, what is m \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2803.jpg"
-  },
-  {
-    "id": 2863,
-    "problem_id": 2804,
-    "problem": "line S A Q, line P Q, line P A R, line S R, line P S, line Q R, line S A Q, line P Q, line P A R, line S R, line P S, line Q R\nPQRS is a parallelogram. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2804.jpg"
-  },
-  {
-    "id": 2864,
-    "problem_id": 2805,
-    "problem": "line S A Q, line P Q, line P A R, line S R, line P S, line Q R, line S A Q, line P Q, line P A R, line S R, line P S, line Q R\nPQRS is a parallelogram. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2805.jpg"
-  },
-  {
-    "id": 2865,
-    "problem_id": 2806,
-    "problem": "line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E, line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E\nCDFE \\sim ABHG. What is the ratio of the areas from the CDFE to the ABHG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2806.jpg"
-  },
-  {
-    "id": 2866,
-    "problem_id": 2807,
-    "problem": "line D E, line A B D, line A E, line A C, line B C, line D E, line A B D, line A E, line A C, line B C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2807.jpg"
-  },
-  {
-    "id": 2867,
-    "problem_id": 2808,
-    "problem": "line D E, line A B D, line A E, line A C, line B C, line D E, line A B D, line A E, line A C, line B C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2808.jpg"
-  },
-  {
-    "id": 2868,
-    "problem_id": 2809,
-    "problem": "line D E, line A B D, line A E, line A C, line B C, line D E, line A B D, line A E, line A C, line B C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2809.jpg"
-  },
-  {
-    "id": 2869,
-    "problem_id": 2810,
-    "problem": "line D B A, line A C, line B C, line D C, line D B A, line A C, line B C, line D C\nIf x = 14, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2810.jpg"
-  },
-  {
-    "id": 2870,
-    "problem_id": 2811,
-    "problem": "line D B A, line F G H, line B E, line E G, line E C, \\odot E lieson D F H C A, line D B A, line F G H, line B E, line E G, line E C, \\odot E lieson D F H C A\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2811.jpg"
-  },
-  {
-    "id": 2871,
-    "problem_id": 2812,
-    "problem": "line D B A, line F G H, line B E, line E G, line E C, \\odot E lieson D F H C A, line D B A, line F G H, line B E, line E G, line E C, \\odot E lieson D F H C A\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2812.jpg"
-  },
-  {
-    "id": 2872,
-    "problem_id": 2813,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2813.jpg"
-  },
-  {
-    "id": 2873,
-    "problem_id": 2814,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2814.jpg"
-  },
-  {
-    "id": 2874,
-    "problem_id": 2815,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2815.jpg"
-  },
-  {
-    "id": 2875,
-    "problem_id": 2816,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2816.jpg"
-  },
-  {
-    "id": 2876,
-    "problem_id": 2817,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nUse the Law of Sines to find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2817.jpg"
-  },
-  {
-    "id": 2877,
-    "problem_id": 2818,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nUse the Law of Sines to find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2818.jpg"
-  },
-  {
-    "id": 2878,
-    "problem_id": 2819,
-    "problem": "line J B K, line H K, line H J, \\odot B lieson H J K, line J B K, line H K, line H J, \\odot B lieson H J K\nSolve for m \\angle HKB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2819.jpg"
-  },
-  {
-    "id": 2879,
-    "problem_id": 2820,
-    "problem": "line B T C, line D U V E, line A T U F, line B T C, line D U V E, line A T U F\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2820.jpg"
-  },
-  {
-    "id": 2880,
-    "problem_id": 2821,
-    "problem": "line B T C, line D U V E, line A T U F, line B T C, line D U V E, line A T U F\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2821.jpg"
-  },
-  {
-    "id": 2881,
-    "problem_id": 2822,
-    "problem": "line Q U T, line Q R, line S U R, line S T, \\odot A lieson Q S T R, line Q U T, line Q R, line S U R, line S T, \\odot A lieson Q S T R\nm \\widehat TR = 100, and SR \\perp QT. What is the measure of \\angle 4?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2822.jpg"
-  },
-  {
-    "id": 2882,
-    "problem_id": 2823,
-    "problem": "line B C D E, line F C A, line G E, \\odot H lieson B F G D A, line B C D E, line F C A, line G E, \\odot H lieson B F G D A\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2823.jpg"
-  },
-  {
-    "id": 2883,
-    "problem_id": 2824,
-    "problem": "line P M, line P Q, \\odot P lieson M Q, line P M, line P Q, \\odot P lieson M Q\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2824.jpg"
-  },
-  {
-    "id": 2884,
-    "problem_id": 2825,
-    "problem": "line P M, line P Q, \\odot P lieson M Q, line P M, line P Q, \\odot P lieson M Q\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2825.jpg"
-  },
-  {
-    "id": 2885,
-    "problem_id": 2826,
-    "problem": "line A B D, line C D, line C B, line A C, line A B D, line C D, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2826.jpg"
-  },
-  {
-    "id": 2886,
-    "problem_id": 2827,
-    "problem": "line A B D, line C D, line C B, line A C, line A B D, line C D, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2827.jpg"
-  },
-  {
-    "id": 2887,
-    "problem_id": 2828,
-    "problem": "line A B D, line C D, line C B, line A C, line A B D, line C D, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2828.jpg"
-  },
-  {
-    "id": 2888,
-    "problem_id": 2829,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2829.jpg"
-  },
-  {
-    "id": 2889,
-    "problem_id": 2830,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2830.jpg"
-  },
-  {
-    "id": 2890,
-    "problem_id": 2831,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2831.jpg"
-  },
-  {
-    "id": 2891,
-    "problem_id": 2832,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2832.jpg"
-  },
-  {
-    "id": 2892,
-    "problem_id": 2833,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2833.jpg"
-  },
-  {
-    "id": 2893,
-    "problem_id": 2834,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2834.jpg"
-  },
-  {
-    "id": 2894,
-    "problem_id": 2835,
-    "problem": "line A B C D, line A B C D\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2835.jpg"
-  },
-  {
-    "id": 2895,
-    "problem_id": 2836,
-    "problem": "line E A B D F, line G C B, line E A B D F, line G C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2836.jpg"
-  },
-  {
-    "id": 2896,
-    "problem_id": 2837,
-    "problem": "line E A B D F, line G C B, line E A B D F, line G C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2837.jpg"
-  },
-  {
-    "id": 2897,
-    "problem_id": 2838,
-    "problem": "line E A B D F, line G C B, line E A B D F, line G C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2838.jpg"
-  },
-  {
-    "id": 2898,
-    "problem_id": 2839,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the perimeter of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2839.jpg"
-  },
-  {
-    "id": 2899,
-    "problem_id": 2840,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the perimeter of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2840.jpg"
-  },
-  {
-    "id": 2900,
-    "problem_id": 2841,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the perimeter of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2841.jpg"
-  },
-  {
-    "id": 2901,
-    "problem_id": 2842,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the perimeter of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2842.jpg"
-  },
-  {
-    "id": 2902,
-    "problem_id": 2843,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the perimeter of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2843.jpg"
-  },
-  {
-    "id": 2903,
-    "problem_id": 2844,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nUse a Pythagorean Triple to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2844.jpg"
-  },
-  {
-    "id": 2904,
-    "problem_id": 2845,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2845.jpg"
-  },
-  {
-    "id": 2905,
-    "problem_id": 2846,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2846.jpg"
-  },
-  {
-    "id": 2906,
-    "problem_id": 2847,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2847.jpg"
-  },
-  {
-    "id": 2907,
-    "problem_id": 2848,
-    "problem": "line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R, line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R\nPolygon BCDE \\cong polygon RSTU. Find w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2848.jpg"
-  },
-  {
-    "id": 2908,
-    "problem_id": 2849,
-    "problem": "line D F G A, line D E, line F E, line D F G A, line D E, line F E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2849.jpg"
-  },
-  {
-    "id": 2909,
-    "problem_id": 2850,
-    "problem": "line D F G A, line D E, line F E, line D F G A, line D E, line F E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2850.jpg"
-  },
-  {
-    "id": 2910,
-    "problem_id": 2851,
-    "problem": "line D F G A, line D E, line F E, line D F G A, line D E, line F E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2851.jpg"
-  },
-  {
-    "id": 2911,
-    "problem_id": 2852,
-    "problem": "line C A, line A B, line C B, line D E, line F D, line F E, line C A, line A B, line C B, line D E, line F D, line F E\nFor the pair of similar figures, the area of the blue figure is 13.5 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2852.jpg"
-  },
-  {
-    "id": 2912,
-    "problem_id": 2853,
-    "problem": "line C A, line A B, line C B, line D E, line F D, line F E, line C A, line A B, line C B, line D E, line F D, line F E\nFor the pair of similar figures, the area of the blue figure is 13.5 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2853.jpg"
-  },
-  {
-    "id": 2913,
-    "problem_id": 2854,
-    "problem": "line C A, line A B, line C B, line D E, line F D, line F E, line C A, line A B, line C B, line D E, line F D, line F E\nFor the pair of similar figures, the area of the blue figure is 13.5 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2854.jpg"
-  },
-  {
-    "id": 2914,
-    "problem_id": 2855,
-    "problem": "line C A, line A B, line C B, line D E, line F D, line F E, line C A, line A B, line C B, line D E, line F D, line F E\nFor the pair of similar figures, the area of the blue figure is 13.5 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2855.jpg"
-  },
-  {
-    "id": 2915,
-    "problem_id": 2856,
-    "problem": "line C A, line A B, line C B, line D E, line F D, line F E, line C A, line A B, line C B, line D E, line F D, line F E\nFor the pair of similar figures, the area of the blue figure is 13.5 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2856.jpg"
-  },
-  {
-    "id": 2916,
-    "problem_id": 2857,
-    "problem": "line C A, line A B, line C B, line D E, line F D, line F E, line C A, line A B, line C B, line D E, line F D, line F E\nFor the pair of similar figures, the area of the blue figure is 13.5 ft^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2857.jpg"
-  },
-  {
-    "id": 2917,
-    "problem_id": 2858,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2858.jpg"
-  },
-  {
-    "id": 2918,
-    "problem_id": 2859,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2859.jpg"
-  },
-  {
-    "id": 2919,
-    "problem_id": 2860,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2860.jpg"
-  },
-  {
-    "id": 2921,
-    "problem_id": 2861,
-    "problem": "line A B, line C B, line A C, \\odot O lieson A B C, line A B, line C B, line A C, \\odot O lieson A B C\nFind m \\widehat BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2861.jpg"
-  },
-  {
-    "id": 2922,
-    "problem_id": 2862,
-    "problem": "line A B, line C B, line A C, \\odot O lieson A B C, line A B, line C B, line A C, \\odot O lieson A B C\nFind m \\widehat BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2862.jpg"
-  },
-  {
-    "id": 2923,
-    "problem_id": 2863,
-    "problem": "line A B, line C B, line A C, \\odot O lieson A B C, line A B, line C B, line A C, \\odot O lieson A B C\nFind m \\widehat BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2863.jpg"
-  },
-  {
-    "id": 2924,
-    "problem_id": 2864,
-    "problem": "line A D, line C B D, line C A, line A B, line A D, line C B D, line C A, line A B\nFind the value of variable d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2864.jpg"
-  },
-  {
-    "id": 2925,
-    "problem_id": 2865,
-    "problem": "line A S O, line O T B, line C R O, line A S O, line O T B, line C R O\nIf m \\angle RQT = 155, what is m \\angle RQS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2865.jpg"
-  },
-  {
-    "id": 2926,
-    "problem_id": 2866,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2866.jpg"
-  },
-  {
-    "id": 2927,
-    "problem_id": 2867,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2867.jpg"
-  },
-  {
-    "id": 2928,
-    "problem_id": 2868,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2868.jpg"
-  },
-  {
-    "id": 2929,
-    "problem_id": 2869,
-    "problem": "line A D, line A B, line B C, line D C, line A D, line A B, line B C, line D C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2869.jpg"
-  },
-  {
-    "id": 2930,
-    "problem_id": 2870,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2870.jpg"
-  },
-  {
-    "id": 2931,
-    "problem_id": 2871,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2871.jpg"
-  },
-  {
-    "id": 2932,
-    "problem_id": 2872,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2872.jpg"
-  },
-  {
-    "id": 2933,
-    "problem_id": 2873,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2873.jpg"
-  },
-  {
-    "id": 2934,
-    "problem_id": 2874,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 5 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2874.jpg"
-  },
-  {
-    "id": 2935,
-    "problem_id": 2875,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 5 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2875.jpg"
-  },
-  {
-    "id": 2936,
-    "problem_id": 2876,
-    "problem": "line D B A, line D E C, \\odot F lieson B E C A, line D B A, line D E C, \\odot F lieson B E C A\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2876.jpg"
-  },
-  {
-    "id": 2937,
-    "problem_id": 2877,
-    "problem": "line A D, line A B, line A C, line B C, line C D, line A D, line A B, line A C, line B C, line C D\nWhat is the perimeter of polygon ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2877.jpg"
-  },
-  {
-    "id": 2938,
-    "problem_id": 2878,
-    "problem": "line A D, line A B, line A C, line B C, line C D, line A D, line A B, line A C, line B C, line C D\nWhat is the perimeter of polygon ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2878.jpg"
-  },
-  {
-    "id": 2939,
-    "problem_id": 2879,
-    "problem": "line A D, line A B, line A C, line B C, line C D, line A D, line A B, line A C, line B C, line C D\nWhat is the perimeter of polygon ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2879.jpg"
-  },
-  {
-    "id": 2940,
-    "problem_id": 2880,
-    "problem": "line A D, line A B, line A C, line B C, line C D, line A D, line A B, line A C, line B C, line C D\nWhat is the perimeter of polygon ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2880.jpg"
-  },
-  {
-    "id": 2941,
-    "problem_id": 2881,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2881.jpg"
-  },
-  {
-    "id": 2942,
-    "problem_id": 2882,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2882.jpg"
-  },
-  {
-    "id": 2943,
-    "problem_id": 2883,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2883.jpg"
-  },
-  {
-    "id": 2944,
-    "problem_id": 2884,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2884.jpg"
-  },
-  {
-    "id": 2945,
-    "problem_id": 2885,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2885.jpg"
-  },
-  {
-    "id": 2946,
-    "problem_id": 2886,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2886.jpg"
-  },
-  {
-    "id": 2947,
-    "problem_id": 2887,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat TR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2887.jpg"
-  },
-  {
-    "id": 2949,
-    "problem_id": 2888,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat TR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2888.jpg"
-  },
-  {
-    "id": 2950,
-    "problem_id": 2889,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat TR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2889.jpg"
-  },
-  {
-    "id": 2951,
-    "problem_id": 2890,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat TR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2890.jpg"
-  },
-  {
-    "id": 2952,
-    "problem_id": 2891,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat TR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2891.jpg"
-  },
-  {
-    "id": 2953,
-    "problem_id": 2892,
-    "problem": "line N M, line K N, line N L, \\odot N lieson K M L, line N M, line K N, line N L, \\odot N lieson K M L\nFind the length of \\widehat KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2892.jpg"
-  },
-  {
-    "id": 2954,
-    "problem_id": 2893,
-    "problem": "line A B C, line A D, line D B, line D C, line A B C, line A D, line D B, line D C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2893.jpg"
-  },
-  {
-    "id": 2955,
-    "problem_id": 2894,
-    "problem": "line A B C, line A D, line D B, line D C, line A B C, line A D, line D B, line D C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2894.jpg"
-  },
-  {
-    "id": 2956,
-    "problem_id": 2895,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the measure of DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2895.jpg"
-  },
-  {
-    "id": 2957,
-    "problem_id": 2896,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the measure of DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2896.jpg"
-  },
-  {
-    "id": 2958,
-    "problem_id": 2897,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle F?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2897.jpg"
-  },
-  {
-    "id": 2959,
-    "problem_id": 2898,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle F?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2898.jpg"
-  },
-  {
-    "id": 2960,
-    "problem_id": 2899,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle F?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2899.jpg"
-  },
-  {
-    "id": 2961,
-    "problem_id": 2900,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle F?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2900.jpg"
-  },
-  {
-    "id": 2962,
-    "problem_id": 2901,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle F?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2901.jpg"
-  },
-  {
-    "id": 2963,
-    "problem_id": 2902,
-    "problem": "line M K Q P, line M L N, line J Q N, \\odot A lieson J K L N P, line M K Q P, line M L N, line J Q N, \\odot A lieson J K L N P\nFind m \\widehat PN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2902.jpg"
-  },
-  {
-    "id": 2964,
-    "problem_id": 2903,
-    "problem": "line M K Q P, line M L N, line J Q N, \\odot A lieson J K L N P, line M K Q P, line M L N, line J Q N, \\odot A lieson J K L N P\nFind m \\widehat PN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2903.jpg"
-  },
-  {
-    "id": 2966,
-    "problem_id": 2904,
-    "problem": "line R U V, line R S T, \\odot A lieson S U V T, line R U V, line R S T, \\odot A lieson S U V T\nFind m \\widehat SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2904.jpg"
-  },
-  {
-    "id": 2967,
-    "problem_id": 2905,
-    "problem": "line R U V, line R S T, \\odot A lieson S U V T, line R U V, line R S T, \\odot A lieson S U V T\nFind m \\widehat SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2905.jpg"
-  },
-  {
-    "id": 2968,
-    "problem_id": 2906,
-    "problem": "line R U V, line R S T, \\odot A lieson S U V T, line R U V, line R S T, \\odot A lieson S U V T\nFind m \\widehat SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2906.jpg"
-  },
-  {
-    "id": 2969,
-    "problem_id": 2907,
-    "problem": "line R U V, line R S T, \\odot A lieson S U V T, line R U V, line R S T, \\odot A lieson S U V T\nFind m \\widehat SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2907.jpg"
-  },
-  {
-    "id": 2970,
-    "problem_id": 2908,
-    "problem": "line B A, line A D, line C D, line B C, line B D, line B A, line A D, line C D, line B C, line B D\nFind the value of variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2908.jpg"
-  },
-  {
-    "id": 2971,
-    "problem_id": 2909,
-    "problem": "line B A, line A D, line C D, line B C, line B D, line B A, line A D, line C D, line B C, line B D\nFind the value of variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2909.jpg"
-  },
-  {
-    "id": 2972,
-    "problem_id": 2910,
-    "problem": "line B A, line A D, line C D, line B C, line B D, line B A, line A D, line C D, line B C, line B D\nFind the value of variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2910.jpg"
-  },
-  {
-    "id": 2973,
-    "problem_id": 2911,
-    "problem": "line B A, line A D, line C D, line B C, line B D, line B A, line A D, line C D, line B C, line B D\nFind the value of variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2911.jpg"
-  },
-  {
-    "id": 2974,
-    "problem_id": 2912,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2912.jpg"
-  },
-  {
-    "id": 2975,
-    "problem_id": 2913,
-    "problem": "line A D, line A B, line A C, line B C D, line A D, line A B, line A C, line B C D\nFind the value of variable d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2913.jpg"
-  },
-  {
-    "id": 2976,
-    "problem_id": 2914,
-    "problem": "line A D, line A B, line A C, line B C D, line A D, line A B, line A C, line B C D\nFind the value of variable d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2914.jpg"
-  },
-  {
-    "id": 2977,
-    "problem_id": 2915,
-    "problem": "line B N K, line A L K, line C J K, line B N K, line A L K, line C J K\nKM is the angle bisector of \\angle JKL. Find m \\angle JKL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2915.jpg"
-  },
-  {
-    "id": 2979,
-    "problem_id": 2916,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2916.jpg"
-  },
-  {
-    "id": 2980,
-    "problem_id": 2917,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2917.jpg"
-  },
-  {
-    "id": 2981,
-    "problem_id": 2918,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2918.jpg"
-  },
-  {
-    "id": 2982,
-    "problem_id": 2919,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2919.jpg"
-  },
-  {
-    "id": 2983,
-    "problem_id": 2920,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2920.jpg"
-  },
-  {
-    "id": 2984,
-    "problem_id": 2921,
-    "problem": "line A B C, line C D, line A D, line B D, line A B C, line C D, line A D, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2921.jpg"
-  },
-  {
-    "id": 2985,
-    "problem_id": 2922,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2922.jpg"
-  },
-  {
-    "id": 2986,
-    "problem_id": 2923,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2923.jpg"
-  },
-  {
-    "id": 2987,
-    "problem_id": 2924,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2924.jpg"
-  },
-  {
-    "id": 2988,
-    "problem_id": 2925,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2925.jpg"
-  },
-  {
-    "id": 2989,
-    "problem_id": 2926,
-    "problem": "line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F, line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2926.jpg"
-  },
-  {
-    "id": 2990,
-    "problem_id": 2927,
-    "problem": "line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F, line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2927.jpg"
-  },
-  {
-    "id": 2991,
-    "problem_id": 2928,
-    "problem": "line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F, line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2928.jpg"
-  },
-  {
-    "id": 2992,
-    "problem_id": 2929,
-    "problem": "line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F, line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2929.jpg"
-  },
-  {
-    "id": 2993,
-    "problem_id": 2930,
-    "problem": "line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F, line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2930.jpg"
-  },
-  {
-    "id": 2994,
-    "problem_id": 2931,
-    "problem": "line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F, line A D B, line B E C, line A G C, line A F, line F G, line F C, line F E, line D F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2931.jpg"
-  },
-  {
-    "id": 2995,
-    "problem_id": 2932,
-    "problem": "line C A B, line C D E, \\odot F lieson A D E B, line C A B, line C D E, \\odot F lieson A D E B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2932.jpg"
-  },
-  {
-    "id": 2996,
-    "problem_id": 2933,
-    "problem": "line C A B, line C D E, \\odot F lieson A D E B, line C A B, line C D E, \\odot F lieson A D E B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2933.jpg"
-  },
-  {
-    "id": 2997,
-    "problem_id": 2934,
-    "problem": "line C A B, line C D E, \\odot F lieson A D E B, line C A B, line C D E, \\odot F lieson A D E B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2934.jpg"
-  },
-  {
-    "id": 2998,
-    "problem_id": 2935,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2935.jpg"
-  },
-  {
-    "id": 2999,
-    "problem_id": 2936,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2936.jpg"
-  },
-  {
-    "id": 3000,
-    "problem_id": 2937,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2937.jpg"
-  },
-  {
-    "id": 3001,
-    "problem_id": 2938,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2938.jpg"
-  },
-  {
-    "id": 3002,
-    "problem_id": 2939,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2939.jpg"
-  },
-  {
-    "id": 3003,
-    "problem_id": 2940,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2940.jpg"
-  },
-  {
-    "id": 3004,
-    "problem_id": 2941,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2941.jpg"
-  },
-  {
-    "id": 3005,
-    "problem_id": 2942,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2942.jpg"
-  },
-  {
-    "id": 3006,
-    "problem_id": 2943,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the diameter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2943.jpg"
-  },
-  {
-    "id": 3007,
-    "problem_id": 2944,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the diameter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2944.jpg"
-  },
-  {
-    "id": 3008,
-    "problem_id": 2945,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the diameter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2945.jpg"
-  },
-  {
-    "id": 3009,
-    "problem_id": 2946,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the diameter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2946.jpg"
-  },
-  {
-    "id": 3010,
-    "problem_id": 2947,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the diameter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2947.jpg"
-  },
-  {
-    "id": 3011,
-    "problem_id": 2948,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the diameter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2948.jpg"
-  },
-  {
-    "id": 3012,
-    "problem_id": 2949,
-    "problem": "line K P L, line L H M, line K J M, line P J, line J H, line P H, line K P L, line L H M, line K J M, line P J, line J H, line P H\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2949.jpg"
-  },
-  {
-    "id": 3013,
-    "problem_id": 2950,
-    "problem": "line K P L, line L H M, line K J M, line P J, line J H, line P H, line K P L, line L H M, line K J M, line P J, line J H, line P H\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2950.jpg"
-  },
-  {
-    "id": 3014,
-    "problem_id": 2951,
-    "problem": "line K P L, line L H M, line K J M, line P J, line J H, line P H, line K P L, line L H M, line K J M, line P J, line J H, line P H\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2951.jpg"
-  },
-  {
-    "id": 3015,
-    "problem_id": 2952,
-    "problem": "line K P L, line L H M, line K J M, line P J, line J H, line P H, line K P L, line L H M, line K J M, line P J, line J H, line P H\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2952.jpg"
-  },
-  {
-    "id": 3016,
-    "problem_id": 2953,
-    "problem": "line D C, line A B, line D A, line C B, line D C, line A B, line D A, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2953.jpg"
-  },
-  {
-    "id": 3017,
-    "problem_id": 2954,
-    "problem": "line D C, line A B, line D A, line C B, line D C, line A B, line D A, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2954.jpg"
-  },
-  {
-    "id": 3018,
-    "problem_id": 2955,
-    "problem": "line D C, line A B, line D A, line C B, line D C, line A B, line D A, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2955.jpg"
-  },
-  {
-    "id": 3019,
-    "problem_id": 2956,
-    "problem": "line D C, line A B, line D A, line C B, line D C, line A B, line D A, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2956.jpg"
-  },
-  {
-    "id": 3020,
-    "problem_id": 2957,
-    "problem": "line D C, line A B, line D A, line C B, line D C, line A B, line D A, line C B\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2957.jpg"
-  },
-  {
-    "id": 3021,
-    "problem_id": 2958,
-    "problem": "line t lieson D E F G, line u lieson H I J K, line s lieson A C E I M, line r lieson B C F J L, line t lieson D E F G, line u lieson H I J K, line s lieson A C E I M, line r lieson B C F J L\nm \\angle 5 = 72 and m \\angle 9 = 102. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2958.jpg"
-  },
-  {
-    "id": 3022,
-    "problem_id": 2959,
-    "problem": "line t lieson D E F G, line u lieson H I J K, line s lieson A C E I M, line r lieson B C F J L, line t lieson D E F G, line u lieson H I J K, line s lieson A C E I M, line r lieson B C F J L\nm \\angle 5 = 72 and m \\angle 9 = 102. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2959.jpg"
-  },
-  {
-    "id": 3023,
-    "problem_id": 2960,
-    "problem": "line J X K, line J Z Y, line W Z K, line J W L, line L Y K, line X Z L, line J X K, line J Z Y, line W Z K, line J W L, line L Y K, line X Z L\nIn \\triangle JKL, ZW = 7, and LX = 8.1. Determine the length of KW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2960.jpg"
-  },
-  {
-    "id": 3024,
-    "problem_id": 2961,
-    "problem": "line N M, line P Q, \\odot K lieson P Q, \\odot J lieson N M, line N M, line P Q, \\odot K lieson P Q, \\odot J lieson N M\n\\odot J \\cong \\odot K and \\widehat MN = \\widehat PQ. Find PQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2961.jpg"
-  },
-  {
-    "id": 3025,
-    "problem_id": 2962,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2962.jpg"
-  },
-  {
-    "id": 3026,
-    "problem_id": 2963,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2963.jpg"
-  },
-  {
-    "id": 3027,
-    "problem_id": 2964,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2964.jpg"
-  },
-  {
-    "id": 3028,
-    "problem_id": 2965,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2965.jpg"
-  },
-  {
-    "id": 3029,
-    "problem_id": 2966,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2966.jpg"
-  },
-  {
-    "id": 3030,
-    "problem_id": 2967,
-    "problem": "line C D E, line B E, line A B, line A D, line A C, line C D E, line B E, line A B, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2967.jpg"
-  },
-  {
-    "id": 3031,
-    "problem_id": 2968,
-    "problem": "line C D E, line B E, line A B, line A D, line A C, line C D E, line B E, line A B, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2968.jpg"
-  },
-  {
-    "id": 3032,
-    "problem_id": 2969,
-    "problem": "line C D E, line B E, line A B, line A D, line A C, line C D E, line B E, line A B, line A D, line A C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2969.jpg"
-  },
-  {
-    "id": 3033,
-    "problem_id": 2970,
-    "problem": "line A C E, line B C D, line A C E, line B C D\nm \\angle 1 = 65, find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2970.jpg"
-  },
-  {
-    "id": 3034,
-    "problem_id": 2971,
-    "problem": "line A C E, line B C D, line A C E, line B C D\nm \\angle 1 = 65, find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2971.jpg"
-  },
-  {
-    "id": 3035,
-    "problem_id": 2972,
-    "problem": "line H G, line J H, line J K, line G K, line H G, line J H, line J K, line G K\nFind the measure of \\angle HJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2972.jpg"
-  },
-  {
-    "id": 3037,
-    "problem_id": 2973,
-    "problem": "line H G, line J H, line J K, line G K, line H G, line J H, line J K, line G K\nFind the measure of \\angle HJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2973.jpg"
-  },
-  {
-    "id": 3038,
-    "problem_id": 2974,
-    "problem": "line H G, line J H, line J K, line G K, line H G, line J H, line J K, line G K\nFind the measure of \\angle HJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2974.jpg"
-  },
-  {
-    "id": 3039,
-    "problem_id": 2975,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable s in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2975.jpg"
-  },
-  {
-    "id": 3040,
-    "problem_id": 2976,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable s in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2976.jpg"
-  },
-  {
-    "id": 3041,
-    "problem_id": 2977,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable s in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2977.jpg"
-  },
-  {
-    "id": 3042,
-    "problem_id": 2978,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable s in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2978.jpg"
-  },
-  {
-    "id": 3043,
-    "problem_id": 2979,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2979.jpg"
-  },
-  {
-    "id": 3044,
-    "problem_id": 2980,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2980.jpg"
-  },
-  {
-    "id": 3045,
-    "problem_id": 2981,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2981.jpg"
-  },
-  {
-    "id": 3046,
-    "problem_id": 2982,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2982.jpg"
-  },
-  {
-    "id": 3047,
-    "problem_id": 2983,
-    "problem": "line C A B, line D A, line C A B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2983.jpg"
-  },
-  {
-    "id": 3048,
-    "problem_id": 2984,
-    "problem": "line C A B, line D A, line C A B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2984.jpg"
-  },
-  {
-    "id": 3049,
-    "problem_id": 2985,
-    "problem": "line C A B, line D A, line C A B, line D A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2985.jpg"
-  },
-  {
-    "id": 3050,
-    "problem_id": 2986,
-    "problem": "line C A, line A B, line C B, line D A, line D C, line C A, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2986.jpg"
-  },
-  {
-    "id": 3051,
-    "problem_id": 2987,
-    "problem": "line C A, line A B, line C B, line D A, line D C, line C A, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2987.jpg"
-  },
-  {
-    "id": 3052,
-    "problem_id": 2988,
-    "problem": "line C A, line A B, line C B, line D A, line D C, line C A, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2988.jpg"
-  },
-  {
-    "id": 3053,
-    "problem_id": 2989,
-    "problem": "line A B, line P B, line C P, line A C, \\odot P lieson A C B, line A B, line P B, line C P, line A C, \\odot P lieson A C B\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2989.jpg"
-  },
-  {
-    "id": 3054,
-    "problem_id": 2990,
-    "problem": "line A B, line P B, line C P, line A C, \\odot P lieson A C B, line A B, line P B, line C P, line A C, \\odot P lieson A C B\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2990.jpg"
-  },
-  {
-    "id": 3055,
-    "problem_id": 2991,
-    "problem": "line A B, line P B, line C P, line A C, \\odot P lieson A C B, line A B, line P B, line C P, line A C, \\odot P lieson A C B\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2991.jpg"
-  },
-  {
-    "id": 3056,
-    "problem_id": 2992,
-    "problem": "line A C, line A B, \\odot A lieson B C, line A C, line A B, \\odot A lieson B C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2992.jpg"
-  },
-  {
-    "id": 3057,
-    "problem_id": 2993,
-    "problem": "line A C, line A B, \\odot A lieson B C, line A C, line A B, \\odot A lieson B C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2993.jpg"
-  },
-  {
-    "id": 3058,
-    "problem_id": 2994,
-    "problem": "line A C, line A B, \\odot A lieson B C, line A C, line A B, \\odot A lieson B C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2994.jpg"
-  },
-  {
-    "id": 3059,
-    "problem_id": 2995,
-    "problem": "line A C, line A B, \\odot A lieson B C, line A C, line A B, \\odot A lieson B C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2995.jpg"
-  },
-  {
-    "id": 3060,
-    "problem_id": 2996,
-    "problem": "line A C, line A B, \\odot A lieson B C, line A C, line A B, \\odot A lieson B C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2996.jpg"
-  },
-  {
-    "id": 3062,
-    "problem_id": 2997,
-    "problem": "line A D F G E B, line C B, line C E, line C G, line C F, line C D, line A C, line A D F G E B, line C B, line C E, line C G, line C F, line C D, line A C\n\\triangle ABC is isosceles, \\triangle DCE is equilateral, and \\triangle FCG is isosceles. Find the measure of the \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2997.jpg"
-  },
-  {
-    "id": 3063,
-    "problem_id": 2998,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2998.jpg"
-  },
-  {
-    "id": 3064,
-    "problem_id": 2999,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/2999.jpg"
-  },
-  {
-    "id": 3065,
-    "problem_id": 3000,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3000.jpg"
-  },
-  {
-    "id": 3066,
-    "problem_id": 3001,
-    "problem": "line V T, line V U, line S T, line S V, line T U, line V T, line V U, line S T, line S V, line T U\nFind the measure of VT in rectangle STUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3001.jpg"
-  },
-  {
-    "id": 3067,
-    "problem_id": 3002,
-    "problem": "line V T, line V U, line S T, line S V, line T U, line V T, line V U, line S T, line S V, line T U\nFind the measure of VT in rectangle STUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3002.jpg"
-  },
-  {
-    "id": 3068,
-    "problem_id": 3003,
-    "problem": "line V T, line V U, line S T, line S V, line T U, line V T, line V U, line S T, line S V, line T U\nFind the measure of VT in rectangle STUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3003.jpg"
-  },
-  {
-    "id": 3069,
-    "problem_id": 3004,
-    "problem": "line A B, line A D C, line B C, line B D, line A B, line A D C, line B C, line B D\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3004.jpg"
-  },
-  {
-    "id": 3070,
-    "problem_id": 3005,
-    "problem": "line A B, line A D C, line B C, line B D, line A B, line A D C, line B C, line B D\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3005.jpg"
-  },
-  {
-    "id": 3071,
-    "problem_id": 3006,
-    "problem": "line X M Y, line X M Y\nM is the midpoint of XY. Find the length of XM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3006.jpg"
-  },
-  {
-    "id": 3072,
-    "problem_id": 3007,
-    "problem": "line X M Y, line X M Y\nM is the midpoint of XY. Find the length of XM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3007.jpg"
-  },
-  {
-    "id": 3073,
-    "problem_id": 3008,
-    "problem": "line X M Y, line X M Y\nM is the midpoint of XY. Find the length of XM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3008.jpg"
-  },
-  {
-    "id": 3074,
-    "problem_id": 3009,
-    "problem": "line S T, line S U, \\odot A lieson U T S, line S T, line S U, \\odot A lieson U T S\nFind the measure of \\angle UST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3009.jpg"
-  },
-  {
-    "id": 3075,
-    "problem_id": 3010,
-    "problem": "line A B, line C B, line E D C, line E A, line D A, line A B, line C B, line E D C, line E A, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3010.jpg"
-  },
-  {
-    "id": 3076,
-    "problem_id": 3011,
-    "problem": "line A B, line C B, line E D C, line E A, line D A, line A B, line C B, line E D C, line E A, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3011.jpg"
-  },
-  {
-    "id": 3077,
-    "problem_id": 3012,
-    "problem": "line A B, line C B, line E D C, line E A, line D A, line A B, line C B, line E D C, line E A, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3012.jpg"
-  },
-  {
-    "id": 3078,
-    "problem_id": 3013,
-    "problem": "line A B, line C B, line E D C, line E A, line D A, line A B, line C B, line E D C, line E A, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3013.jpg"
-  },
-  {
-    "id": 3079,
-    "problem_id": 3014,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3014.jpg"
-  },
-  {
-    "id": 3080,
-    "problem_id": 3015,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3015.jpg"
-  },
-  {
-    "id": 3081,
-    "problem_id": 3016,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3016.jpg"
-  },
-  {
-    "id": 3082,
-    "problem_id": 3017,
-    "problem": "line B A, line C D, line A D, line B C, line B A, line C D, line A D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3017.jpg"
-  },
-  {
-    "id": 3083,
-    "problem_id": 3018,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3018.jpg"
-  },
-  {
-    "id": 3084,
-    "problem_id": 3019,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3019.jpg"
-  },
-  {
-    "id": 3085,
-    "problem_id": 3020,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3020.jpg"
-  },
-  {
-    "id": 3086,
-    "problem_id": 3021,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3021.jpg"
-  },
-  {
-    "id": 3087,
-    "problem_id": 3022,
-    "problem": "line P A R, line N A Q, \\odot B lieson N R Q P, line P A R, line N A Q, \\odot B lieson N R Q P\nFind m \\widehat RQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3022.jpg"
-  },
-  {
-    "id": 3088,
-    "problem_id": 3023,
-    "problem": "line C M, line C B, line A M B, line A C, line C M, line C B, line A M B, line A C\nFind the perimeter of \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3023.jpg"
-  },
-  {
-    "id": 3089,
-    "problem_id": 3024,
-    "problem": "line C M, line C B, line A M B, line A C, line C M, line C B, line A M B, line A C\nFind the perimeter of \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3024.jpg"
-  },
-  {
-    "id": 3090,
-    "problem_id": 3025,
-    "problem": "line C M, line C B, line A M B, line A C, line C M, line C B, line A M B, line A C\nFind the perimeter of \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3025.jpg"
-  },
-  {
-    "id": 3091,
-    "problem_id": 3026,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3026.jpg"
-  },
-  {
-    "id": 3092,
-    "problem_id": 3027,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3027.jpg"
-  },
-  {
-    "id": 3093,
-    "problem_id": 3028,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3028.jpg"
-  },
-  {
-    "id": 3094,
-    "problem_id": 3029,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3029.jpg"
-  },
-  {
-    "id": 3095,
-    "problem_id": 3030,
-    "problem": "line A B, line B R, line R S Q, line P R, line P S, line P Q, line C Q, line A C, line A B, line B R, line R S Q, line P R, line P S, line P Q, line C Q, line A C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3030.jpg"
-  },
-  {
-    "id": 3096,
-    "problem_id": 3031,
-    "problem": "line A B, line B R, line R S Q, line P R, line P S, line P Q, line C Q, line A C, line A B, line B R, line R S Q, line P R, line P S, line P Q, line C Q, line A C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3031.jpg"
-  },
-  {
-    "id": 3097,
-    "problem_id": 3032,
-    "problem": "line A B, line B R, line R S Q, line P R, line P S, line P Q, line C Q, line A C, line A B, line B R, line R S Q, line P R, line P S, line P Q, line C Q, line A C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3032.jpg"
-  },
-  {
-    "id": 3099,
-    "problem_id": 3033,
-    "problem": "line D F, line G D, line G F, line H K, line M K, line M H, line D F, line G D, line G F, line H K, line M K, line M H\n\\triangle DFG \\sim \\triangle HKM. Determine m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3033.jpg"
-  },
-  {
-    "id": 3100,
-    "problem_id": 3034,
-    "problem": "line D F, line G D, line G F, line H K, line M K, line M H, line D F, line G D, line G F, line H K, line M K, line M H\n\\triangle DFG \\sim \\triangle HKM. Determine m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3034.jpg"
-  },
-  {
-    "id": 3101,
-    "problem_id": 3035,
-    "problem": "line D F, line G D, line G F, line H K, line M K, line M H, line D F, line G D, line G F, line H K, line M K, line M H\n\\triangle DFG \\sim \\triangle HKM. Determine m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3035.jpg"
-  },
-  {
-    "id": 3103,
-    "problem_id": 3036,
-    "problem": "line X Z, line Y W Z, line X Y, line X W, line X Z, line Y W Z, line X Y, line X W\nWhat is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3036.jpg"
-  },
-  {
-    "id": 3104,
-    "problem_id": 3037,
-    "problem": "line X Z, line Y W Z, line X Y, line X W, line X Z, line Y W Z, line X Y, line X W\nWhat is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3037.jpg"
-  },
-  {
-    "id": 3105,
-    "problem_id": 3038,
-    "problem": "line X Z, line Y W Z, line X Y, line X W, line X Z, line Y W Z, line X Y, line X W\nWhat is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3038.jpg"
-  },
-  {
-    "id": 3106,
-    "problem_id": 3039,
-    "problem": "line X Z, line Y W Z, line X Y, line X W, line X Z, line Y W Z, line X Y, line X W\nWhat is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3039.jpg"
-  },
-  {
-    "id": 3107,
-    "problem_id": 3040,
-    "problem": "line M N, line R Q, line R P, line L N, line L M, line Q P, line M N, line R Q, line R P, line L N, line L M, line Q P\n\\triangle LMN \\cong \\triangle PQR. What is PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3040.jpg"
-  },
-  {
-    "id": 3108,
-    "problem_id": 3041,
-    "problem": "line M N, line R Q, line R P, line L N, line L M, line Q P, line M N, line R Q, line R P, line L N, line L M, line Q P\n\\triangle LMN \\cong \\triangle PQR. What is PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3041.jpg"
-  },
-  {
-    "id": 3109,
-    "problem_id": 3042,
-    "problem": "line M N, line R Q, line R P, line L N, line L M, line Q P, line M N, line R Q, line R P, line L N, line L M, line Q P\n\\triangle LMN \\cong \\triangle PQR. What is PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3042.jpg"
-  },
-  {
-    "id": 3110,
-    "problem_id": 3043,
-    "problem": "line M N, line R Q, line R P, line L N, line L M, line Q P, line M N, line R Q, line R P, line L N, line L M, line Q P\n\\triangle LMN \\cong \\triangle PQR. What is PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3043.jpg"
-  },
-  {
-    "id": 3111,
-    "problem_id": 3044,
-    "problem": "line B A, line A D, line A E, line A C, \\odot A lieson B C D E, line B A, line A D, line A E, line A C, \\odot A lieson B C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3044.jpg"
-  },
-  {
-    "id": 3112,
-    "problem_id": 3045,
-    "problem": "line B A, line A D, line A E, line A C, \\odot A lieson B C D E, line B A, line A D, line A E, line A C, \\odot A lieson B C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3045.jpg"
-  },
-  {
-    "id": 3113,
-    "problem_id": 3046,
-    "problem": "line B A, line A D, line A E, line A C, \\odot A lieson B C D E, line B A, line A D, line A E, line A C, \\odot A lieson B C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3046.jpg"
-  },
-  {
-    "id": 3114,
-    "problem_id": 3047,
-    "problem": "line B A, line A D, line A E, line A C, \\odot A lieson B C D E, line B A, line A D, line A E, line A C, \\odot A lieson B C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3047.jpg"
-  },
-  {
-    "id": 3115,
-    "problem_id": 3048,
-    "problem": "line B A, line A D, line A E, line A C, \\odot A lieson B C D E, line B A, line A D, line A E, line A C, \\odot A lieson B C D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3048.jpg"
-  },
-  {
-    "id": 3116,
-    "problem_id": 3049,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3049.jpg"
-  },
-  {
-    "id": 3117,
-    "problem_id": 3050,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3050.jpg"
-  },
-  {
-    "id": 3118,
-    "problem_id": 3051,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3051.jpg"
-  },
-  {
-    "id": 3119,
-    "problem_id": 3052,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3052.jpg"
-  },
-  {
-    "id": 3120,
-    "problem_id": 3053,
-    "problem": "line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O, line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3053.jpg"
-  },
-  {
-    "id": 3121,
-    "problem_id": 3054,
-    "problem": "line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O, line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3054.jpg"
-  },
-  {
-    "id": 3122,
-    "problem_id": 3055,
-    "problem": "line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O, line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3055.jpg"
-  },
-  {
-    "id": 3123,
-    "problem_id": 3056,
-    "problem": "line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O, line N K L M, line G H I J, line C D E F, line B E I L P, line A D H K O\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3056.jpg"
-  },
-  {
-    "id": 3124,
-    "problem_id": 3057,
-    "problem": "line S U, line U T, line S T, line S U, line U T, line S T\nSolve for s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3057.jpg"
-  },
-  {
-    "id": 3125,
-    "problem_id": 3058,
-    "problem": "line S U, line U T, line S T, line S U, line U T, line S T\nSolve for s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3058.jpg"
-  },
-  {
-    "id": 3126,
-    "problem_id": 3059,
-    "problem": "line S U, line U T, line S T, line S U, line U T, line S T\nSolve for s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3059.jpg"
-  },
-  {
-    "id": 3127,
-    "problem_id": 3060,
-    "problem": "line S U, line U T, line S T, line S U, line U T, line S T\nSolve for s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3060.jpg"
-  },
-  {
-    "id": 3128,
-    "problem_id": 3061,
-    "problem": "line S U, line U T, line S T, line S U, line U T, line S T\nSolve for s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3061.jpg"
-  },
-  {
-    "id": 3129,
-    "problem_id": 3062,
-    "problem": "line S U, line U T, line S T, line S U, line U T, line S T\nSolve for s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3062.jpg"
-  },
-  {
-    "id": 3130,
-    "problem_id": 3063,
-    "problem": "line A C, line B C, line A B, \\odot B lieson A C, line A C, line B C, line A B, \\odot B lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3063.jpg"
-  },
-  {
-    "id": 3131,
-    "problem_id": 3064,
-    "problem": "line A C, line B C, line A B, \\odot B lieson A C, line A C, line B C, line A B, \\odot B lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3064.jpg"
-  },
-  {
-    "id": 3132,
-    "problem_id": 3065,
-    "problem": "line A B, line D B, line C B, line D C, line D A, line A B, line D B, line C B, line D C, line D A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3065.jpg"
-  },
-  {
-    "id": 3133,
-    "problem_id": 3066,
-    "problem": "line A B, line D B, line C B, line D C, line D A, line A B, line D B, line C B, line D C, line D A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3066.jpg"
-  },
-  {
-    "id": 3134,
-    "problem_id": 3067,
-    "problem": "line A B, line D B, line C B, line D C, line D A, line A B, line D B, line C B, line D C, line D A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3067.jpg"
-  },
-  {
-    "id": 3135,
-    "problem_id": 3068,
-    "problem": "line A B, line D B, line C B, line D C, line D A, line A B, line D B, line C B, line D C, line D A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3068.jpg"
-  },
-  {
-    "id": 3136,
-    "problem_id": 3069,
-    "problem": "line A B, line D B, line C B, line D C, line D A, line A B, line D B, line C B, line D C, line D A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3069.jpg"
-  },
-  {
-    "id": 3137,
-    "problem_id": 3070,
-    "problem": "line A B, line D B, line C B, line D C, line D A, line A B, line D B, line C B, line D C, line D A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3070.jpg"
-  },
-  {
-    "id": 3138,
-    "problem_id": 3071,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3071.jpg"
-  },
-  {
-    "id": 3139,
-    "problem_id": 3072,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3072.jpg"
-  },
-  {
-    "id": 3140,
-    "problem_id": 3073,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3073.jpg"
-  },
-  {
-    "id": 3141,
-    "problem_id": 3074,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3074.jpg"
-  },
-  {
-    "id": 3142,
-    "problem_id": 3075,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3075.jpg"
-  },
-  {
-    "id": 3143,
-    "problem_id": 3076,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3076.jpg"
-  },
-  {
-    "id": 3144,
-    "problem_id": 3077,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3077.jpg"
-  },
-  {
-    "id": 3145,
-    "problem_id": 3078,
-    "problem": "line V T, line U T, \\odot T lieson V U, line V T, line U T, \\odot T lieson V U\nFind the radius.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3078.jpg"
-  },
-  {
-    "id": 3146,
-    "problem_id": 3079,
-    "problem": "line V T, line U T, \\odot T lieson V U, line V T, line U T, \\odot T lieson V U\nFind the radius.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3079.jpg"
-  },
-  {
-    "id": 3147,
-    "problem_id": 3080,
-    "problem": "line D F, line E D, line E F, line D F, line E D, line E F\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3080.jpg"
-  },
-  {
-    "id": 3148,
-    "problem_id": 3081,
-    "problem": "line D F, line E D, line E F, line D F, line E D, line E F\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3081.jpg"
-  },
-  {
-    "id": 3149,
-    "problem_id": 3082,
-    "problem": "line D F, line E D, line E F, line D F, line E D, line E F\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3082.jpg"
-  },
-  {
-    "id": 3150,
-    "problem_id": 3083,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3083.jpg"
-  },
-  {
-    "id": 3151,
-    "problem_id": 3084,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3084.jpg"
-  },
-  {
-    "id": 3152,
-    "problem_id": 3085,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3085.jpg"
-  },
-  {
-    "id": 3153,
-    "problem_id": 3086,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3086.jpg"
-  },
-  {
-    "id": 3154,
-    "problem_id": 3087,
-    "problem": "line S V, line S T, line T U, line V U, line T V, line S V, line S T, line T U, line V U, line T V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3087.jpg"
-  },
-  {
-    "id": 3155,
-    "problem_id": 3088,
-    "problem": "line S V, line S T, line T U, line V U, line T V, line S V, line S T, line T U, line V U, line T V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3088.jpg"
-  },
-  {
-    "id": 3156,
-    "problem_id": 3089,
-    "problem": "line S V, line S T, line T U, line V U, line T V, line S V, line S T, line T U, line V U, line T V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3089.jpg"
-  },
-  {
-    "id": 3157,
-    "problem_id": 3090,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3090.jpg"
-  },
-  {
-    "id": 3158,
-    "problem_id": 3091,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3091.jpg"
-  },
-  {
-    "id": 3159,
-    "problem_id": 3092,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3092.jpg"
-  },
-  {
-    "id": 3160,
-    "problem_id": 3093,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3093.jpg"
-  },
-  {
-    "id": 3161,
-    "problem_id": 3094,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3094.jpg"
-  },
-  {
-    "id": 3162,
-    "problem_id": 3095,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3095.jpg"
-  },
-  {
-    "id": 3163,
-    "problem_id": 3096,
-    "problem": "line J M, line J K, line M K, line J M, line J K, line M K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3096.jpg"
-  },
-  {
-    "id": 3165,
-    "problem_id": 3097,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3097.jpg"
-  },
-  {
-    "id": 3166,
-    "problem_id": 3098,
-    "problem": "line L O K, line J M K, line L N J, line N O, line O M, line N M, line L O K, line J M K, line L N J, line N O, line O M, line N M\nIf JK = 5x+20 and NO = 20, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3098.jpg"
-  },
-  {
-    "id": 3167,
-    "problem_id": 3099,
-    "problem": "line L O K, line J M K, line L N J, line N O, line O M, line N M, line L O K, line J M K, line L N J, line N O, line O M, line N M\nIf JK = 5x+20 and NO = 20, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3099.jpg"
-  },
-  {
-    "id": 3168,
-    "problem_id": 3100,
-    "problem": "line L O K, line J M K, line L N J, line N O, line O M, line N M, line L O K, line J M K, line L N J, line N O, line O M, line N M\nIf JK = 5x+20 and NO = 20, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3100.jpg"
-  },
-  {
-    "id": 3169,
-    "problem_id": 3101,
-    "problem": "line L O K, line J M K, line L N J, line N O, line O M, line N M, line L O K, line J M K, line L N J, line N O, line O M, line N M\nIf JK = 5x+20 and NO = 20, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3101.jpg"
-  },
-  {
-    "id": 3170,
-    "problem_id": 3102,
-    "problem": "line L O K, line J M K, line L N J, line N O, line O M, line N M, line L O K, line J M K, line L N J, line N O, line O M, line N M\nIf JK = 5x+20 and NO = 20, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3102.jpg"
-  },
-  {
-    "id": 3171,
-    "problem_id": 3103,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3103.jpg"
-  },
-  {
-    "id": 3172,
-    "problem_id": 3104,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3104.jpg"
-  },
-  {
-    "id": 3173,
-    "problem_id": 3105,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3105.jpg"
-  },
-  {
-    "id": 3174,
-    "problem_id": 3106,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3106.jpg"
-  },
-  {
-    "id": 3175,
-    "problem_id": 3107,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3107.jpg"
-  },
-  {
-    "id": 3176,
-    "problem_id": 3108,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3108.jpg"
-  },
-  {
-    "id": 3177,
-    "problem_id": 3109,
-    "problem": "line K J, line J L, line K M L, line J M, line E D, line E G C, line D C, line D G, line K J, line J L, line K M L, line J M, line E D, line E G C, line D C, line D G\nFind x if DG and JM are altitudes and \\triangle KJL \\sim \\triangle EDC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3109.jpg"
-  },
-  {
-    "id": 3178,
-    "problem_id": 3110,
-    "problem": "line C B, line A B, line A C, line F E, line D F, line D E, line C B, line A B, line A C, line F E, line D F, line D E\nFind the perimeter of \\triangle DEF if \\triangle DEF \\sim \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3110.jpg"
-  },
-  {
-    "id": 3179,
-    "problem_id": 3111,
-    "problem": "line C B, line A B, line A C, line F E, line D F, line D E, line C B, line A B, line A C, line F E, line D F, line D E\nFind the perimeter of \\triangle DEF if \\triangle DEF \\sim \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3111.jpg"
-  },
-  {
-    "id": 3180,
-    "problem_id": 3112,
-    "problem": "line C B, line A B, line A C, line F E, line D F, line D E, line C B, line A B, line A C, line F E, line D F, line D E\nFind the perimeter of \\triangle DEF if \\triangle DEF \\sim \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3112.jpg"
-  },
-  {
-    "id": 3181,
-    "problem_id": 3113,
-    "problem": "line C B, line A B, line A C, line F E, line D F, line D E, line C B, line A B, line A C, line F E, line D F, line D E\nFind the perimeter of \\triangle DEF if \\triangle DEF \\sim \\triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3113.jpg"
-  },
-  {
-    "id": 3182,
-    "problem_id": 3114,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind ZV in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3114.jpg"
-  },
-  {
-    "id": 3183,
-    "problem_id": 3115,
-    "problem": "line P V M, line J R M, line J Z P, line Z R, line Z V, line R V, line P V M, line J R M, line J Z P, line Z R, line Z V, line R V\nFind ZV in \\triangle JMP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3115.jpg"
-  },
-  {
-    "id": 3184,
-    "problem_id": 3116,
-    "problem": "line A C E, line B C D, line A B, line D E, line A D, line B E, line A C E, line B C D, line A B, line D E, line A D, line B E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3116.jpg"
-  },
-  {
-    "id": 3186,
-    "problem_id": 3117,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3117.jpg"
-  },
-  {
-    "id": 3187,
-    "problem_id": 3118,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3118.jpg"
-  },
-  {
-    "id": 3188,
-    "problem_id": 3119,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3119.jpg"
-  },
-  {
-    "id": 3189,
-    "problem_id": 3120,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3120.jpg"
-  },
-  {
-    "id": 3190,
-    "problem_id": 3121,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 6?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3121.jpg"
-  },
-  {
-    "id": 3191,
-    "problem_id": 3122,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 16.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3122.jpg"
-  },
-  {
-    "id": 3192,
-    "problem_id": 3123,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3123.jpg"
-  },
-  {
-    "id": 3193,
-    "problem_id": 3124,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3124.jpg"
-  },
-  {
-    "id": 3194,
-    "problem_id": 3125,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3125.jpg"
-  },
-  {
-    "id": 3195,
-    "problem_id": 3126,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3126.jpg"
-  },
-  {
-    "id": 3196,
-    "problem_id": 3127,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3127.jpg"
-  },
-  {
-    "id": 3197,
-    "problem_id": 3128,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3128.jpg"
-  },
-  {
-    "id": 3198,
-    "problem_id": 3129,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3129.jpg"
-  },
-  {
-    "id": 3199,
-    "problem_id": 3130,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3130.jpg"
-  },
-  {
-    "id": 3200,
-    "problem_id": 3131,
-    "problem": "line W Y Z, line X Z, line X W, line X Y, line W Y Z, line X Z, line X W, line X Y\n\\triangle WXY and \\triangle XYZ are isosceles and m \\angle XYZ = 128. Find the measure of \\angle YZX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3131.jpg"
-  },
-  {
-    "id": 3201,
-    "problem_id": 3132,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3132.jpg"
-  },
-  {
-    "id": 3202,
-    "problem_id": 3133,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3133.jpg"
-  },
-  {
-    "id": 3203,
-    "problem_id": 3134,
-    "problem": "line A B, line B C E, line D E F, line A D, line A C, line B F, line A B, line B C E, line D E F, line A D, line A C, line B F\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3134.jpg"
-  },
-  {
-    "id": 3204,
-    "problem_id": 3135,
-    "problem": "line C A, line C B, line B A, line C A, line C B, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3135.jpg"
-  },
-  {
-    "id": 3205,
-    "problem_id": 3136,
-    "problem": "line C A, line C B, line B A, line C A, line C B, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3136.jpg"
-  },
-  {
-    "id": 3206,
-    "problem_id": 3137,
-    "problem": "line C A, line C B, line B A, line C A, line C B, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3137.jpg"
-  },
-  {
-    "id": 3207,
-    "problem_id": 3138,
-    "problem": "line C A, line C B, line B A, line C A, line C B, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3138.jpg"
-  },
-  {
-    "id": 3208,
-    "problem_id": 3139,
-    "problem": "line m lieson E F G, line l lieson B C D, line t lieson A C F H, line m lieson E F G, line l lieson B C D, line t lieson A C F H\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3139.jpg"
-  },
-  {
-    "id": 3209,
-    "problem_id": 3140,
-    "problem": "line B H, line C G, line C B, line G H, line B H, line C G, line C B, line G H\nBCGH is a parallelogram. Find the length of HB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3140.jpg"
-  },
-  {
-    "id": 3210,
-    "problem_id": 3141,
-    "problem": "line B H, line C G, line C B, line G H, line B H, line C G, line C B, line G H\nBCGH is a parallelogram. Find the length of HB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3141.jpg"
-  },
-  {
-    "id": 3211,
-    "problem_id": 3142,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3142.jpg"
-  },
-  {
-    "id": 3212,
-    "problem_id": 3143,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3143.jpg"
-  },
-  {
-    "id": 3213,
-    "problem_id": 3144,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3144.jpg"
-  },
-  {
-    "id": 3214,
-    "problem_id": 3145,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3145.jpg"
-  },
-  {
-    "id": 3215,
-    "problem_id": 3146,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3146.jpg"
-  },
-  {
-    "id": 3216,
-    "problem_id": 3147,
-    "problem": "line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B, line S T, line P T, line Q P, line R Q, line R S, line E D, line C D, line B C, line A E, line A B\nIf ABCDE \\sim PQRST, find ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3147.jpg"
-  },
-  {
-    "id": 3217,
-    "problem_id": 3148,
-    "problem": "line B E, line D C E, line A D, line A B, line B C, line B E, line D C E, line A D, line A B, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3148.jpg"
-  },
-  {
-    "id": 3218,
-    "problem_id": 3149,
-    "problem": "line B E, line D C E, line A D, line A B, line B C, line B E, line D C E, line A D, line A B, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3149.jpg"
-  },
-  {
-    "id": 3219,
-    "problem_id": 3150,
-    "problem": "line B E, line D C E, line A D, line A B, line B C, line B E, line D C E, line A D, line A B, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3150.jpg"
-  },
-  {
-    "id": 3220,
-    "problem_id": 3151,
-    "problem": "line B E, line D C E, line A D, line A B, line B C, line B E, line D C E, line A D, line A B, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3151.jpg"
-  },
-  {
-    "id": 3221,
-    "problem_id": 3152,
-    "problem": "line B E, line D C E, line A D, line A B, line B C, line B E, line D C E, line A D, line A B, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3152.jpg"
-  },
-  {
-    "id": 3222,
-    "problem_id": 3153,
-    "problem": "line R S, line T S, line Q T, line Q R, line T R, line R S, line T S, line Q T, line Q R, line T R\nParallelogram QRST has a perimeter of 62 mm. What is TQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3153.jpg"
-  },
-  {
-    "id": 3223,
-    "problem_id": 3154,
-    "problem": "line T Q R, line R S, line P Q S, line P T, line T Q R, line R S, line P Q S, line P T\nFind RS if \\triangle QRS \\sim \\triangle QTP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3154.jpg"
-  },
-  {
-    "id": 3224,
-    "problem_id": 3155,
-    "problem": "line T Q R, line R S, line P Q S, line P T, line T Q R, line R S, line P Q S, line P T\nFind RS if \\triangle QRS \\sim \\triangle QTP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3155.jpg"
-  },
-  {
-    "id": 3226,
-    "problem_id": 3156,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3156.jpg"
-  },
-  {
-    "id": 3227,
-    "problem_id": 3157,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3157.jpg"
-  },
-  {
-    "id": 3228,
-    "problem_id": 3158,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3158.jpg"
-  },
-  {
-    "id": 3229,
-    "problem_id": 3159,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nFind m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3159.jpg"
-  },
-  {
-    "id": 3230,
-    "problem_id": 3160,
-    "problem": "line Y X, line P Q, line Y Z, line P R, line Z X, line Q R, line Y X, line P Q, line Y Z, line P R, line Z X, line Q R\nGiven that \\angle PQR \\cong \\angle XYZ. Determine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3160.jpg"
-  },
-  {
-    "id": 3231,
-    "problem_id": 3161,
-    "problem": "line Y X, line P Q, line Y Z, line P R, line Z X, line Q R, line Y X, line P Q, line Y Z, line P R, line Z X, line Q R\nGiven that \\angle PQR \\cong \\angle XYZ. Determine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3161.jpg"
-  },
-  {
-    "id": 3232,
-    "problem_id": 3162,
-    "problem": "line Y X, line P Q, line Y Z, line P R, line Z X, line Q R, line Y X, line P Q, line Y Z, line P R, line Z X, line Q R\nGiven that \\angle PQR \\cong \\angle XYZ. Determine m \\angle X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3162.jpg"
-  },
-  {
-    "id": 3233,
-    "problem_id": 3163,
-    "problem": "line A E D, line D C, line A B, line B C, line E C, line A E D, line D C, line A B, line B C, line E C\nFind x in the trapezoid. Area = 177 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3163.jpg"
-  },
-  {
-    "id": 3234,
-    "problem_id": 3164,
-    "problem": "line A E D, line D C, line A B, line B C, line E C, line A E D, line D C, line A B, line B C, line E C\nFind x in the trapezoid. Area = 177 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3164.jpg"
-  },
-  {
-    "id": 3235,
-    "problem_id": 3165,
-    "problem": "line A E D, line D C, line A B, line B C, line E C, line A E D, line D C, line A B, line B C, line E C\nFind x in the trapezoid. Area = 177 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3165.jpg"
-  },
-  {
-    "id": 3236,
-    "problem_id": 3166,
-    "problem": "line A E D, line D C, line A B, line B C, line E C, line A E D, line D C, line A B, line B C, line E C\nFind x in the trapezoid. Area = 177 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3166.jpg"
-  },
-  {
-    "id": 3237,
-    "problem_id": 3167,
-    "problem": "line A E, line A B, line E D, line D C, line B C, line S R, line T S, line P T, line P Q, line Q R, line A E, line A B, line E D, line D C, line B C, line S R, line T S, line P T, line P Q, line Q R\nIf pentagons ABCDE and PQRST are similar, find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3167.jpg"
-  },
-  {
-    "id": 3238,
-    "problem_id": 3168,
-    "problem": "line A E, line A B, line E D, line D C, line B C, line S R, line T S, line P T, line P Q, line Q R, line A E, line A B, line E D, line D C, line B C, line S R, line T S, line P T, line P Q, line Q R\nIf pentagons ABCDE and PQRST are similar, find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3168.jpg"
-  },
-  {
-    "id": 3239,
-    "problem_id": 3169,
-    "problem": "line A E, line A B, line E D, line D C, line B C, line S R, line T S, line P T, line P Q, line Q R, line A E, line A B, line E D, line D C, line B C, line S R, line T S, line P T, line P Q, line Q R\nIf pentagons ABCDE and PQRST are similar, find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3169.jpg"
-  },
-  {
-    "id": 3240,
-    "problem_id": 3170,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3170.jpg"
-  },
-  {
-    "id": 3241,
-    "problem_id": 3171,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3171.jpg"
-  },
-  {
-    "id": 3242,
-    "problem_id": 3172,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3172.jpg"
-  },
-  {
-    "id": 3243,
-    "problem_id": 3173,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3173.jpg"
-  },
-  {
-    "id": 3244,
-    "problem_id": 3174,
-    "problem": "line A B, line D A, line D C B, line C A, line A B, line D A, line D C B, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3174.jpg"
-  },
-  {
-    "id": 3245,
-    "problem_id": 3175,
-    "problem": "line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R, line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R\nQS is a diameter of \\odot V. Find m \\widehat TRQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3175.jpg"
-  },
-  {
-    "id": 3246,
-    "problem_id": 3176,
-    "problem": "line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R, line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R\nQS is a diameter of \\odot V. Find m \\widehat TRQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3176.jpg"
-  },
-  {
-    "id": 3247,
-    "problem_id": 3177,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3177.jpg"
-  },
-  {
-    "id": 3248,
-    "problem_id": 3178,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3178.jpg"
-  },
-  {
-    "id": 3249,
-    "problem_id": 3179,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3179.jpg"
-  },
-  {
-    "id": 3250,
-    "problem_id": 3180,
-    "problem": "line H E C, line G F B, line D E F A, line H E C, line G F B, line D E F A\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3180.jpg"
-  },
-  {
-    "id": 3251,
-    "problem_id": 3181,
-    "problem": "line G A B D F L, line J B C H, line K E D I, line G A B D F L, line J B C H, line K E D I\nFind m \\angle EDF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3181.jpg"
-  },
-  {
-    "id": 3253,
-    "problem_id": 3182,
-    "problem": "line A B, line E D B, line A C E, line C D, line A B, line E D B, line A C E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3182.jpg"
-  },
-  {
-    "id": 3254,
-    "problem_id": 3183,
-    "problem": "line A B, line E D B, line A C E, line C D, line A B, line E D B, line A C E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3183.jpg"
-  },
-  {
-    "id": 3255,
-    "problem_id": 3184,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3184.jpg"
-  },
-  {
-    "id": 3257,
-    "problem_id": 3185,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3185.jpg"
-  },
-  {
-    "id": 3258,
-    "problem_id": 3186,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3186.jpg"
-  },
-  {
-    "id": 3259,
-    "problem_id": 3187,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3187.jpg"
-  },
-  {
-    "id": 3260,
-    "problem_id": 3188,
-    "problem": "line B C G, line B D F, line E A B, line A D, line D C, line B C G, line B D F, line E A B, line A D, line D C\nGiven that AD = CD = 61, and m \\angle ABC = 48, find m \\angle CBD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3188.jpg"
-  },
-  {
-    "id": 3261,
-    "problem_id": 3189,
-    "problem": "line J M, line K L, line K J, line L M, line J M, line K L, line K J, line L M\nJKLM is a parallelogram. Find the measure of ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3189.jpg"
-  },
-  {
-    "id": 3262,
-    "problem_id": 3190,
-    "problem": "line J M, line K L, line K J, line L M, line J M, line K L, line K J, line L M\nJKLM is a parallelogram. Find the measure of ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3190.jpg"
-  },
-  {
-    "id": 3263,
-    "problem_id": 3191,
-    "problem": "line J M, line K L, line K J, line L M, line J M, line K L, line K J, line L M\nJKLM is a parallelogram. Find the measure of ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3191.jpg"
-  },
-  {
-    "id": 3264,
-    "problem_id": 3192,
-    "problem": "line J M, line K L, line K J, line L M, line J M, line K L, line K J, line L M\nJKLM is a parallelogram. Find the measure of ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3192.jpg"
-  },
-  {
-    "id": 3265,
-    "problem_id": 3193,
-    "problem": "line J M, line K L, line K J, line L M, line J M, line K L, line K J, line L M\nJKLM is a parallelogram. Find the measure of ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3193.jpg"
-  },
-  {
-    "id": 3266,
-    "problem_id": 3194,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3194.jpg"
-  },
-  {
-    "id": 3267,
-    "problem_id": 3195,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3195.jpg"
-  },
-  {
-    "id": 3268,
-    "problem_id": 3196,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3196.jpg"
-  },
-  {
-    "id": 3269,
-    "problem_id": 3197,
-    "problem": "line C B E, line D B A, \\odot B lieson C A E D, line C B E, line D B A, \\odot B lieson C A E D\nFind the length of \\widehat DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3197.jpg"
-  },
-  {
-    "id": 3270,
-    "problem_id": 3198,
-    "problem": "line C B E, line D B A, \\odot B lieson C A E D, line C B E, line D B A, \\odot B lieson C A E D\nFind the length of \\widehat DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3198.jpg"
-  },
-  {
-    "id": 3271,
-    "problem_id": 3199,
-    "problem": "line C B E, line D B A, \\odot B lieson C A E D, line C B E, line D B A, \\odot B lieson C A E D\nFind the length of \\widehat DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3199.jpg"
-  },
-  {
-    "id": 3272,
-    "problem_id": 3200,
-    "problem": "line G F E, line B D F A, line D G, line D E, line G F E, line B D F A, line D G, line D E\nWhat is the length of FE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3200.jpg"
-  },
-  {
-    "id": 3273,
-    "problem_id": 3201,
-    "problem": "line G F E, line B D F A, line D G, line D E, line G F E, line B D F A, line D G, line D E\nWhat is the length of FE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3201.jpg"
-  },
-  {
-    "id": 3274,
-    "problem_id": 3202,
-    "problem": "line G F E, line B D F A, line D G, line D E, line G F E, line B D F A, line D G, line D E\nWhat is the length of FE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3202.jpg"
-  },
-  {
-    "id": 3275,
-    "problem_id": 3203,
-    "problem": "line G F E, line B D F A, line D G, line D E, line G F E, line B D F A, line D G, line D E\nWhat is the length of FE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3203.jpg"
-  },
-  {
-    "id": 3276,
-    "problem_id": 3204,
-    "problem": "line G F E, line B D F A, line D G, line D E, line G F E, line B D F A, line D G, line D E\nWhat is the length of FE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3204.jpg"
-  },
-  {
-    "id": 3277,
-    "problem_id": 3205,
-    "problem": "line P S R, line Q R, line Q P, line Q S, line P S R, line Q R, line Q P, line Q S\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3205.jpg"
-  },
-  {
-    "id": 3278,
-    "problem_id": 3206,
-    "problem": "line P S R, line Q R, line Q P, line Q S, line P S R, line Q R, line Q P, line Q S\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3206.jpg"
-  },
-  {
-    "id": 3279,
-    "problem_id": 3207,
-    "problem": "line P S R, line Q R, line Q P, line Q S, line P S R, line Q R, line Q P, line Q S\nFind m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3207.jpg"
-  },
-  {
-    "id": 3280,
-    "problem_id": 3208,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat QT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3208.jpg"
-  },
-  {
-    "id": 3281,
-    "problem_id": 3209,
-    "problem": "line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R, line T V, line V S, line V R, line U V, line Q V, \\odot V lieson Q U T S R\nFind the measure of \\widehat QT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3209.jpg"
-  },
-  {
-    "id": 3282,
-    "problem_id": 3210,
-    "problem": "line A G J, line B J C, \\odot D lieson G J H, line A G J, line B J C, \\odot D lieson G J H\nWhat is the measure of \\widehat GHJ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3210.jpg"
-  },
-  {
-    "id": 3283,
-    "problem_id": 3211,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3211.jpg"
-  },
-  {
-    "id": 3284,
-    "problem_id": 3212,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3212.jpg"
-  },
-  {
-    "id": 3285,
-    "problem_id": 3213,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3213.jpg"
-  },
-  {
-    "id": 3286,
-    "problem_id": 3214,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3214.jpg"
-  },
-  {
-    "id": 3287,
-    "problem_id": 3215,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3215.jpg"
-  },
-  {
-    "id": 3288,
-    "problem_id": 3216,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3216.jpg"
-  },
-  {
-    "id": 3289,
-    "problem_id": 3217,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3217.jpg"
-  },
-  {
-    "id": 3290,
-    "problem_id": 3218,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3218.jpg"
-  },
-  {
-    "id": 3291,
-    "problem_id": 3219,
-    "problem": "line A B E, line C E D, \\odot G lieson B E F, line A B E, line C E D, \\odot G lieson B E F\nFind m \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3219.jpg"
-  },
-  {
-    "id": 3292,
-    "problem_id": 3220,
-    "problem": "line A B E, line C E D, \\odot G lieson B E F, line A B E, line C E D, \\odot G lieson B E F\nFind m \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3220.jpg"
-  },
-  {
-    "id": 3293,
-    "problem_id": 3221,
-    "problem": "line A B E, line C E D, \\odot G lieson B E F, line A B E, line C E D, \\odot G lieson B E F\nFind m \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3221.jpg"
-  },
-  {
-    "id": 3294,
-    "problem_id": 3222,
-    "problem": "line A B, line B D, line C D, line A C, \\odot P lieson A C D B, line A B, line B D, line C D, line A C, \\odot P lieson A C D B\nSolve for m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3222.jpg"
-  },
-  {
-    "id": 3295,
-    "problem_id": 3223,
-    "problem": "line A B, line B D, line C D, line A C, \\odot P lieson A C D B, line A B, line B D, line C D, line A C, \\odot P lieson A C D B\nSolve for m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3223.jpg"
-  },
-  {
-    "id": 3296,
-    "problem_id": 3224,
-    "problem": "line A B, line B P C, line A Q C, line A K P, line B K Q, line A B, line B P C, line A Q C, line A K P, line B K Q\nIf AP = 18, what is AK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3224.jpg"
-  },
-  {
-    "id": 3297,
-    "problem_id": 3225,
-    "problem": "line A B, line B P C, line A Q C, line A K P, line B K Q, line A B, line B P C, line A Q C, line A K P, line B K Q\nIf AP = 18, what is AK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3225.jpg"
-  },
-  {
-    "id": 3298,
-    "problem_id": 3226,
-    "problem": "line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J, line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J\nP is the incenter of \\angle XYZ. Find XL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3226.jpg"
-  },
-  {
-    "id": 3299,
-    "problem_id": 3227,
-    "problem": "line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J, line Z J Y, line X L Z, line X K Y, line X P, line K P, line L P, line P Y, line P Z, line P J\nP is the incenter of \\angle XYZ. Find XL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3227.jpg"
-  },
-  {
-    "id": 3300,
-    "problem_id": 3228,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the length of \\widehat DF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3228.jpg"
-  },
-  {
-    "id": 3301,
-    "problem_id": 3229,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the length of \\widehat DF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3229.jpg"
-  },
-  {
-    "id": 3302,
-    "problem_id": 3230,
-    "problem": "line A B, line A C D, line B C E, line D E, line A B, line A C D, line B C E, line D E\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3230.jpg"
-  },
-  {
-    "id": 3303,
-    "problem_id": 3231,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3231.jpg"
-  },
-  {
-    "id": 3304,
-    "problem_id": 3232,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3232.jpg"
-  },
-  {
-    "id": 3305,
-    "problem_id": 3233,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3233.jpg"
-  },
-  {
-    "id": 3306,
-    "problem_id": 3234,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3234.jpg"
-  },
-  {
-    "id": 3307,
-    "problem_id": 3235,
-    "problem": "line R T A, line S A, line T S, line R S, line E F, line G F, line E G B, line F B, line R T A, line S A, line T S, line R S, line E F, line G F, line E G B, line F B\nFind FB if SA and FB are altitudes and \\triangle RST \\sim \\triangle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3235.jpg"
-  },
-  {
-    "id": 3308,
-    "problem_id": 3236,
-    "problem": "line R T A, line S A, line T S, line R S, line E F, line G F, line E G B, line F B, line R T A, line S A, line T S, line R S, line E F, line G F, line E G B, line F B\nFind FB if SA and FB are altitudes and \\triangle RST \\sim \\triangle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3236.jpg"
-  },
-  {
-    "id": 3309,
-    "problem_id": 3237,
-    "problem": "line R T A, line S A, line T S, line R S, line E F, line G F, line E G B, line F B, line R T A, line S A, line T S, line R S, line E F, line G F, line E G B, line F B\nFind FB if SA and FB are altitudes and \\triangle RST \\sim \\triangle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3237.jpg"
-  },
-  {
-    "id": 3310,
-    "problem_id": 3238,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind AD in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3238.jpg"
-  },
-  {
-    "id": 3311,
-    "problem_id": 3239,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind AD in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3239.jpg"
-  },
-  {
-    "id": 3312,
-    "problem_id": 3240,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind AD in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3240.jpg"
-  },
-  {
-    "id": 3313,
-    "problem_id": 3241,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind AD in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3241.jpg"
-  },
-  {
-    "id": 3314,
-    "problem_id": 3242,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind AD in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3242.jpg"
-  },
-  {
-    "id": 3315,
-    "problem_id": 3243,
-    "problem": "line C B A, line C D E, \\odot N lieson B D E A, line C B A, line C D E, \\odot N lieson B D E A\nFind the value of variable y in \\odot N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3243.jpg"
-  },
-  {
-    "id": 3316,
-    "problem_id": 3244,
-    "problem": "line E D C, line B A, line A C, line B E, line B D, line E D C, line B A, line A C, line B E, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3244.jpg"
-  },
-  {
-    "id": 3317,
-    "problem_id": 3245,
-    "problem": "line E D C, line B A, line A C, line B E, line B D, line E D C, line B A, line A C, line B E, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3245.jpg"
-  },
-  {
-    "id": 3318,
-    "problem_id": 3246,
-    "problem": "line E D C, line B A, line A C, line B E, line B D, line E D C, line B A, line A C, line B E, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3246.jpg"
-  },
-  {
-    "id": 3319,
-    "problem_id": 3247,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3247.jpg"
-  },
-  {
-    "id": 3320,
-    "problem_id": 3248,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3248.jpg"
-  },
-  {
-    "id": 3321,
-    "problem_id": 3249,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3249.jpg"
-  },
-  {
-    "id": 3322,
-    "problem_id": 3250,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3250.jpg"
-  },
-  {
-    "id": 3323,
-    "problem_id": 3251,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3251.jpg"
-  },
-  {
-    "id": 3324,
-    "problem_id": 3252,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of t?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3252.jpg"
-  },
-  {
-    "id": 3325,
-    "problem_id": 3253,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of t?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3253.jpg"
-  },
-  {
-    "id": 3326,
-    "problem_id": 3254,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of t?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3254.jpg"
-  },
-  {
-    "id": 3327,
-    "problem_id": 3255,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of t?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3255.jpg"
-  },
-  {
-    "id": 3328,
-    "problem_id": 3256,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of t?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3256.jpg"
-  },
-  {
-    "id": 3329,
-    "problem_id": 3257,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of t?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3257.jpg"
-  },
-  {
-    "id": 3331,
-    "problem_id": 3258,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3258.jpg"
-  },
-  {
-    "id": 3332,
-    "problem_id": 3259,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3259.jpg"
-  },
-  {
-    "id": 3333,
-    "problem_id": 3260,
-    "problem": "line H B, line H G, line H C, line B G C, line D H, line F H, line A F C, line A D B, line A H, line H B, line H G, line H C, line B G C, line D H, line F H, line A F C, line A D B, line A H\nH is the incenter of \\triangle ABC. Find HC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3260.jpg"
-  },
-  {
-    "id": 3334,
-    "problem_id": 3261,
-    "problem": "line G F C, line H B C, line I E C, line A C D, line G F C, line H B C, line I E C, line A C D\nIf m \\angle FCD = 130 and m \\angle BCD = 95, find m \\angle FCB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3261.jpg"
-  },
-  {
-    "id": 3335,
-    "problem_id": 3262,
-    "problem": "line G F C, line H B C, line I E C, line A C D, line G F C, line H B C, line I E C, line A C D\nIf m \\angle FCD = 130 and m \\angle BCD = 95, find m \\angle FCB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3262.jpg"
-  },
-  {
-    "id": 3336,
-    "problem_id": 3263,
-    "problem": "line G A H, line G P B, line G C J, line C P H, line A P J, line H B J, line G A H, line G P B, line G C J, line C P H, line A P J, line H B J\nPA = 2.9, and HC = 10.8. Solve for the length of PC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3263.jpg"
-  },
-  {
-    "id": 3338,
-    "problem_id": 3264,
-    "problem": "line P R, line P Q, line Q R, line P R, line P Q, line Q R\nWhat is the length of RQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3264.jpg"
-  },
-  {
-    "id": 3339,
-    "problem_id": 3265,
-    "problem": "line P R, line P Q, line Q R, line P R, line P Q, line Q R\nWhat is the length of RQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3265.jpg"
-  },
-  {
-    "id": 3340,
-    "problem_id": 3266,
-    "problem": "line P R, line P Q, line Q R, line P R, line P Q, line Q R\nWhat is the length of RQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3266.jpg"
-  },
-  {
-    "id": 3342,
-    "problem_id": 3267,
-    "problem": "line A E, line D E, line B C E, line D C A, line B D, line B A, line A E, line D E, line B C E, line D C A, line B D, line B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3267.jpg"
-  },
-  {
-    "id": 3343,
-    "problem_id": 3268,
-    "problem": "line A E, line D E, line B C E, line D C A, line B D, line B A, line A E, line D E, line B C E, line D C A, line B D, line B A\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3268.jpg"
-  },
-  {
-    "id": 3344,
-    "problem_id": 3269,
-    "problem": "line N P, line L P, line L M N, line M P A, line N P, line L P, line L M N, line M P A\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3269.jpg"
-  },
-  {
-    "id": 3345,
-    "problem_id": 3270,
-    "problem": "line N P, line L P, line L M N, line M P A, line N P, line L P, line L M N, line M P A\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3270.jpg"
-  },
-  {
-    "id": 3346,
-    "problem_id": 3271,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3271.jpg"
-  },
-  {
-    "id": 3347,
-    "problem_id": 3272,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3272.jpg"
-  },
-  {
-    "id": 3348,
-    "problem_id": 3273,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3273.jpg"
-  },
-  {
-    "id": 3349,
-    "problem_id": 3274,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3274.jpg"
-  },
-  {
-    "id": 3350,
-    "problem_id": 3275,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind AE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3275.jpg"
-  },
-  {
-    "id": 3351,
-    "problem_id": 3276,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle EOA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3276.jpg"
-  },
-  {
-    "id": 3352,
-    "problem_id": 3277,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle EOA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3277.jpg"
-  },
-  {
-    "id": 3353,
-    "problem_id": 3278,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle EOA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3278.jpg"
-  },
-  {
-    "id": 3354,
-    "problem_id": 3279,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle EOA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3279.jpg"
-  },
-  {
-    "id": 3355,
-    "problem_id": 3280,
-    "problem": "line B C D, line E D, line A E, line A B, line E C, line B C D, line E D, line A E, line A B, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3280.jpg"
-  },
-  {
-    "id": 3356,
-    "problem_id": 3281,
-    "problem": "line B C D, line E D, line A E, line A B, line E C, line B C D, line E D, line A E, line A B, line E C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3281.jpg"
-  },
-  {
-    "id": 3357,
-    "problem_id": 3282,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3282.jpg"
-  },
-  {
-    "id": 3358,
-    "problem_id": 3283,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3283.jpg"
-  },
-  {
-    "id": 3359,
-    "problem_id": 3284,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3284.jpg"
-  },
-  {
-    "id": 3360,
-    "problem_id": 3285,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3285.jpg"
-  },
-  {
-    "id": 3361,
-    "problem_id": 3286,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3286.jpg"
-  },
-  {
-    "id": 3362,
-    "problem_id": 3287,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3287.jpg"
-  },
-  {
-    "id": 3363,
-    "problem_id": 3288,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3288.jpg"
-  },
-  {
-    "id": 3364,
-    "problem_id": 3289,
-    "problem": "line A B C, line E C, line D E, line D A, line E B, line A B C, line E C, line D E, line D A, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3289.jpg"
-  },
-  {
-    "id": 3365,
-    "problem_id": 3290,
-    "problem": "line A B C, line E C, line D E, line D A, line E B, line A B C, line E C, line D E, line D A, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3290.jpg"
-  },
-  {
-    "id": 3366,
-    "problem_id": 3291,
-    "problem": "line A B C, line E C, line D E, line D A, line E B, line A B C, line E C, line D E, line D A, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3291.jpg"
-  },
-  {
-    "id": 3367,
-    "problem_id": 3292,
-    "problem": "line A B C, line E C, line D E, line D A, line E B, line A B C, line E C, line D E, line D A, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3292.jpg"
-  },
-  {
-    "id": 3368,
-    "problem_id": 3293,
-    "problem": "line A B C, line E C, line D E, line D A, line E B, line A B C, line E C, line D E, line D A, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3293.jpg"
-  },
-  {
-    "id": 3369,
-    "problem_id": 3294,
-    "problem": "line D B, line C D, line C B, line A B, line C A, line D B, line C D, line C B, line A B, line C A\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3294.jpg"
-  },
-  {
-    "id": 3370,
-    "problem_id": 3295,
-    "problem": "line B A, line A C, line D C, line B D, line B C, line B A, line A C, line D C, line B D, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3295.jpg"
-  },
-  {
-    "id": 3371,
-    "problem_id": 3296,
-    "problem": "line B A, line A C, line D C, line B D, line B C, line B A, line A C, line D C, line B D, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3296.jpg"
-  },
-  {
-    "id": 3372,
-    "problem_id": 3297,
-    "problem": "line B A, line A C, line D C, line B D, line B C, line B A, line A C, line D C, line B D, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3297.jpg"
-  },
-  {
-    "id": 3373,
-    "problem_id": 3298,
-    "problem": "line B A, line A C, line D C, line B D, line B C, line B A, line A C, line D C, line B D, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3298.jpg"
-  },
-  {
-    "id": 3374,
-    "problem_id": 3299,
-    "problem": "line B A, line A C, line D C, line B D, line B C, line B A, line A C, line D C, line B D, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3299.jpg"
-  },
-  {
-    "id": 3375,
-    "problem_id": 3300,
-    "problem": "line D A E, line B A, \\odot F lieson B A C, line D A E, line B A, \\odot F lieson B A C\nWhat is m \\widehat BCA?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3300.jpg"
-  },
-  {
-    "id": 3377,
-    "problem_id": 3301,
-    "problem": "line A D, line C D, line B C, line B A, line B D, line A D, line C D, line B C, line B A, line B D\nWhat is the perimeter of \\parallelogram ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3301.jpg"
-  },
-  {
-    "id": 3378,
-    "problem_id": 3302,
-    "problem": "line A D, line C D, line B C, line B A, line B D, line A D, line C D, line B C, line B A, line B D\nWhat is the perimeter of \\parallelogram ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3302.jpg"
-  },
-  {
-    "id": 3379,
-    "problem_id": 3303,
-    "problem": "line A D, line C D, line B C, line B A, line B D, line A D, line C D, line B C, line B A, line B D\nWhat is the perimeter of \\parallelogram ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3303.jpg"
-  },
-  {
-    "id": 3380,
-    "problem_id": 3304,
-    "problem": "line A D, line C D, line B C, line B A, line B D, line A D, line C D, line B C, line B A, line B D\nWhat is the perimeter of \\parallelogram ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3304.jpg"
-  },
-  {
-    "id": 3381,
-    "problem_id": 3305,
-    "problem": "line A C D, line B C E, line A C D, line B C E\nm \\angle 19 = 100+20x, m \\angle 20 = 20x. Find the measure of \\angle 19.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3305.jpg"
-  },
-  {
-    "id": 3382,
-    "problem_id": 3306,
-    "problem": "line Y Z W, line Y X, line W X, line T Y, line T W, line T Z, line Y Z W, line Y X, line W X, line T Y, line T W, line T Z\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3306.jpg"
-  },
-  {
-    "id": 3384,
-    "problem_id": 3307,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3307.jpg"
-  },
-  {
-    "id": 3385,
-    "problem_id": 3308,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3308.jpg"
-  },
-  {
-    "id": 3386,
-    "problem_id": 3309,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3309.jpg"
-  },
-  {
-    "id": 3387,
-    "problem_id": 3310,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3310.jpg"
-  },
-  {
-    "id": 3388,
-    "problem_id": 3311,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3311.jpg"
-  },
-  {
-    "id": 3389,
-    "problem_id": 3312,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3312.jpg"
-  },
-  {
-    "id": 3390,
-    "problem_id": 3313,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line A B, line B C D, line A D, line E D, line A C E, line B E, line A B\nSolve for the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3313.jpg"
-  },
-  {
-    "id": 3391,
-    "problem_id": 3314,
-    "problem": "line J L N, line M N, line J K M, line K L, line J L N, line M N, line J K M, line K L\nKL \\parallel MN. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3314.jpg"
-  },
-  {
-    "id": 3392,
-    "problem_id": 3315,
-    "problem": "line R S, line R U, line R T, line S T U, line R S, line R U, line R T, line S T U\nWhat is m \\angle SRU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3315.jpg"
-  },
-  {
-    "id": 3393,
-    "problem_id": 3316,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3316.jpg"
-  },
-  {
-    "id": 3394,
-    "problem_id": 3317,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3317.jpg"
-  },
-  {
-    "id": 3395,
-    "problem_id": 3318,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3318.jpg"
-  },
-  {
-    "id": 3396,
-    "problem_id": 3319,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3319.jpg"
-  },
-  {
-    "id": 3397,
-    "problem_id": 3320,
-    "problem": "line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E, line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E\nFind the perimeter of a regular hexagon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3320.jpg"
-  },
-  {
-    "id": 3398,
-    "problem_id": 3321,
-    "problem": "line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E, line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E\nFind the perimeter of a regular hexagon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3321.jpg"
-  },
-  {
-    "id": 3399,
-    "problem_id": 3322,
-    "problem": "line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E, line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E\nFind the perimeter of a regular hexagon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3322.jpg"
-  },
-  {
-    "id": 3400,
-    "problem_id": 3323,
-    "problem": "line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E, line A F, line F G E, line D E, line C D, line B C, line B A, line H F, line H G, line H E\nFind the perimeter of a regular hexagon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3323.jpg"
-  },
-  {
-    "id": 3402,
-    "problem_id": 3324,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3324.jpg"
-  },
-  {
-    "id": 3403,
-    "problem_id": 3325,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3325.jpg"
-  },
-  {
-    "id": 3404,
-    "problem_id": 3326,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3326.jpg"
-  },
-  {
-    "id": 3405,
-    "problem_id": 3327,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nDetermine m \\widehat AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3327.jpg"
-  },
-  {
-    "id": 3406,
-    "problem_id": 3328,
-    "problem": "line A C, line B A, \\odot D lieson B A C, line A C, line B A, \\odot D lieson B A C\nDetermine m \\widehat AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3328.jpg"
-  },
-  {
-    "id": 3407,
-    "problem_id": 3329,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3329.jpg"
-  },
-  {
-    "id": 3408,
-    "problem_id": 3330,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3330.jpg"
-  },
-  {
-    "id": 3409,
-    "problem_id": 3331,
-    "problem": "line B C D E, line A B, line A D F, \\odot G lieson E F C A, line B C D E, line A B, line A D F, \\odot G lieson E F C A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3331.jpg"
-  },
-  {
-    "id": 3410,
-    "problem_id": 3332,
-    "problem": "line B C D E, line A B, line A D F, \\odot G lieson E F C A, line B C D E, line A B, line A D F, \\odot G lieson E F C A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3332.jpg"
-  },
-  {
-    "id": 3411,
-    "problem_id": 3333,
-    "problem": "line B C D E, line A B, line A D F, \\odot G lieson E F C A, line B C D E, line A B, line A D F, \\odot G lieson E F C A\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3333.jpg"
-  },
-  {
-    "id": 3412,
-    "problem_id": 3334,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nSolve for the value of x if y = 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3334.jpg"
-  },
-  {
-    "id": 3413,
-    "problem_id": 3335,
-    "problem": "line X Z, line Y Z, line X Y, line X Z, line Y Z, line X Y\nSolve for the value of x if y = 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3335.jpg"
-  },
-  {
-    "id": 3414,
-    "problem_id": 3336,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3336.jpg"
-  },
-  {
-    "id": 3415,
-    "problem_id": 3337,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3337.jpg"
-  },
-  {
-    "id": 3416,
-    "problem_id": 3338,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3338.jpg"
-  },
-  {
-    "id": 3417,
-    "problem_id": 3339,
-    "problem": "line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R, line P L Q, line P K M, line P N R, line Q M R, line N K Q, line L K R\nIn \\triangle PQR, NQ = 6, RK = 3, and PK = 4. Find the length of LR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3339.jpg"
-  },
-  {
-    "id": 3418,
-    "problem_id": 3340,
-    "problem": "line A B C, line E B, line D B, line A B C, line E B, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3340.jpg"
-  },
-  {
-    "id": 3419,
-    "problem_id": 3341,
-    "problem": "line A B C, line E B, line D B, line A B C, line E B, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3341.jpg"
-  },
-  {
-    "id": 3420,
-    "problem_id": 3342,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3342.jpg"
-  },
-  {
-    "id": 3421,
-    "problem_id": 3343,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3343.jpg"
-  },
-  {
-    "id": 3422,
-    "problem_id": 3344,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3344.jpg"
-  },
-  {
-    "id": 3423,
-    "problem_id": 3345,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3345.jpg"
-  },
-  {
-    "id": 3424,
-    "problem_id": 3346,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3346.jpg"
-  },
-  {
-    "id": 3425,
-    "problem_id": 3347,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3347.jpg"
-  },
-  {
-    "id": 3426,
-    "problem_id": 3348,
-    "problem": "line S T, line Z X, line Z Y, line R S, line X Y, line R T, line S T, line Z X, line Z Y, line R S, line X Y, line R T\nGiven \\triangle XYZ \\cong \\triangle RST, find m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3348.jpg"
-  },
-  {
-    "id": 3427,
-    "problem_id": 3349,
-    "problem": "line A B D, line C B, line C D, line A B D, line C B, line C D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3349.jpg"
-  },
-  {
-    "id": 3428,
-    "problem_id": 3350,
-    "problem": "line A B D, line C B, line C D, line A B D, line C B, line C D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3350.jpg"
-  },
-  {
-    "id": 3429,
-    "problem_id": 3351,
-    "problem": "line A B D, line C B, line C D, line A B D, line C B, line C D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3351.jpg"
-  },
-  {
-    "id": 3430,
-    "problem_id": 3352,
-    "problem": "line A B D, line C B, line C D, line A B D, line C B, line C D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3352.jpg"
-  },
-  {
-    "id": 3431,
-    "problem_id": 3353,
-    "problem": "line A B D, line C B, line C D, line A B D, line C B, line C D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3353.jpg"
-  },
-  {
-    "id": 3432,
-    "problem_id": 3354,
-    "problem": "line A B D, line C B, line C D, line A B D, line C B, line C D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3354.jpg"
-  },
-  {
-    "id": 3433,
-    "problem_id": 3355,
-    "problem": "line S T, line T R, line S R, line S T, line T R, line S R\nFind \\tan R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3355.jpg"
-  },
-  {
-    "id": 3434,
-    "problem_id": 3356,
-    "problem": "line S T, line T R, line S R, line S T, line T R, line S R\nFind \\tan R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3356.jpg"
-  },
-  {
-    "id": 3435,
-    "problem_id": 3357,
-    "problem": "line H G, line D E, line D I, line F G, line E F, line I H, line H G, line D E, line D I, line F G, line E F, line I H\nDetermine the measure of \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3357.jpg"
-  },
-  {
-    "id": 3436,
-    "problem_id": 3358,
-    "problem": "line H G, line D E, line D I, line F G, line E F, line I H, line H G, line D E, line D I, line F G, line E F, line I H\nDetermine the measure of \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3358.jpg"
-  },
-  {
-    "id": 3437,
-    "problem_id": 3359,
-    "problem": "line H G, line D E, line D I, line F G, line E F, line I H, line H G, line D E, line D I, line F G, line E F, line I H\nDetermine the measure of \\angle F.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3359.jpg"
-  },
-  {
-    "id": 3438,
-    "problem_id": 3360,
-    "problem": "line B Q D, line A Q C, \\odot Q lieson B A D C, line B Q D, line A Q C, \\odot Q lieson B A D C\nFind m \\widehat BCA of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3360.jpg"
-  },
-  {
-    "id": 3439,
-    "problem_id": 3361,
-    "problem": "line B Q D, line A Q C, \\odot Q lieson B A D C, line B Q D, line A Q C, \\odot Q lieson B A D C\nFind m \\widehat BCA of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3361.jpg"
-  },
-  {
-    "id": 3440,
-    "problem_id": 3362,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3362.jpg"
-  },
-  {
-    "id": 3441,
-    "problem_id": 3363,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3363.jpg"
-  },
-  {
-    "id": 3442,
-    "problem_id": 3364,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3364.jpg"
-  },
-  {
-    "id": 3443,
-    "problem_id": 3365,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nm \\angle 15 = x, m \\angle 16 = 6x-290, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3365.jpg"
-  },
-  {
-    "id": 3444,
-    "problem_id": 3366,
-    "problem": "line A B, line B C D, line A C E F, line D E, line A B, line B C D, line A C E F, line D E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3366.jpg"
-  },
-  {
-    "id": 3445,
-    "problem_id": 3367,
-    "problem": "line A B, line B C D, line A C E F, line D E, line A B, line B C D, line A C E F, line D E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3367.jpg"
-  },
-  {
-    "id": 3446,
-    "problem_id": 3368,
-    "problem": "line A B, line B C D, line A C E F, line D E, line A B, line B C D, line A C E F, line D E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3368.jpg"
-  },
-  {
-    "id": 3447,
-    "problem_id": 3369,
-    "problem": "line A B, line B C D, line A C E F, line D E, line A B, line B C D, line A C E F, line D E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3369.jpg"
-  },
-  {
-    "id": 3448,
-    "problem_id": 3370,
-    "problem": "line A B, line B C D, line A C E F, line D E, line A B, line B C D, line A C E F, line D E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3370.jpg"
-  },
-  {
-    "id": 3449,
-    "problem_id": 3371,
-    "problem": "line A B, line B C D, line A C E F, line D E, line A B, line B C D, line A C E F, line D E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3371.jpg"
-  },
-  {
-    "id": 3450,
-    "problem_id": 3372,
-    "problem": "line B D, line A C, line A B, line A D, line C D, line B D, line A C, line A B, line A D, line C D\nFind m \\angle 2 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3372.jpg"
-  },
-  {
-    "id": 3451,
-    "problem_id": 3373,
-    "problem": "line B D, line A C, line A B, line A D, line C D, line B D, line A C, line A B, line A D, line C D\nFind m \\angle 2 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3373.jpg"
-  },
-  {
-    "id": 3452,
-    "problem_id": 3374,
-    "problem": "line A B, line A D, line A C, line C D, line D B, line A B, line A D, line A C, line C D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3374.jpg"
-  },
-  {
-    "id": 3453,
-    "problem_id": 3375,
-    "problem": "line A B, line A D, line A C, line C D, line D B, line A B, line A D, line A C, line C D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3375.jpg"
-  },
-  {
-    "id": 3454,
-    "problem_id": 3376,
-    "problem": "line A B, line A D, line A C, line C D, line D B, line A B, line A D, line A C, line C D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3376.jpg"
-  },
-  {
-    "id": 3455,
-    "problem_id": 3377,
-    "problem": "line A B, line A D, line A C, line C D, line D B, line A B, line A D, line A C, line C D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3377.jpg"
-  },
-  {
-    "id": 3456,
-    "problem_id": 3378,
-    "problem": "line A B, line A D, line A C, line C D, line D B, line A B, line A D, line A C, line C D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3378.jpg"
-  },
-  {
-    "id": 3457,
-    "problem_id": 3379,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3379.jpg"
-  },
-  {
-    "id": 3458,
-    "problem_id": 3380,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3380.jpg"
-  },
-  {
-    "id": 3459,
-    "problem_id": 3381,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3381.jpg"
-  },
-  {
-    "id": 3460,
-    "problem_id": 3382,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3382.jpg"
-  },
-  {
-    "id": 3461,
-    "problem_id": 3383,
-    "problem": "line P T R, line S R, line Q R, line Q T S, line P S, line P Q, line P T R, line S R, line Q R, line Q T S, line P S, line P Q\nIn kite PQRS, m \\angle SRT = 24, and m \\angle TSP = 53. Find m \\angle QPS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3383.jpg"
-  },
-  {
-    "id": 3462,
-    "problem_id": 3384,
-    "problem": "line W A Y, line X Y, line Y Z, line W Z, line X W, line X A Z, line W A Y, line X Y, line Y Z, line W Z, line X W, line X A Z\nWXYZ is a parallelogram. Find m \\angle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3384.jpg"
-  },
-  {
-    "id": 3463,
-    "problem_id": 3385,
-    "problem": "line A B, line A C, line C B, line D F, line D E, line F E, line A B, line A C, line C B, line D F, line D E, line F E\nFind the measure of ED, if \\triangle DEF \\sim \\triangle ACB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3385.jpg"
-  },
-  {
-    "id": 3464,
-    "problem_id": 3386,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the circle. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3386.jpg"
-  },
-  {
-    "id": 3465,
-    "problem_id": 3387,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the circle. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3387.jpg"
-  },
-  {
-    "id": 3466,
-    "problem_id": 3388,
-    "problem": "line A B, line D B, line B C, line A C, \\odot D lieson A C B, line A B, line D B, line B C, line A C, \\odot D lieson A C B\nFind the area of the shaded region. Assume that the triangle is equilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3388.jpg"
-  },
-  {
-    "id": 3467,
-    "problem_id": 3389,
-    "problem": "line A B, line D B, line B C, line A C, \\odot D lieson A C B, line A B, line D B, line B C, line A C, \\odot D lieson A C B\nFind the area of the shaded region. Assume that the triangle is equilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3389.jpg"
-  },
-  {
-    "id": 3468,
-    "problem_id": 3390,
-    "problem": "line A B, line D B, line B C, line A C, \\odot D lieson A C B, line A B, line D B, line B C, line A C, \\odot D lieson A C B\nFind the area of the shaded region. Assume that the triangle is equilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3390.jpg"
-  },
-  {
-    "id": 3469,
-    "problem_id": 3391,
-    "problem": "line A B, line D B, line B C, line A C, \\odot D lieson A C B, line A B, line D B, line B C, line A C, \\odot D lieson A C B\nFind the area of the shaded region. Assume that the triangle is equilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3391.jpg"
-  },
-  {
-    "id": 3470,
-    "problem_id": 3392,
-    "problem": "line A C D, line B A, line B D, \\odot A lieson C B, line A C D, line B A, line B D, \\odot A lieson C B\nThe segment is tangent to the circle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3392.jpg"
-  },
-  {
-    "id": 3471,
-    "problem_id": 3393,
-    "problem": "line A C D, line B A, line B D, \\odot A lieson C B, line A C D, line B A, line B D, \\odot A lieson C B\nThe segment is tangent to the circle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3393.jpg"
-  },
-  {
-    "id": 3472,
-    "problem_id": 3394,
-    "problem": "line P Q, line Q A S, line S R, line P A R, \\odot B lieson P S R Q, line P Q, line Q A S, line S R, line P A R, \\odot B lieson P S R Q\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3394.jpg"
-  },
-  {
-    "id": 3473,
-    "problem_id": 3395,
-    "problem": "line P Q, line Q A S, line S R, line P A R, \\odot B lieson P S R Q, line P Q, line Q A S, line S R, line P A R, \\odot B lieson P S R Q\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3395.jpg"
-  },
-  {
-    "id": 3474,
-    "problem_id": 3396,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nWhat is the value of a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3396.jpg"
-  },
-  {
-    "id": 3475,
-    "problem_id": 3397,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nWhat is the value of a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3397.jpg"
-  },
-  {
-    "id": 3476,
-    "problem_id": 3398,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nWhat is the value of a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3398.jpg"
-  },
-  {
-    "id": 3477,
-    "problem_id": 3399,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nWhat is the value of a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3399.jpg"
-  },
-  {
-    "id": 3478,
-    "problem_id": 3400,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nWhat is the value of a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3400.jpg"
-  },
-  {
-    "id": 3479,
-    "problem_id": 3401,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3401.jpg"
-  },
-  {
-    "id": 3480,
-    "problem_id": 3402,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3402.jpg"
-  },
-  {
-    "id": 3481,
-    "problem_id": 3403,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3403.jpg"
-  },
-  {
-    "id": 3482,
-    "problem_id": 3404,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3404.jpg"
-  },
-  {
-    "id": 3483,
-    "problem_id": 3405,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3405.jpg"
-  },
-  {
-    "id": 3484,
-    "problem_id": 3406,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3406.jpg"
-  },
-  {
-    "id": 3485,
-    "problem_id": 3407,
-    "problem": "line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W, line Y X, line B C, line D C, line Y Z, line X W, line A B, line A D, line Z W\nABCD \\cong WXYZ. What is WX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3407.jpg"
-  },
-  {
-    "id": 3486,
-    "problem_id": 3408,
-    "problem": "line K M, line L M, line K L, \\odot L lieson K M, line K M, line L M, line K L, \\odot L lieson K M\nDetermine the measure of \\angle LMK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3408.jpg"
-  },
-  {
-    "id": 3487,
-    "problem_id": 3409,
-    "problem": "line C A, line B O C, line B A, \\odot O lieson C A B, line C A, line B O C, line B A, \\odot O lieson C A B\nIn \\odot O, what is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3409.jpg"
-  },
-  {
-    "id": 3488,
-    "problem_id": 3410,
-    "problem": "line C A, line B O C, line B A, \\odot O lieson C A B, line C A, line B O C, line B A, \\odot O lieson C A B\nIn \\odot O, what is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3410.jpg"
-  },
-  {
-    "id": 3489,
-    "problem_id": 3411,
-    "problem": "line V W, line P S V, line P T W, line S T, line V W, line P S V, line P T W, line S T\nFind PV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3411.jpg"
-  },
-  {
-    "id": 3490,
-    "problem_id": 3412,
-    "problem": "line W X Y, line W X Y\nFind the measurement of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3412.jpg"
-  },
-  {
-    "id": 3491,
-    "problem_id": 3413,
-    "problem": "line W X Y, line W X Y\nFind the measurement of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3413.jpg"
-  },
-  {
-    "id": 3492,
-    "problem_id": 3414,
-    "problem": "line W X Y, line W X Y\nFind the measurement of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3414.jpg"
-  },
-  {
-    "id": 3493,
-    "problem_id": 3415,
-    "problem": "line W X Y, line W X Y\nFind the measurement of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3415.jpg"
-  },
-  {
-    "id": 3494,
-    "problem_id": 3416,
-    "problem": "line W X Y, line W X Y\nFind the measurement of WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3416.jpg"
-  },
-  {
-    "id": 3495,
-    "problem_id": 3417,
-    "problem": "line T S E, line C Q T, line D R T, \\odot B lieson R S, \\odot A lieson Q R, line T S E, line C Q T, line D R T, \\odot B lieson R S, \\odot A lieson Q R\nThe segment is tangent to the circle. Find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3417.jpg"
-  },
-  {
-    "id": 3496,
-    "problem_id": 3418,
-    "problem": "line T S E, line C Q T, line D R T, \\odot B lieson R S, \\odot A lieson Q R, line T S E, line C Q T, line D R T, \\odot B lieson R S, \\odot A lieson Q R\nThe segment is tangent to the circle. Find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3418.jpg"
-  },
-  {
-    "id": 3497,
-    "problem_id": 3419,
-    "problem": "line T S E, line C Q T, line D R T, \\odot B lieson R S, \\odot A lieson Q R, line T S E, line C Q T, line D R T, \\odot B lieson R S, \\odot A lieson Q R\nThe segment is tangent to the circle. Find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3419.jpg"
-  },
-  {
-    "id": 3498,
-    "problem_id": 3420,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3420.jpg"
-  },
-  {
-    "id": 3499,
-    "problem_id": 3421,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3421.jpg"
-  },
-  {
-    "id": 3500,
-    "problem_id": 3422,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3422.jpg"
-  },
-  {
-    "id": 3501,
-    "problem_id": 3423,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3423.jpg"
-  },
-  {
-    "id": 3502,
-    "problem_id": 3424,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3424.jpg"
-  },
-  {
-    "id": 3503,
-    "problem_id": 3425,
-    "problem": "line K D R, line L Q K, line K P J, line Q D J, line L R J, line L D P, line K D R, line L Q K, line K P J, line Q D J, line L R J, line L D P\nPoints P, Q, and R are the midpoints of JK, KL, and JL, respectively. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3425.jpg"
-  },
-  {
-    "id": 3504,
-    "problem_id": 3426,
-    "problem": "\\odot A lieson E F, \\odot A lieson E F\nFind the diameter of circle if \\widehat EF = 8\\pi.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3426.jpg"
-  },
-  {
-    "id": 3506,
-    "problem_id": 3427,
-    "problem": "line C E F, line A D F, line A B C, line B D, line D E, line C E F, line A D F, line A B C, line B D, line D E\nIf BD \\perp CF and m \\angle 3 = 140, find m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3427.jpg"
-  },
-  {
-    "id": 3507,
-    "problem_id": 3428,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat MJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3428.jpg"
-  },
-  {
-    "id": 3509,
-    "problem_id": 3429,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat MJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3429.jpg"
-  },
-  {
-    "id": 3510,
-    "problem_id": 3430,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat MJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3430.jpg"
-  },
-  {
-    "id": 3511,
-    "problem_id": 3431,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat MJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3431.jpg"
-  },
-  {
-    "id": 3512,
-    "problem_id": 3432,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat MJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3432.jpg"
-  },
-  {
-    "id": 3513,
-    "problem_id": 3433,
-    "problem": "line A R C, line A S B, line B C, line S R, line A R C, line A S B, line B C, line S R\nFind AS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3433.jpg"
-  },
-  {
-    "id": 3514,
-    "problem_id": 3434,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3434.jpg"
-  },
-  {
-    "id": 3515,
-    "problem_id": 3435,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3435.jpg"
-  },
-  {
-    "id": 3516,
-    "problem_id": 3436,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3436.jpg"
-  },
-  {
-    "id": 3517,
-    "problem_id": 3437,
-    "problem": "line B D E G, line F D A, line H E C, line B D E G, line F D A, line H E C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3437.jpg"
-  },
-  {
-    "id": 3518,
-    "problem_id": 3438,
-    "problem": "line B D E G, line F D A, line H E C, line B D E G, line F D A, line H E C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3438.jpg"
-  },
-  {
-    "id": 3519,
-    "problem_id": 3439,
-    "problem": "line B D E G, line F D A, line H E C, line B D E G, line F D A, line H E C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3439.jpg"
-  },
-  {
-    "id": 3520,
-    "problem_id": 3440,
-    "problem": "line B D E G, line F D A, line H E C, line B D E G, line F D A, line H E C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3440.jpg"
-  },
-  {
-    "id": 3521,
-    "problem_id": 3441,
-    "problem": "line B D E G, line F D A, line H E C, line B D E G, line F D A, line H E C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3441.jpg"
-  },
-  {
-    "id": 3522,
-    "problem_id": 3442,
-    "problem": "line W X, line W Z, line X Z, line Y Z, line Y X, line W X, line W Z, line X Z, line Y Z, line Y X\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3442.jpg"
-  },
-  {
-    "id": 3523,
-    "problem_id": 3443,
-    "problem": "line W X, line W Z, line X Z, line Y Z, line Y X, line W X, line W Z, line X Z, line Y Z, line Y X\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3443.jpg"
-  },
-  {
-    "id": 3524,
-    "problem_id": 3444,
-    "problem": "line A D E F, line B D I G, line C D J, line E I H, line A D E F, line B D I G, line C D J, line E I H\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3444.jpg"
-  },
-  {
-    "id": 3525,
-    "problem_id": 3445,
-    "problem": "line A D E F, line B D I G, line C D J, line E I H, line A D E F, line B D I G, line C D J, line E I H\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3445.jpg"
-  },
-  {
-    "id": 3526,
-    "problem_id": 3446,
-    "problem": "line A B C, line D B, line D C, line A D, line A B C, line D B, line D C, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3446.jpg"
-  },
-  {
-    "id": 3527,
-    "problem_id": 3447,
-    "problem": "line A B C, line D B, line D C, line A D, line A B C, line D B, line D C, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3447.jpg"
-  },
-  {
-    "id": 3528,
-    "problem_id": 3448,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3448.jpg"
-  },
-  {
-    "id": 3529,
-    "problem_id": 3449,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3449.jpg"
-  },
-  {
-    "id": 3530,
-    "problem_id": 3450,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3450.jpg"
-  },
-  {
-    "id": 3531,
-    "problem_id": 3451,
-    "problem": "line S W V, line T W R, line T V, line S T, line S R, line R V, line S W V, line T W R, line T V, line S T, line S R, line R V\nRSTV is a rhombus. Find the measure of RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3451.jpg"
-  },
-  {
-    "id": 3532,
-    "problem_id": 3452,
-    "problem": "line R Q, line Q T, line T S, line R S, line Q A S, \\odot Q lieson T A R, line R Q, line Q T, line T S, line R S, line Q A S, \\odot Q lieson T A R\nThe segment is tangent to the circle. Find the length of RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3452.jpg"
-  },
-  {
-    "id": 3533,
-    "problem_id": 3453,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line A E C, line B C, line C D, line A D, line B A, line B E D, line A E C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3453.jpg"
-  },
-  {
-    "id": 3534,
-    "problem_id": 3454,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line A E C, line B C, line C D, line A D, line B A, line B E D, line A E C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3454.jpg"
-  },
-  {
-    "id": 3535,
-    "problem_id": 3455,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line A E C, line B C, line C D, line A D, line B A, line B E D, line A E C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3455.jpg"
-  },
-  {
-    "id": 3536,
-    "problem_id": 3456,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line A E C, line B C, line C D, line A D, line B A, line B E D, line A E C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3456.jpg"
-  },
-  {
-    "id": 3537,
-    "problem_id": 3457,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line A E C, line B C, line C D, line A D, line B A, line B E D, line A E C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3457.jpg"
-  },
-  {
-    "id": 3538,
-    "problem_id": 3458,
-    "problem": "line D E F, line A B C, line A D, line B E, line C F, line D E F, line A B C, line A D, line B E, line C F\nFind the height of parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3458.jpg"
-  },
-  {
-    "id": 3539,
-    "problem_id": 3459,
-    "problem": "line D E F, line A B C, line A D, line B E, line C F, line D E F, line A B C, line A D, line B E, line C F\nFind the height of parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3459.jpg"
-  },
-  {
-    "id": 3540,
-    "problem_id": 3460,
-    "problem": "line D E F, line A B C, line A D, line B E, line C F, line D E F, line A B C, line A D, line B E, line C F\nFind the height of parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3460.jpg"
-  },
-  {
-    "id": 3541,
-    "problem_id": 3461,
-    "problem": "line D E F, line A B C, line A D, line B E, line C F, line D E F, line A B C, line A D, line B E, line C F\nFind the height of parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3461.jpg"
-  },
-  {
-    "id": 3542,
-    "problem_id": 3462,
-    "problem": "line D E F, line A B C, line A D, line B E, line C F, line D E F, line A B C, line A D, line B E, line C F\nFind the height of parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3462.jpg"
-  },
-  {
-    "id": 3543,
-    "problem_id": 3463,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3463.jpg"
-  },
-  {
-    "id": 3544,
-    "problem_id": 3464,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3464.jpg"
-  },
-  {
-    "id": 3545,
-    "problem_id": 3465,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3465.jpg"
-  },
-  {
-    "id": 3546,
-    "problem_id": 3466,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nDetermine the measure of \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3466.jpg"
-  },
-  {
-    "id": 3547,
-    "problem_id": 3467,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nDetermine the measure of \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3467.jpg"
-  },
-  {
-    "id": 3548,
-    "problem_id": 3468,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nDetermine the measure of \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3468.jpg"
-  },
-  {
-    "id": 3549,
-    "problem_id": 3469,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nDetermine the measure of \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3469.jpg"
-  },
-  {
-    "id": 3550,
-    "problem_id": 3470,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nDetermine the measure of \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3470.jpg"
-  },
-  {
-    "id": 3551,
-    "problem_id": 3471,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nDetermine the measure of \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3471.jpg"
-  },
-  {
-    "id": 3552,
-    "problem_id": 3472,
-    "problem": "line G E, line G F, line E F, line G E, line G F, line E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3472.jpg"
-  },
-  {
-    "id": 3553,
-    "problem_id": 3473,
-    "problem": "line G E, line G F, line E F, line G E, line G F, line E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3473.jpg"
-  },
-  {
-    "id": 3554,
-    "problem_id": 3474,
-    "problem": "line G E, line G F, line E F, line G E, line G F, line E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3474.jpg"
-  },
-  {
-    "id": 3555,
-    "problem_id": 3475,
-    "problem": "line G E, line G F, line E F, line G E, line G F, line E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3475.jpg"
-  },
-  {
-    "id": 3556,
-    "problem_id": 3476,
-    "problem": "line S M P N R, line S M P N R\nFind the measurement of MP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3476.jpg"
-  },
-  {
-    "id": 3557,
-    "problem_id": 3477,
-    "problem": "line S M P N R, line S M P N R\nFind the measurement of MP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3477.jpg"
-  },
-  {
-    "id": 3558,
-    "problem_id": 3478,
-    "problem": "line S M P N R, line S M P N R\nFind the measurement of MP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3478.jpg"
-  },
-  {
-    "id": 3559,
-    "problem_id": 3479,
-    "problem": "line S M P N R, line S M P N R\nFind the measurement of MP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3479.jpg"
-  },
-  {
-    "id": 3560,
-    "problem_id": 3480,
-    "problem": "line D C B, line A B, line D E, line B E, line A D, line A C E, line D C B, line A B, line D E, line B E, line A D, line A C E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3480.jpg"
-  },
-  {
-    "id": 3561,
-    "problem_id": 3481,
-    "problem": "line D C B, line A B, line D E, line B E, line A D, line A C E, line D C B, line A B, line D E, line B E, line A D, line A C E\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3481.jpg"
-  },
-  {
-    "id": 3562,
-    "problem_id": 3482,
-    "problem": "line E H, line A C, line C F, line B E, line A B, line D G, line F G H, line E H, line A C, line C F, line B E, line A B, line D G, line F G H\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3482.jpg"
-  },
-  {
-    "id": 3563,
-    "problem_id": 3483,
-    "problem": "line E H, line A C, line C F, line B E, line A B, line D G, line F G H, line E H, line A C, line C F, line B E, line A B, line D G, line F G H\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3483.jpg"
-  },
-  {
-    "id": 3564,
-    "problem_id": 3484,
-    "problem": "line E H, line A C, line C F, line B E, line A B, line D G, line F G H, line E H, line A C, line C F, line B E, line A B, line D G, line F G H\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3484.jpg"
-  },
-  {
-    "id": 3565,
-    "problem_id": 3485,
-    "problem": "line Q R S, line P R T, line P Q, line S T, line Q R S, line P R T, line P Q, line S T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3485.jpg"
-  },
-  {
-    "id": 3566,
-    "problem_id": 3486,
-    "problem": "line B C D, line A D, line B E F, line A B, line A C, line D F, line C E, line B C D, line A D, line B E F, line A B, line A C, line D F, line C E\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3486.jpg"
-  },
-  {
-    "id": 3567,
-    "problem_id": 3487,
-    "problem": "line B C D, line A D, line B E F, line A B, line A C, line D F, line C E, line B C D, line A D, line B E F, line A B, line A C, line D F, line C E\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3487.jpg"
-  },
-  {
-    "id": 3568,
-    "problem_id": 3488,
-    "problem": "line B C D, line A D, line B E F, line A B, line A C, line D F, line C E, line B C D, line A D, line B E F, line A B, line A C, line D F, line C E\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3488.jpg"
-  },
-  {
-    "id": 3569,
-    "problem_id": 3489,
-    "problem": "line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D, line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D\nGiven ABCD \\cong EFGH, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3489.jpg"
-  },
-  {
-    "id": 3570,
-    "problem_id": 3490,
-    "problem": "line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D, line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D\nGiven ABCD \\cong EFGH, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3490.jpg"
-  },
-  {
-    "id": 3571,
-    "problem_id": 3491,
-    "problem": "line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D, line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D\nGiven ABCD \\cong EFGH, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3491.jpg"
-  },
-  {
-    "id": 3572,
-    "problem_id": 3492,
-    "problem": "line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D, line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D\nGiven ABCD \\cong EFGH, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3492.jpg"
-  },
-  {
-    "id": 3573,
-    "problem_id": 3493,
-    "problem": "line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D, line E H, line A D, line E F, line A B, line F G, line B C, line H G, line C D\nGiven ABCD \\cong EFGH, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3493.jpg"
-  },
-  {
-    "id": 3574,
-    "problem_id": 3494,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nFind the measure of \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3494.jpg"
-  },
-  {
-    "id": 3575,
-    "problem_id": 3495,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nFind the measure of \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3495.jpg"
-  },
-  {
-    "id": 3576,
-    "problem_id": 3496,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nFind the measure of \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3496.jpg"
-  },
-  {
-    "id": 3577,
-    "problem_id": 3497,
-    "problem": "line F E, line D E, line D F, line F E, line D E, line D F\nFind the measure of \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3497.jpg"
-  },
-  {
-    "id": 3578,
-    "problem_id": 3498,
-    "problem": "line K J, line J G, line K H, line H G, line K J, line J G, line K H, line H G\nFind r in rhombus JKHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3498.jpg"
-  },
-  {
-    "id": 3579,
-    "problem_id": 3499,
-    "problem": "line K J, line J G, line K H, line H G, line K J, line J G, line K H, line H G\nFind r in rhombus JKHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3499.jpg"
-  },
-  {
-    "id": 3580,
-    "problem_id": 3500,
-    "problem": "line K J, line J G, line K H, line H G, line K J, line J G, line K H, line H G\nFind r in rhombus JKHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3500.jpg"
-  },
-  {
-    "id": 3581,
-    "problem_id": 3501,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3501.jpg"
-  },
-  {
-    "id": 3582,
-    "problem_id": 3502,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3502.jpg"
-  },
-  {
-    "id": 3583,
-    "problem_id": 3503,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3503.jpg"
-  },
-  {
-    "id": 3584,
-    "problem_id": 3504,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3504.jpg"
-  },
-  {
-    "id": 3585,
-    "problem_id": 3505,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3505.jpg"
-  },
-  {
-    "id": 3586,
-    "problem_id": 3506,
-    "problem": "line V Z X, line V W, line V Y, line W X, line Y X, line W Z Y, line V Z X, line V W, line V Y, line W X, line Y X, line W Z Y\nVWXY is a rhombus. Find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3506.jpg"
-  },
-  {
-    "id": 3587,
-    "problem_id": 3507,
-    "problem": "line V Z X, line V W, line V Y, line W X, line Y X, line W Z Y, line V Z X, line V W, line V Y, line W X, line Y X, line W Z Y\nVWXY is a rhombus. Find a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3507.jpg"
-  },
-  {
-    "id": 3588,
-    "problem_id": 3508,
-    "problem": "line K L, line N L, line K N, line N M, line M L, line J L, line K J, line K L, line N L, line K N, line N M, line M L, line J L, line K J\n\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle LNM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3508.jpg"
-  },
-  {
-    "id": 3589,
-    "problem_id": 3509,
-    "problem": "line C N M B, line A L M D, \\odot E lieson Q N L, line C N M B, line A L M D, \\odot E lieson Q N L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3509.jpg"
-  },
-  {
-    "id": 3590,
-    "problem_id": 3510,
-    "problem": "line C N M B, line A L M D, \\odot E lieson Q N L, line C N M B, line A L M D, \\odot E lieson Q N L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3510.jpg"
-  },
-  {
-    "id": 3591,
-    "problem_id": 3511,
-    "problem": "line C N M B, line A L M D, \\odot E lieson Q N L, line C N M B, line A L M D, \\odot E lieson Q N L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3511.jpg"
-  },
-  {
-    "id": 3592,
-    "problem_id": 3512,
-    "problem": "line Z B W, line X Z, line X A Y, line Y V Z, line S A V B T, line X V W, \\odot V lieson X S Y W T Z, line Z B W, line X Z, line X A Y, line Y V Z, line S A V B T, line X V W, \\odot V lieson X S Y W T Z\nIf m \\widehat XZ = 100, XY \\perp ST, and ZW \\perp ST. What is m \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3512.jpg"
-  },
-  {
-    "id": 3593,
-    "problem_id": 3513,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3513.jpg"
-  },
-  {
-    "id": 3594,
-    "problem_id": 3514,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3514.jpg"
-  },
-  {
-    "id": 3595,
-    "problem_id": 3515,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3515.jpg"
-  },
-  {
-    "id": 3596,
-    "problem_id": 3516,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3516.jpg"
-  },
-  {
-    "id": 3597,
-    "problem_id": 3517,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3517.jpg"
-  },
-  {
-    "id": 3598,
-    "problem_id": 3518,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3518.jpg"
-  },
-  {
-    "id": 3599,
-    "problem_id": 3519,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3519.jpg"
-  },
-  {
-    "id": 3600,
-    "problem_id": 3520,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3520.jpg"
-  },
-  {
-    "id": 3601,
-    "problem_id": 3521,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3521.jpg"
-  },
-  {
-    "id": 3602,
-    "problem_id": 3522,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3522.jpg"
-  },
-  {
-    "id": 3603,
-    "problem_id": 3523,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3523.jpg"
-  },
-  {
-    "id": 3604,
-    "problem_id": 3524,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3524.jpg"
-  },
-  {
-    "id": 3605,
-    "problem_id": 3525,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3525.jpg"
-  },
-  {
-    "id": 3606,
-    "problem_id": 3526,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3526.jpg"
-  },
-  {
-    "id": 3608,
-    "problem_id": 3527,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3527.jpg"
-  },
-  {
-    "id": 3609,
-    "problem_id": 3528,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3528.jpg"
-  },
-  {
-    "id": 3611,
-    "problem_id": 3529,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3529.jpg"
-  },
-  {
-    "id": 3612,
-    "problem_id": 3530,
-    "problem": "line A B, line B D, line D H, line G F H, line C G, line A C, line E F, line A B, line B D, line D H, line G F H, line C G, line A C, line E F\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3530.jpg"
-  },
-  {
-    "id": 3613,
-    "problem_id": 3531,
-    "problem": "line A B, line B D, line D H, line G F H, line C G, line A C, line E F, line A B, line B D, line D H, line G F H, line C G, line A C, line E F\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3531.jpg"
-  },
-  {
-    "id": 3614,
-    "problem_id": 3532,
-    "problem": "line A B, line B D, line D H, line G F H, line C G, line A C, line E F, line A B, line B D, line D H, line G F H, line C G, line A C, line E F\nWhat is the area of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3532.jpg"
-  },
-  {
-    "id": 3615,
-    "problem_id": 3533,
-    "problem": "line B C, line B A, \\odot B lieson C A, line B C, line B A, \\odot B lieson C A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3533.jpg"
-  },
-  {
-    "id": 3616,
-    "problem_id": 3534,
-    "problem": "line B C, line B A, \\odot B lieson C A, line B C, line B A, \\odot B lieson C A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3534.jpg"
-  },
-  {
-    "id": 3617,
-    "problem_id": 3535,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3535.jpg"
-  },
-  {
-    "id": 3618,
-    "problem_id": 3536,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3536.jpg"
-  },
-  {
-    "id": 3619,
-    "problem_id": 3537,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3537.jpg"
-  },
-  {
-    "id": 3620,
-    "problem_id": 3538,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3538.jpg"
-  },
-  {
-    "id": 3621,
-    "problem_id": 3539,
-    "problem": "line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O, line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3539.jpg"
-  },
-  {
-    "id": 3622,
-    "problem_id": 3540,
-    "problem": "line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O, line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3540.jpg"
-  },
-  {
-    "id": 3623,
-    "problem_id": 3541,
-    "problem": "line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O, line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3541.jpg"
-  },
-  {
-    "id": 3624,
-    "problem_id": 3542,
-    "problem": "line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O, line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3542.jpg"
-  },
-  {
-    "id": 3625,
-    "problem_id": 3543,
-    "problem": "line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O, line C D E F, line G H I J, line K L M N, line A D H L P, line B E I M O\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3543.jpg"
-  },
-  {
-    "id": 3626,
-    "problem_id": 3544,
-    "problem": "line W R X, line W R X\nFind the measurement of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3544.jpg"
-  },
-  {
-    "id": 3627,
-    "problem_id": 3545,
-    "problem": "line W R X, line W R X\nFind the measurement of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3545.jpg"
-  },
-  {
-    "id": 3628,
-    "problem_id": 3546,
-    "problem": "line C E F, line A D F, line A B C, line B D, line D E, line C E F, line A D F, line A B C, line B D, line D E\nIf AC \\parallel DE, BD \\parallel CF and m \\angle 2 = 55, find m \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3546.jpg"
-  },
-  {
-    "id": 3629,
-    "problem_id": 3547,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3547.jpg"
-  },
-  {
-    "id": 3630,
-    "problem_id": 3548,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3548.jpg"
-  },
-  {
-    "id": 3631,
-    "problem_id": 3549,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3549.jpg"
-  },
-  {
-    "id": 3632,
-    "problem_id": 3550,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3550.jpg"
-  },
-  {
-    "id": 3633,
-    "problem_id": 3551,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3551.jpg"
-  },
-  {
-    "id": 3634,
-    "problem_id": 3552,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3552.jpg"
-  },
-  {
-    "id": 3635,
-    "problem_id": 3553,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3553.jpg"
-  },
-  {
-    "id": 3636,
-    "problem_id": 3554,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3554.jpg"
-  },
-  {
-    "id": 3637,
-    "problem_id": 3555,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3555.jpg"
-  },
-  {
-    "id": 3638,
-    "problem_id": 3556,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3556.jpg"
-  },
-  {
-    "id": 3639,
-    "problem_id": 3557,
-    "problem": "line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F, line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F\nm \\angle 4 = 104, m \\angle 14 = 118. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3557.jpg"
-  },
-  {
-    "id": 3640,
-    "problem_id": 3558,
-    "problem": "line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F, line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F\nm \\angle 4 = 104, m \\angle 14 = 118. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3558.jpg"
-  },
-  {
-    "id": 3641,
-    "problem_id": 3559,
-    "problem": "line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F, line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F\nm \\angle 4 = 104, m \\angle 14 = 118. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3559.jpg"
-  },
-  {
-    "id": 3642,
-    "problem_id": 3560,
-    "problem": "line C D, line A C, line C B, \\odot C lieson A D B, line C D, line A C, line C B, \\odot C lieson A D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3560.jpg"
-  },
-  {
-    "id": 3643,
-    "problem_id": 3561,
-    "problem": "line C D, line A C, line C B, \\odot C lieson A D B, line C D, line A C, line C B, \\odot C lieson A D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3561.jpg"
-  },
-  {
-    "id": 3644,
-    "problem_id": 3562,
-    "problem": "line C D, line A C, line C B, \\odot C lieson A D B, line C D, line A C, line C B, \\odot C lieson A D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3562.jpg"
-  },
-  {
-    "id": 3645,
-    "problem_id": 3563,
-    "problem": "line C D, line A C, line C B, \\odot C lieson A D B, line C D, line A C, line C B, \\odot C lieson A D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3563.jpg"
-  },
-  {
-    "id": 3646,
-    "problem_id": 3564,
-    "problem": "line C D, line A C, line C B, \\odot C lieson A D B, line C D, line A C, line C B, \\odot C lieson A D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3564.jpg"
-  },
-  {
-    "id": 3647,
-    "problem_id": 3565,
-    "problem": "line W X C, line W Z, line Z Y A, line D X Y B, line W X C, line W Z, line Z Y A, line D X Y B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3565.jpg"
-  },
-  {
-    "id": 3649,
-    "problem_id": 3566,
-    "problem": "line W X C, line W Z, line Z Y A, line D X Y B, line W X C, line W Z, line Z Y A, line D X Y B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3566.jpg"
-  },
-  {
-    "id": 3650,
-    "problem_id": 3567,
-    "problem": "line W X C, line W Z, line Z Y A, line D X Y B, line W X C, line W Z, line Z Y A, line D X Y B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3567.jpg"
-  },
-  {
-    "id": 3651,
-    "problem_id": 3568,
-    "problem": "line S Q, line Q R, \\odot Q lieson R S, line S Q, line Q R, \\odot Q lieson R S\nFind SQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3568.jpg"
-  },
-  {
-    "id": 3652,
-    "problem_id": 3569,
-    "problem": "line B A, line B D C, line A D, line A C, line B A, line B D C, line A D, line A C\nThe perimeter of \\triangle ABC is 29 cm. AD bisects \\angle A. Find AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3569.jpg"
-  },
-  {
-    "id": 3653,
-    "problem_id": 3570,
-    "problem": "line B F, line G F, line A F, line D E F, line A C E G, \\odot C lieson D G F A, line B F, line G F, line A F, line D E F, line A C E G, \\odot C lieson D G F A\nFind the value of variable a. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3570.jpg"
-  },
-  {
-    "id": 3654,
-    "problem_id": 3571,
-    "problem": "line m lieson B D F G, line l lieson A I H, line C D I, line I F E, line C E, line m lieson B D F G, line l lieson A I H, line C D I, line I F E, line C E\nLine l is parallel to line m. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3571.jpg"
-  },
-  {
-    "id": 3655,
-    "problem_id": 3572,
-    "problem": "line m lieson B D F G, line l lieson A I H, line C D I, line I F E, line C E, line m lieson B D F G, line l lieson A I H, line C D I, line I F E, line C E\nLine l is parallel to line m. What is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3572.jpg"
-  },
-  {
-    "id": 3656,
-    "problem_id": 3573,
-    "problem": "line A B, line B D E, line C E, line C D, line A C, line A B, line B D E, line C E, line C D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3573.jpg"
-  },
-  {
-    "id": 3657,
-    "problem_id": 3574,
-    "problem": "line A B, line B D E, line C E, line C D, line A C, line A B, line B D E, line C E, line C D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3574.jpg"
-  },
-  {
-    "id": 3658,
-    "problem_id": 3575,
-    "problem": "line A B, line B D E, line C E, line C D, line A C, line A B, line B D E, line C E, line C D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3575.jpg"
-  },
-  {
-    "id": 3659,
-    "problem_id": 3576,
-    "problem": "line A B, line B D E, line C E, line C D, line A C, line A B, line B D E, line C E, line C D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3576.jpg"
-  },
-  {
-    "id": 3661,
-    "problem_id": 3577,
-    "problem": "line W Z, line W X, line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y\nWXYZ is a parallelogram. Solve for the measure of \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3577.jpg"
-  },
-  {
-    "id": 3662,
-    "problem_id": 3578,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3578.jpg"
-  },
-  {
-    "id": 3663,
-    "problem_id": 3579,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3579.jpg"
-  },
-  {
-    "id": 3664,
-    "problem_id": 3580,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3580.jpg"
-  },
-  {
-    "id": 3665,
-    "problem_id": 3581,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3581.jpg"
-  },
-  {
-    "id": 3666,
-    "problem_id": 3582,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3582.jpg"
-  },
-  {
-    "id": 3667,
-    "problem_id": 3583,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nFind the measure of \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3583.jpg"
-  },
-  {
-    "id": 3668,
-    "problem_id": 3584,
-    "problem": "line B E F, line A D G, line C D, line C E, line B E F, line A D G, line C D, line C E\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3584.jpg"
-  },
-  {
-    "id": 3669,
-    "problem_id": 3585,
-    "problem": "line B E F, line A D G, line C D, line C E, line B E F, line A D G, line C D, line C E\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3585.jpg"
-  },
-  {
-    "id": 3670,
-    "problem_id": 3586,
-    "problem": "line B E F, line A D G, line C D, line C E, line B E F, line A D G, line C D, line C E\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3586.jpg"
-  },
-  {
-    "id": 3672,
-    "problem_id": 3587,
-    "problem": "line A B C, line C D, line E D, line B E, line A B C, line C D, line E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3587.jpg"
-  },
-  {
-    "id": 3673,
-    "problem_id": 3588,
-    "problem": "line A B C, line C D, line E D, line B E, line A B C, line C D, line E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3588.jpg"
-  },
-  {
-    "id": 3674,
-    "problem_id": 3589,
-    "problem": "line A B C, line C D, line E D, line B E, line A B C, line C D, line E D, line B E\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3589.jpg"
-  },
-  {
-    "id": 3675,
-    "problem_id": 3590,
-    "problem": "line B A, line A D C, line B C, line B D, line B A, line A D C, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3590.jpg"
-  },
-  {
-    "id": 3676,
-    "problem_id": 3591,
-    "problem": "line B A, line A D C, line B C, line B D, line B A, line A D C, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3591.jpg"
-  },
-  {
-    "id": 3677,
-    "problem_id": 3592,
-    "problem": "line B A, line A D C, line B C, line B D, line B A, line A D C, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3592.jpg"
-  },
-  {
-    "id": 3678,
-    "problem_id": 3593,
-    "problem": "line B A, line A D C, line B C, line B D, line B A, line A D C, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3593.jpg"
-  },
-  {
-    "id": 3679,
-    "problem_id": 3594,
-    "problem": "line B A, line A D C, line B C, line B D, line B A, line A D C, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3594.jpg"
-  },
-  {
-    "id": 3680,
-    "problem_id": 3595,
-    "problem": "line B A, line A D C, line B C, line B D, line B A, line A D C, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3595.jpg"
-  },
-  {
-    "id": 3681,
-    "problem_id": 3596,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3596.jpg"
-  },
-  {
-    "id": 3682,
-    "problem_id": 3597,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3597.jpg"
-  },
-  {
-    "id": 3683,
-    "problem_id": 3598,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3598.jpg"
-  },
-  {
-    "id": 3684,
-    "problem_id": 3599,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3599.jpg"
-  },
-  {
-    "id": 3685,
-    "problem_id": 3600,
-    "problem": "line A B C, line E D C, line B D F, line E F G, line A B C, line E D C, line B D F, line E F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3600.jpg"
-  },
-  {
-    "id": 3686,
-    "problem_id": 3601,
-    "problem": "line A B C, line E D C, line B D F, line E F G, line A B C, line E D C, line B D F, line E F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3601.jpg"
-  },
-  {
-    "id": 3687,
-    "problem_id": 3602,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3602.jpg"
-  },
-  {
-    "id": 3688,
-    "problem_id": 3603,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3603.jpg"
-  },
-  {
-    "id": 3689,
-    "problem_id": 3604,
-    "problem": "line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G, line A B C, line A D E, \\odot H lieson C G E, \\odot F lieson B D G\nAssume the segments that appear to be tangent are tangent. Find the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3604.jpg"
-  },
-  {
-    "id": 3690,
-    "problem_id": 3605,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of AH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3605.jpg"
-  },
-  {
-    "id": 3691,
-    "problem_id": 3606,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of AH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3606.jpg"
-  },
-  {
-    "id": 3692,
-    "problem_id": 3607,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of AH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3607.jpg"
-  },
-  {
-    "id": 3693,
-    "problem_id": 3608,
-    "problem": "line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A, line A G B, line E H B, line E D F, line A H F, line C D H G, line C F B, line C E A\nWhat is the length of AH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3608.jpg"
-  },
-  {
-    "id": 3694,
-    "problem_id": 3609,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3609.jpg"
-  },
-  {
-    "id": 3695,
-    "problem_id": 3610,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3610.jpg"
-  },
-  {
-    "id": 3696,
-    "problem_id": 3611,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3611.jpg"
-  },
-  {
-    "id": 3697,
-    "problem_id": 3612,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3612.jpg"
-  },
-  {
-    "id": 3698,
-    "problem_id": 3613,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3613.jpg"
-  },
-  {
-    "id": 3699,
-    "problem_id": 3614,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3614.jpg"
-  },
-  {
-    "id": 3700,
-    "problem_id": 3615,
-    "problem": "line F E D, line C L M B, line A K L E G, line F E D, line C L M B, line A K L E G\nFind m \\angle KLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3615.jpg"
-  },
-  {
-    "id": 3701,
-    "problem_id": 3616,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3616.jpg"
-  },
-  {
-    "id": 3703,
-    "problem_id": 3617,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3617.jpg"
-  },
-  {
-    "id": 3704,
-    "problem_id": 3618,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3618.jpg"
-  },
-  {
-    "id": 3705,
-    "problem_id": 3619,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3619.jpg"
-  },
-  {
-    "id": 3706,
-    "problem_id": 3620,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3620.jpg"
-  },
-  {
-    "id": 3707,
-    "problem_id": 3621,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3621.jpg"
-  },
-  {
-    "id": 3708,
-    "problem_id": 3622,
-    "problem": "line A E C, line B C, line B D A, line D E, line A E C, line B C, line B D A, line D E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3622.jpg"
-  },
-  {
-    "id": 3709,
-    "problem_id": 3623,
-    "problem": "line D M B, line B C, line A M C, line A D, line D M B, line B C, line A M C, line A D\nWhat is the length of DM?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3623.jpg"
-  },
-  {
-    "id": 3710,
-    "problem_id": 3624,
-    "problem": "line D J E, line F H E, line D G F, line G H, line G J, line J H, line D J E, line F H E, line D G F, line G H, line G J, line J H\nGH, HJ, and JG are midsegments of \\triangle DEF. Solve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3624.jpg"
-  },
-  {
-    "id": 3711,
-    "problem_id": 3625,
-    "problem": "line D J E, line F H E, line D G F, line G H, line G J, line J H, line D J E, line F H E, line D G F, line G H, line G J, line J H\nGH, HJ, and JG are midsegments of \\triangle DEF. Solve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3625.jpg"
-  },
-  {
-    "id": 3712,
-    "problem_id": 3626,
-    "problem": "line D J E, line F H E, line D G F, line G H, line G J, line J H, line D J E, line F H E, line D G F, line G H, line G J, line J H\nGH, HJ, and JG are midsegments of \\triangle DEF. Solve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3626.jpg"
-  },
-  {
-    "id": 3713,
-    "problem_id": 3627,
-    "problem": "line D J E, line F H E, line D G F, line G H, line G J, line J H, line D J E, line F H E, line D G F, line G H, line G J, line J H\nGH, HJ, and JG are midsegments of \\triangle DEF. Solve for the length of FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3627.jpg"
-  },
-  {
-    "id": 3714,
-    "problem_id": 3628,
-    "problem": "line A B, line C A, line C B, line D E, line E F, line D F, line A B, line C A, line C B, line D E, line E F, line D F\nFor the pair of similar figures, the area of the blue figure is 25 mm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3628.jpg"
-  },
-  {
-    "id": 3715,
-    "problem_id": 3629,
-    "problem": "line A B, line C A, line C B, line D E, line E F, line D F, line A B, line C A, line C B, line D E, line E F, line D F\nFor the pair of similar figures, the area of the blue figure is 25 mm^{2}, find the area of the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3629.jpg"
-  },
-  {
-    "id": 3716,
-    "problem_id": 3630,
-    "problem": "line F E D, line C D, line A B C, line A F, line B E, line F E D, line C D, line A B C, line A F, line B E\nIf BEFA \\sim EDCB, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3630.jpg"
-  },
-  {
-    "id": 3717,
-    "problem_id": 3631,
-    "problem": "line B D, line A C, line A B, line A D, line C D, line B D, line A C, line A B, line A D, line C D\nFind m \\angle 3 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3631.jpg"
-  },
-  {
-    "id": 3718,
-    "problem_id": 3632,
-    "problem": "line B D, line A C, line A B, line A D, line C D, line B D, line A C, line A B, line A D, line C D\nFind m \\angle 3 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3632.jpg"
-  },
-  {
-    "id": 3719,
-    "problem_id": 3633,
-    "problem": "line B D, line A C, line A B, line A D, line C D, line B D, line A C, line A B, line A D, line C D\nFind m \\angle 3 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3633.jpg"
-  },
-  {
-    "id": 3720,
-    "problem_id": 3634,
-    "problem": "line D E F, line D E F\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3634.jpg"
-  },
-  {
-    "id": 3721,
-    "problem_id": 3635,
-    "problem": "line D E F, line D E F\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3635.jpg"
-  },
-  {
-    "id": 3722,
-    "problem_id": 3636,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3636.jpg"
-  },
-  {
-    "id": 3723,
-    "problem_id": 3637,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3637.jpg"
-  },
-  {
-    "id": 3724,
-    "problem_id": 3638,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3638.jpg"
-  },
-  {
-    "id": 3725,
-    "problem_id": 3639,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3639.jpg"
-  },
-  {
-    "id": 3726,
-    "problem_id": 3640,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3640.jpg"
-  },
-  {
-    "id": 3727,
-    "problem_id": 3641,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3641.jpg"
-  },
-  {
-    "id": 3728,
-    "problem_id": 3642,
-    "problem": "line A B C, line B D, \\odot B lieson A D C, line A B C, line B D, \\odot B lieson A D C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3642.jpg"
-  },
-  {
-    "id": 3729,
-    "problem_id": 3643,
-    "problem": "line A B C, line B D, \\odot B lieson A D C, line A B C, line B D, \\odot B lieson A D C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3643.jpg"
-  },
-  {
-    "id": 3730,
-    "problem_id": 3644,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3644.jpg"
-  },
-  {
-    "id": 3731,
-    "problem_id": 3645,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3645.jpg"
-  },
-  {
-    "id": 3732,
-    "problem_id": 3646,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3646.jpg"
-  },
-  {
-    "id": 3733,
-    "problem_id": 3647,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3647.jpg"
-  },
-  {
-    "id": 3734,
-    "problem_id": 3648,
-    "problem": "line M R, line Q R, line N M, line N Q, line M L Q, line N L R, line M R, line Q R, line N M, line N Q, line M L Q, line N L R\nUse parallelogram NQRM to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3648.jpg"
-  },
-  {
-    "id": 3735,
-    "problem_id": 3649,
-    "problem": "line F A E D I, line H C E B G, line F A E D I, line H C E B G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3649.jpg"
-  },
-  {
-    "id": 3736,
-    "problem_id": 3650,
-    "problem": "line F A E D I, line H C E B G, line F A E D I, line H C E B G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3650.jpg"
-  },
-  {
-    "id": 3737,
-    "problem_id": 3651,
-    "problem": "line A Y Z, line X Y, line X W, line C W Z, line B X Z, line A Y Z, line X Y, line X W, line C W Z, line B X Z\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3651.jpg"
-  },
-  {
-    "id": 3738,
-    "problem_id": 3652,
-    "problem": "line A Y Z, line X Y, line X W, line C W Z, line B X Z, line A Y Z, line X Y, line X W, line C W Z, line B X Z\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3652.jpg"
-  },
-  {
-    "id": 3739,
-    "problem_id": 3653,
-    "problem": "line A Y Z, line X Y, line X W, line C W Z, line B X Z, line A Y Z, line X Y, line X W, line C W Z, line B X Z\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3653.jpg"
-  },
-  {
-    "id": 3740,
-    "problem_id": 3654,
-    "problem": "line M L, line J M, line J K, line K L, line M L, line J M, line J K, line K L\nFind the value of f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3654.jpg"
-  },
-  {
-    "id": 3741,
-    "problem_id": 3655,
-    "problem": "line M L, line J M, line J K, line K L, line M L, line J M, line J K, line K L\nFind the value of f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3655.jpg"
-  },
-  {
-    "id": 3742,
-    "problem_id": 3656,
-    "problem": "line M L, line J M, line J K, line K L, line M L, line J M, line J K, line K L\nFind the value of f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3656.jpg"
-  },
-  {
-    "id": 3743,
-    "problem_id": 3657,
-    "problem": "line M L, line J M, line J K, line K L, line M L, line J M, line J K, line K L\nFind the value of f in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3657.jpg"
-  },
-  {
-    "id": 3744,
-    "problem_id": 3658,
-    "problem": "line A C F H, line D C B, line E F G, line A C F H, line D C B, line E F G\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3658.jpg"
-  },
-  {
-    "id": 3745,
-    "problem_id": 3659,
-    "problem": "line A C F H, line D C B, line E F G, line A C F H, line D C B, line E F G\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3659.jpg"
-  },
-  {
-    "id": 3746,
-    "problem_id": 3660,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nWhat is the measure of \\widehat PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3660.jpg"
-  },
-  {
-    "id": 3747,
-    "problem_id": 3661,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nWhat is the measure of \\widehat PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3661.jpg"
-  },
-  {
-    "id": 3748,
-    "problem_id": 3662,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nWhat is the measure of \\widehat PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3662.jpg"
-  },
-  {
-    "id": 3749,
-    "problem_id": 3663,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3663.jpg"
-  },
-  {
-    "id": 3750,
-    "problem_id": 3664,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3664.jpg"
-  },
-  {
-    "id": 3751,
-    "problem_id": 3665,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3665.jpg"
-  },
-  {
-    "id": 3752,
-    "problem_id": 3666,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3666.jpg"
-  },
-  {
-    "id": 3753,
-    "problem_id": 3667,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find the measure of \\angle 14.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3667.jpg"
-  },
-  {
-    "id": 3754,
-    "problem_id": 3668,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find the measure of \\angle 14.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3668.jpg"
-  },
-  {
-    "id": 3755,
-    "problem_id": 3669,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find the measure of \\angle 14.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3669.jpg"
-  },
-  {
-    "id": 3756,
-    "problem_id": 3670,
-    "problem": "line B E, line B D, line A B C, line B E, line B D, line A B C\nm \\angle 14 = x+25, m \\angle 15 = 4x+50, m \\angle 16 = x+45, find the measure of \\angle 14.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3670.jpg"
-  },
-  {
-    "id": 3757,
-    "problem_id": 3671,
-    "problem": "line G F, line D A, line D C, line A B, line C B, line E F, line H G, line H E, line G F, line D A, line D C, line A B, line C B, line E F, line H G, line H E\n\\parallelogram ABCD \\sim \\parallelogram EFGH. Find the scale factor of \\parallelogram ABCD to \\parallelogram EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3671.jpg"
-  },
-  {
-    "id": 3758,
-    "problem_id": 3672,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3672.jpg"
-  },
-  {
-    "id": 3759,
-    "problem_id": 3673,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3673.jpg"
-  },
-  {
-    "id": 3761,
-    "problem_id": 3674,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3674.jpg"
-  },
-  {
-    "id": 3762,
-    "problem_id": 3675,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the length of DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3675.jpg"
-  },
-  {
-    "id": 3763,
-    "problem_id": 3676,
-    "problem": "line B C D, line F G H, line E C A, line E G I, line B C D, line F G H, line E C A, line E G I\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3676.jpg"
-  },
-  {
-    "id": 3764,
-    "problem_id": 3677,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3677.jpg"
-  },
-  {
-    "id": 3765,
-    "problem_id": 3678,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3678.jpg"
-  },
-  {
-    "id": 3766,
-    "problem_id": 3679,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3679.jpg"
-  },
-  {
-    "id": 3767,
-    "problem_id": 3680,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3680.jpg"
-  },
-  {
-    "id": 3769,
-    "problem_id": 3681,
-    "problem": "line D A B E, line F C B, \\odot G lieson B C, line D A B E, line F C B, \\odot G lieson B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3681.jpg"
-  },
-  {
-    "id": 3770,
-    "problem_id": 3682,
-    "problem": "line D A B E, line F C B, \\odot G lieson B C, line D A B E, line F C B, \\odot G lieson B C\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3682.jpg"
-  },
-  {
-    "id": 3771,
-    "problem_id": 3683,
-    "problem": "line D E, line A C D, line A B, line B E, line C E, line D E, line A C D, line A B, line B E, line C E\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3683.jpg"
-  },
-  {
-    "id": 3772,
-    "problem_id": 3684,
-    "problem": "line D E, line A C D, line A B, line B E, line C E, line D E, line A C D, line A B, line B E, line C E\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3684.jpg"
-  },
-  {
-    "id": 3773,
-    "problem_id": 3685,
-    "problem": "line S P Q, line T P R, line U P, \\odot P lieson U T S R Q, line S P Q, line T P R, line U P, \\odot P lieson U T S R Q\nFind m \\widehat SU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3685.jpg"
-  },
-  {
-    "id": 3774,
-    "problem_id": 3686,
-    "problem": "line R T, line U T, line R S, line R U, line S T, line R T, line U T, line R S, line R U, line S T\n\\triangle RST \\cong \\triangle TUR, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3686.jpg"
-  },
-  {
-    "id": 3775,
-    "problem_id": 3687,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3687.jpg"
-  },
-  {
-    "id": 3776,
-    "problem_id": 3688,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3688.jpg"
-  },
-  {
-    "id": 3777,
-    "problem_id": 3689,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3689.jpg"
-  },
-  {
-    "id": 3778,
-    "problem_id": 3690,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3690.jpg"
-  },
-  {
-    "id": 3779,
-    "problem_id": 3691,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3691.jpg"
-  },
-  {
-    "id": 3780,
-    "problem_id": 3692,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3692.jpg"
-  },
-  {
-    "id": 3781,
-    "problem_id": 3693,
-    "problem": "line W X, line X A Y, \\odot A lieson W Y X, line W X, line X A Y, \\odot A lieson W Y X\nFind m \\widehat WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3693.jpg"
-  },
-  {
-    "id": 3782,
-    "problem_id": 3694,
-    "problem": "line W X, line X A Y, \\odot A lieson W Y X, line W X, line X A Y, \\odot A lieson W Y X\nFind m \\widehat WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3694.jpg"
-  },
-  {
-    "id": 3783,
-    "problem_id": 3695,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3695.jpg"
-  },
-  {
-    "id": 3784,
-    "problem_id": 3696,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3696.jpg"
-  },
-  {
-    "id": 3785,
-    "problem_id": 3697,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3697.jpg"
-  },
-  {
-    "id": 3786,
-    "problem_id": 3698,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3698.jpg"
-  },
-  {
-    "id": 3787,
-    "problem_id": 3699,
-    "problem": "line D C A, line A B, line C B, line D B, line D C A, line A B, line C B, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3699.jpg"
-  },
-  {
-    "id": 3788,
-    "problem_id": 3700,
-    "problem": "line D C A, line A B, line C B, line D B, line D C A, line A B, line C B, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3700.jpg"
-  },
-  {
-    "id": 3789,
-    "problem_id": 3701,
-    "problem": "line D C A, line A B, line C B, line D B, line D C A, line A B, line C B, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3701.jpg"
-  },
-  {
-    "id": 3790,
-    "problem_id": 3702,
-    "problem": "line D C A, line A B, line C B, line D B, line D C A, line A B, line C B, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3702.jpg"
-  },
-  {
-    "id": 3791,
-    "problem_id": 3703,
-    "problem": "line A C, line C B, line A D B, \\odot D lieson A C B, line A C, line C B, line A D B, \\odot D lieson A C B\nAB is a diameter, AC = 8 inches, and BC = 15 inches. Find the diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3703.jpg"
-  },
-  {
-    "id": 3792,
-    "problem_id": 3704,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3704.jpg"
-  },
-  {
-    "id": 3793,
-    "problem_id": 3705,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3705.jpg"
-  },
-  {
-    "id": 3794,
-    "problem_id": 3706,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3706.jpg"
-  },
-  {
-    "id": 3795,
-    "problem_id": 3707,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3707.jpg"
-  },
-  {
-    "id": 3796,
-    "problem_id": 3708,
-    "problem": "line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G, line B G F, line F E, line C D E, line B A C, \\odot H lieson A D G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3708.jpg"
-  },
-  {
-    "id": 3797,
-    "problem_id": 3709,
-    "problem": "line A C, line C B, line A B, \\odot O lieson A B C, line A C, line C B, line A B, \\odot O lieson A B C\nFind m \\widehat AB for \\odot O.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3709.jpg"
-  },
-  {
-    "id": 3798,
-    "problem_id": 3710,
-    "problem": "line C D, line A D, line E A, line C E, line C B A, line F B D, line C D, line A D, line E A, line C E, line C B A, line F B D\nDB \\perp AC and BA = BC. Find BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3710.jpg"
-  },
-  {
-    "id": 3799,
-    "problem_id": 3711,
-    "problem": "line C D, line A D, line E A, line C E, line C B A, line F B D, line C D, line A D, line E A, line C E, line C B A, line F B D\nDB \\perp AC and BA = BC. Find BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3711.jpg"
-  },
-  {
-    "id": 3800,
-    "problem_id": 3712,
-    "problem": "line l lieson A E F, line B E, line C D E, \\odot D lieson B C E, line l lieson A E F, line B E, line C D E, \\odot D lieson B C E\nSolve for a. Line l is the tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3712.jpg"
-  },
-  {
-    "id": 3801,
-    "problem_id": 3713,
-    "problem": "line A D, line D C, line D E, line B E C, line A B, line A D, line D C, line D E, line B E C, line A B\nFind the area of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3713.jpg"
-  },
-  {
-    "id": 3803,
-    "problem_id": 3714,
-    "problem": "line A D, line D C, line D E, line B E C, line A B, line A D, line D C, line D E, line B E C, line A B\nFind the area of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3714.jpg"
-  },
-  {
-    "id": 3804,
-    "problem_id": 3715,
-    "problem": "line D E C, line A E B, \\odot F lieson D B C A, line D E C, line A E B, \\odot F lieson D B C A\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3715.jpg"
-  },
-  {
-    "id": 3805,
-    "problem_id": 3716,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nFind m \\angle QRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3716.jpg"
-  },
-  {
-    "id": 3806,
-    "problem_id": 3717,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nFind m \\angle QRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3717.jpg"
-  },
-  {
-    "id": 3807,
-    "problem_id": 3718,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nFind KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3718.jpg"
-  },
-  {
-    "id": 3808,
-    "problem_id": 3719,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nFind KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3719.jpg"
-  },
-  {
-    "id": 3809,
-    "problem_id": 3720,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nFind KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3720.jpg"
-  },
-  {
-    "id": 3810,
-    "problem_id": 3721,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nFind KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3721.jpg"
-  },
-  {
-    "id": 3811,
-    "problem_id": 3722,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nFind KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3722.jpg"
-  },
-  {
-    "id": 3812,
-    "problem_id": 3723,
-    "problem": "line J L, line J K, line K L, line J L, line J K, line K L\nFind KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3723.jpg"
-  },
-  {
-    "id": 3813,
-    "problem_id": 3724,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3724.jpg"
-  },
-  {
-    "id": 3814,
-    "problem_id": 3725,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3725.jpg"
-  },
-  {
-    "id": 3815,
-    "problem_id": 3726,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3726.jpg"
-  },
-  {
-    "id": 3816,
-    "problem_id": 3727,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3727.jpg"
-  },
-  {
-    "id": 3817,
-    "problem_id": 3728,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3728.jpg"
-  },
-  {
-    "id": 3818,
-    "problem_id": 3729,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3729.jpg"
-  },
-  {
-    "id": 3819,
-    "problem_id": 3730,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3730.jpg"
-  },
-  {
-    "id": 3820,
-    "problem_id": 3731,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3731.jpg"
-  },
-  {
-    "id": 3821,
-    "problem_id": 3732,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3732.jpg"
-  },
-  {
-    "id": 3822,
-    "problem_id": 3733,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3733.jpg"
-  },
-  {
-    "id": 3823,
-    "problem_id": 3734,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3734.jpg"
-  },
-  {
-    "id": 3824,
-    "problem_id": 3735,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3735.jpg"
-  },
-  {
-    "id": 3825,
-    "problem_id": 3736,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3736.jpg"
-  },
-  {
-    "id": 3826,
-    "problem_id": 3737,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3737.jpg"
-  },
-  {
-    "id": 3827,
-    "problem_id": 3738,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3738.jpg"
-  },
-  {
-    "id": 3829,
-    "problem_id": 3739,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3739.jpg"
-  },
-  {
-    "id": 3830,
-    "problem_id": 3740,
-    "problem": "line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E, line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E\nFind the area of the shaded figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3740.jpg"
-  },
-  {
-    "id": 3831,
-    "problem_id": 3741,
-    "problem": "line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E, line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E\nFind the area of the shaded figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3741.jpg"
-  },
-  {
-    "id": 3832,
-    "problem_id": 3742,
-    "problem": "line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E, line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E\nFind the area of the shaded figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3742.jpg"
-  },
-  {
-    "id": 3833,
-    "problem_id": 3743,
-    "problem": "line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E, line A B, line G H, line B H, line A G, line C D, line E F, line D F, line C E\nFind the area of the shaded figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3743.jpg"
-  },
-  {
-    "id": 3834,
-    "problem_id": 3744,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3744.jpg"
-  },
-  {
-    "id": 3835,
-    "problem_id": 3745,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3745.jpg"
-  },
-  {
-    "id": 3836,
-    "problem_id": 3746,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3746.jpg"
-  },
-  {
-    "id": 3837,
-    "problem_id": 3747,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3747.jpg"
-  },
-  {
-    "id": 3838,
-    "problem_id": 3748,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3748.jpg"
-  },
-  {
-    "id": 3839,
-    "problem_id": 3749,
-    "problem": "line A B C, line E A, line E D, line D C, line E B, line A B C, line E A, line E D, line D C, line E B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3749.jpg"
-  },
-  {
-    "id": 3840,
-    "problem_id": 3750,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3750.jpg"
-  },
-  {
-    "id": 3841,
-    "problem_id": 3751,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3751.jpg"
-  },
-  {
-    "id": 3842,
-    "problem_id": 3752,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3752.jpg"
-  },
-  {
-    "id": 3843,
-    "problem_id": 3753,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3753.jpg"
-  },
-  {
-    "id": 3844,
-    "problem_id": 3754,
-    "problem": "line P Q, line S P, line R Q, line S R, line P Q, line S P, line R Q, line S R\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3754.jpg"
-  },
-  {
-    "id": 3845,
-    "problem_id": 3755,
-    "problem": "line A C, line B A, line A D, line A C, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3755.jpg"
-  },
-  {
-    "id": 3846,
-    "problem_id": 3756,
-    "problem": "line A C, line B A, line A D, line A C, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3756.jpg"
-  },
-  {
-    "id": 3847,
-    "problem_id": 3757,
-    "problem": "line A C, line B A, line A D, line A C, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3757.jpg"
-  },
-  {
-    "id": 3848,
-    "problem_id": 3758,
-    "problem": "line A C, line B A, line A D, line A C, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3758.jpg"
-  },
-  {
-    "id": 3849,
-    "problem_id": 3759,
-    "problem": "line A C, line B A, line A D, line A C, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3759.jpg"
-  },
-  {
-    "id": 3850,
-    "problem_id": 3760,
-    "problem": "line E C A, line E B, line A B, line D A, line D C B, line D E, line E C A, line E B, line A B, line D A, line D C B, line D E\nFind the value of variable u in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3760.jpg"
-  },
-  {
-    "id": 3851,
-    "problem_id": 3761,
-    "problem": "line E C A, line E B, line A B, line D A, line D C B, line D E, line E C A, line E B, line A B, line D A, line D C B, line D E\nFind the value of variable u in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3761.jpg"
-  },
-  {
-    "id": 3852,
-    "problem_id": 3762,
-    "problem": "line E C A, line E B, line A B, line D A, line D C B, line D E, line E C A, line E B, line A B, line D A, line D C B, line D E\nFind the value of variable u in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3762.jpg"
-  },
-  {
-    "id": 3853,
-    "problem_id": 3763,
-    "problem": "line E C A, line E B, line A B, line D A, line D C B, line D E, line E C A, line E B, line A B, line D A, line D C B, line D E\nFind the value of variable u in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3763.jpg"
-  },
-  {
-    "id": 3854,
-    "problem_id": 3764,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nWhat is the value of \\tan x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3764.jpg"
-  },
-  {
-    "id": 3855,
-    "problem_id": 3765,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nWhat is the value of \\tan x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3765.jpg"
-  },
-  {
-    "id": 3856,
-    "problem_id": 3766,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nWhat is the value of \\tan x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3766.jpg"
-  },
-  {
-    "id": 3857,
-    "problem_id": 3767,
-    "problem": "line P K L R, line P J I H Q, line Q G R, line n lieson A J T G D, line l lieson C H T K F, line m lieson B I T L E, line P T, line T R, line T Q, line P K L R, line P J I H Q, line Q G R, line n lieson A J T G D, line l lieson C H T K F, line m lieson B I T L E, line P T, line T R, line T Q\nLines l, m, and n are perpendicular bisectors of \\triangle PQR and meet at T. If TQ = 2x, PT = 3y-1, and TR = 8, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3767.jpg"
-  },
-  {
-    "id": 3858,
-    "problem_id": 3768,
-    "problem": "line C N, line E F, line E N, line D N F, \\odot N lieson D C F E, line C N, line E F, line E N, line D N F, \\odot N lieson D C F E\nIf CN = 8. Find NF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3768.jpg"
-  },
-  {
-    "id": 3859,
-    "problem_id": 3769,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3769.jpg"
-  },
-  {
-    "id": 3860,
-    "problem_id": 3770,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3770.jpg"
-  },
-  {
-    "id": 3861,
-    "problem_id": 3771,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3771.jpg"
-  },
-  {
-    "id": 3862,
-    "problem_id": 3772,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3772.jpg"
-  },
-  {
-    "id": 3863,
-    "problem_id": 3773,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3773.jpg"
-  },
-  {
-    "id": 3864,
-    "problem_id": 3774,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3774.jpg"
-  },
-  {
-    "id": 3865,
-    "problem_id": 3775,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3775.jpg"
-  },
-  {
-    "id": 3866,
-    "problem_id": 3776,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3776.jpg"
-  },
-  {
-    "id": 3867,
-    "problem_id": 3777,
-    "problem": "line E G H, line D H, line A E, line A B C D, line F G, line C F, line B F, line E G H, line D H, line A E, line A B C D, line F G, line C F, line B F\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3777.jpg"
-  },
-  {
-    "id": 3868,
-    "problem_id": 3778,
-    "problem": "line E G H, line D H, line A E, line A B C D, line F G, line C F, line B F, line E G H, line D H, line A E, line A B C D, line F G, line C F, line B F\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3778.jpg"
-  },
-  {
-    "id": 3869,
-    "problem_id": 3779,
-    "problem": "line E G H, line D H, line A E, line A B C D, line F G, line C F, line B F, line E G H, line D H, line A E, line A B C D, line F G, line C F, line B F\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3779.jpg"
-  },
-  {
-    "id": 3870,
-    "problem_id": 3780,
-    "problem": "line H A G, line H E, line E F, line G F, line E A, line H A G, line H E, line E F, line G F, line E A\nFind the area of \\parallelogram EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3780.jpg"
-  },
-  {
-    "id": 3871,
-    "problem_id": 3781,
-    "problem": "line H A G, line H E, line E F, line G F, line E A, line H A G, line H E, line E F, line G F, line E A\nFind the area of \\parallelogram EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3781.jpg"
-  },
-  {
-    "id": 3872,
-    "problem_id": 3782,
-    "problem": "line H A G, line H E, line E F, line G F, line E A, line H A G, line H E, line E F, line G F, line E A\nFind the area of \\parallelogram EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3782.jpg"
-  },
-  {
-    "id": 3873,
-    "problem_id": 3783,
-    "problem": "line H A G, line H E, line E F, line G F, line E A, line H A G, line H E, line E F, line G F, line E A\nFind the area of \\parallelogram EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3783.jpg"
-  },
-  {
-    "id": 3874,
-    "problem_id": 3784,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3784.jpg"
-  },
-  {
-    "id": 3875,
-    "problem_id": 3785,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3785.jpg"
-  },
-  {
-    "id": 3876,
-    "problem_id": 3786,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3786.jpg"
-  },
-  {
-    "id": 3877,
-    "problem_id": 3787,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3787.jpg"
-  },
-  {
-    "id": 3878,
-    "problem_id": 3788,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the length of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3788.jpg"
-  },
-  {
-    "id": 3879,
-    "problem_id": 3789,
-    "problem": "line D E, line A B, line F E, line C B, line D F, line A C, line D E, line A B, line F E, line C B, line D F, line A C\nDetermine y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3789.jpg"
-  },
-  {
-    "id": 3880,
-    "problem_id": 3790,
-    "problem": "line D E, line A B, line F E, line C B, line D F, line A C, line D E, line A B, line F E, line C B, line D F, line A C\nDetermine y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3790.jpg"
-  },
-  {
-    "id": 3881,
-    "problem_id": 3791,
-    "problem": "line D E, line A B, line F E, line C B, line D F, line A C, line D E, line A B, line F E, line C B, line D F, line A C\nDetermine y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3791.jpg"
-  },
-  {
-    "id": 3882,
-    "problem_id": 3792,
-    "problem": "line D E, line A B, line F E, line C B, line D F, line A C, line D E, line A B, line F E, line C B, line D F, line A C\nDetermine y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3792.jpg"
-  },
-  {
-    "id": 3883,
-    "problem_id": 3793,
-    "problem": "line D E, line A B, line F E, line C B, line D F, line A C, line D E, line A B, line F E, line C B, line D F, line A C\nDetermine y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3793.jpg"
-  },
-  {
-    "id": 3884,
-    "problem_id": 3794,
-    "problem": "line D E, line A B, line F E, line C B, line D F, line A C, line D E, line A B, line F E, line C B, line D F, line A C\nDetermine y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3794.jpg"
-  },
-  {
-    "id": 3885,
-    "problem_id": 3795,
-    "problem": "line A E B, line B F C, line A G C, line A D F, line E D C, line B D G, line A E B, line B F C, line A G C, line A D F, line E D C, line B D G\nGiven that D is the centroid of \\triangle ABC, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3795.jpg"
-  },
-  {
-    "id": 3886,
-    "problem_id": 3796,
-    "problem": "line A E B, line B F C, line A G C, line A D F, line E D C, line B D G, line A E B, line B F C, line A G C, line A D F, line E D C, line B D G\nGiven that D is the centroid of \\triangle ABC, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3796.jpg"
-  },
-  {
-    "id": 3887,
-    "problem_id": 3797,
-    "problem": "line A E B, line B F C, line A G C, line A D F, line E D C, line B D G, line A E B, line B F C, line A G C, line A D F, line E D C, line B D G\nGiven that D is the centroid of \\triangle ABC, find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3797.jpg"
-  },
-  {
-    "id": 3888,
-    "problem_id": 3798,
-    "problem": "line E H, line F G, line F E, line G H, line E H, line F G, line F E, line G H\nEFGH is a parallelogram. Find w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3798.jpg"
-  },
-  {
-    "id": 3889,
-    "problem_id": 3799,
-    "problem": "line P Q, line S R, line P S, line Q R, line P Q, line S R, line P S, line Q R\nFor what value of y must PQRS be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3799.jpg"
-  },
-  {
-    "id": 3890,
-    "problem_id": 3800,
-    "problem": "line P Q, line S R, line P S, line Q R, line P Q, line S R, line P S, line Q R\nFor what value of y must PQRS be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3800.jpg"
-  },
-  {
-    "id": 3891,
-    "problem_id": 3801,
-    "problem": "line P Q, line S R, line P S, line Q R, line P Q, line S R, line P S, line Q R\nFor what value of y must PQRS be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3801.jpg"
-  },
-  {
-    "id": 3892,
-    "problem_id": 3802,
-    "problem": "line P Q, line S R, line P S, line Q R, line P Q, line S R, line P S, line Q R\nFor what value of y must PQRS be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3802.jpg"
-  },
-  {
-    "id": 3893,
-    "problem_id": 3803,
-    "problem": "line D A, line A B, line B E, line D E, line D C B, \\odot C lieson D E B A, line D A, line A B, line B E, line D E, line D C B, \\odot C lieson D E B A\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3803.jpg"
-  },
-  {
-    "id": 3894,
-    "problem_id": 3804,
-    "problem": "line D A, line A B, line B E, line D E, line D C B, \\odot C lieson D E B A, line D A, line A B, line B E, line D E, line D C B, \\odot C lieson D E B A\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3804.jpg"
-  },
-  {
-    "id": 3895,
-    "problem_id": 3805,
-    "problem": "line D A, line A B, line B E, line D E, line D C B, \\odot C lieson D E B A, line D A, line A B, line B E, line D E, line D C B, \\odot C lieson D E B A\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3805.jpg"
-  },
-  {
-    "id": 3896,
-    "problem_id": 3806,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3806.jpg"
-  },
-  {
-    "id": 3897,
-    "problem_id": 3807,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3807.jpg"
-  },
-  {
-    "id": 3898,
-    "problem_id": 3808,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3808.jpg"
-  },
-  {
-    "id": 3899,
-    "problem_id": 3809,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3809.jpg"
-  },
-  {
-    "id": 3900,
-    "problem_id": 3810,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3810.jpg"
-  },
-  {
-    "id": 3901,
-    "problem_id": 3811,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3811.jpg"
-  },
-  {
-    "id": 3902,
-    "problem_id": 3812,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3812.jpg"
-  },
-  {
-    "id": 3903,
-    "problem_id": 3813,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3813.jpg"
-  },
-  {
-    "id": 3904,
-    "problem_id": 3814,
-    "problem": "line B C, line B A, line A C, line C D, line A D, line B C, line B A, line A C, line C D, line A D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3814.jpg"
-  },
-  {
-    "id": 3905,
-    "problem_id": 3815,
-    "problem": "line B C, line B A, line A C, line C D, line A D, line B C, line B A, line A C, line C D, line A D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3815.jpg"
-  },
-  {
-    "id": 3906,
-    "problem_id": 3816,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle A of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3816.jpg"
-  },
-  {
-    "id": 3908,
-    "problem_id": 3817,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle A of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3817.jpg"
-  },
-  {
-    "id": 3909,
-    "problem_id": 3818,
-    "problem": "line L M, line J L, line J M, line T S, line S Q, line T Q, line L M, line J L, line J M, line T S, line S Q, line T Q\nFind y if \\triangle JLM \\sim \\triangle QST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3818.jpg"
-  },
-  {
-    "id": 3910,
-    "problem_id": 3819,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3819.jpg"
-  },
-  {
-    "id": 3911,
-    "problem_id": 3820,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3820.jpg"
-  },
-  {
-    "id": 3912,
-    "problem_id": 3821,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3821.jpg"
-  },
-  {
-    "id": 3913,
-    "problem_id": 3822,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3822.jpg"
-  },
-  {
-    "id": 3914,
-    "problem_id": 3823,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3823.jpg"
-  },
-  {
-    "id": 3915,
-    "problem_id": 3824,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3824.jpg"
-  },
-  {
-    "id": 3916,
-    "problem_id": 3825,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3825.jpg"
-  },
-  {
-    "id": 3917,
-    "problem_id": 3826,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3826.jpg"
-  },
-  {
-    "id": 3918,
-    "problem_id": 3827,
-    "problem": "line A C E, line D C B, line D E, line A B, line A C E, line D C B, line D E, line A B\nEach pair of polygons is similar. Find DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3827.jpg"
-  },
-  {
-    "id": 3919,
-    "problem_id": 3828,
-    "problem": "line A C E, line D C B, line D E, line A B, line A C E, line D C B, line D E, line A B\nEach pair of polygons is similar. Find DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3828.jpg"
-  },
-  {
-    "id": 3920,
-    "problem_id": 3829,
-    "problem": "line A C E, line D C B, line D E, line A B, line A C E, line D C B, line D E, line A B\nEach pair of polygons is similar. Find DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3829.jpg"
-  },
-  {
-    "id": 3921,
-    "problem_id": 3830,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3830.jpg"
-  },
-  {
-    "id": 3922,
-    "problem_id": 3831,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3831.jpg"
-  },
-  {
-    "id": 3923,
-    "problem_id": 3832,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3832.jpg"
-  },
-  {
-    "id": 3924,
-    "problem_id": 3833,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3833.jpg"
-  },
-  {
-    "id": 3925,
-    "problem_id": 3834,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3834.jpg"
-  },
-  {
-    "id": 3926,
-    "problem_id": 3835,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3835.jpg"
-  },
-  {
-    "id": 3927,
-    "problem_id": 3836,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3836.jpg"
-  },
-  {
-    "id": 3928,
-    "problem_id": 3837,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3837.jpg"
-  },
-  {
-    "id": 3929,
-    "problem_id": 3838,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3838.jpg"
-  },
-  {
-    "id": 3930,
-    "problem_id": 3839,
-    "problem": "line D C B, line A D, line A B, line A C, line D C B, line A D, line A B, line A C\nFind m \\angle CAB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3839.jpg"
-  },
-  {
-    "id": 3931,
-    "problem_id": 3840,
-    "problem": "line E A B, line D B, \\odot F lieson C B D, line E A B, line D B, \\odot F lieson C B D\nFind m \\angle ABD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3840.jpg"
-  },
-  {
-    "id": 3932,
-    "problem_id": 3841,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the perimeter of figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3841.jpg"
-  },
-  {
-    "id": 3933,
-    "problem_id": 3842,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the perimeter of figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3842.jpg"
-  },
-  {
-    "id": 3934,
-    "problem_id": 3843,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind the perimeter of figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3843.jpg"
-  },
-  {
-    "id": 3935,
-    "problem_id": 3844,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3844.jpg"
-  },
-  {
-    "id": 3936,
-    "problem_id": 3845,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3845.jpg"
-  },
-  {
-    "id": 3937,
-    "problem_id": 3846,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3846.jpg"
-  },
-  {
-    "id": 3938,
-    "problem_id": 3847,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3847.jpg"
-  },
-  {
-    "id": 3939,
-    "problem_id": 3848,
-    "problem": "line G E, line F G, line B F, line B A, line A C, line C E, line D E, line G E, line F G, line B F, line B A, line A C, line C E, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3848.jpg"
-  },
-  {
-    "id": 3940,
-    "problem_id": 3849,
-    "problem": "line G E, line F G, line B F, line B A, line A C, line C E, line D E, line G E, line F G, line B F, line B A, line A C, line C E, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3849.jpg"
-  },
-  {
-    "id": 3942,
-    "problem_id": 3850,
-    "problem": "line G E, line F G, line B F, line B A, line A C, line C E, line D E, line G E, line F G, line B F, line B A, line A C, line C E, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3850.jpg"
-  },
-  {
-    "id": 3943,
-    "problem_id": 3851,
-    "problem": "line G E, line F G, line B F, line B A, line A C, line C E, line D E, line G E, line F G, line B F, line B A, line A C, line C E, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3851.jpg"
-  },
-  {
-    "id": 3944,
-    "problem_id": 3852,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3852.jpg"
-  },
-  {
-    "id": 3945,
-    "problem_id": 3853,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3853.jpg"
-  },
-  {
-    "id": 3946,
-    "problem_id": 3854,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3854.jpg"
-  },
-  {
-    "id": 3947,
-    "problem_id": 3855,
-    "problem": "line E D, line B A D, line E A C, line B C, line E D, line B A D, line E A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3855.jpg"
-  },
-  {
-    "id": 3948,
-    "problem_id": 3856,
-    "problem": "line E D, line B A D, line E A C, line B C, line E D, line B A D, line E A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3856.jpg"
-  },
-  {
-    "id": 3949,
-    "problem_id": 3857,
-    "problem": "line E D, line B A D, line E A C, line B C, line E D, line B A D, line E A C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3857.jpg"
-  },
-  {
-    "id": 3950,
-    "problem_id": 3858,
-    "problem": "line G P H, line G R J, line H Q J, line P Q, line P R, line G P H, line G R J, line H Q J, line P Q, line P R\nFind m \\angle PQJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3858.jpg"
-  },
-  {
-    "id": 3951,
-    "problem_id": 3859,
-    "problem": "line B A, line A D, line E D, line B E, \\odot C lieson B E D A, line B A, line A D, line E D, line B E, \\odot C lieson B E D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3859.jpg"
-  },
-  {
-    "id": 3952,
-    "problem_id": 3860,
-    "problem": "line B A, line A D, line E D, line B E, \\odot C lieson B E D A, line B A, line A D, line E D, line B E, \\odot C lieson B E D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3860.jpg"
-  },
-  {
-    "id": 3953,
-    "problem_id": 3861,
-    "problem": "line B A, line A D, line E D, line B E, \\odot C lieson B E D A, line B A, line A D, line E D, line B E, \\odot C lieson B E D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3861.jpg"
-  },
-  {
-    "id": 3954,
-    "problem_id": 3862,
-    "problem": "line B A, line A D, line E D, line B E, \\odot C lieson B E D A, line B A, line A D, line E D, line B E, \\odot C lieson B E D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3862.jpg"
-  },
-  {
-    "id": 3955,
-    "problem_id": 3863,
-    "problem": "line B A, line A D, line E D, line B E, \\odot C lieson B E D A, line B A, line A D, line E D, line B E, \\odot C lieson B E D A\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3863.jpg"
-  },
-  {
-    "id": 3956,
-    "problem_id": 3864,
-    "problem": "line A D, line A B, line B C, line D F C, line D E, line E F, \\odot E lieson A D C B, line A D, line A B, line B C, line D F C, line D E, line E F, \\odot E lieson A D C B\nFind the perimeter of the inscribed regular polygon shown.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3864.jpg"
-  },
-  {
-    "id": 3957,
-    "problem_id": 3865,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3865.jpg"
-  },
-  {
-    "id": 3958,
-    "problem_id": 3866,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3866.jpg"
-  },
-  {
-    "id": 3959,
-    "problem_id": 3867,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3867.jpg"
-  },
-  {
-    "id": 3960,
-    "problem_id": 3868,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3868.jpg"
-  },
-  {
-    "id": 3961,
-    "problem_id": 3869,
-    "problem": "line B C, line F G, line A C, line F H, line A B, line H G, line B C, line F G, line A C, line F H, line A B, line H G\nWhat is the measure of \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3869.jpg"
-  },
-  {
-    "id": 3962,
-    "problem_id": 3870,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3870.jpg"
-  },
-  {
-    "id": 3963,
-    "problem_id": 3871,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3871.jpg"
-  },
-  {
-    "id": 3964,
-    "problem_id": 3872,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3872.jpg"
-  },
-  {
-    "id": 3965,
-    "problem_id": 3873,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3873.jpg"
-  },
-  {
-    "id": 3966,
-    "problem_id": 3874,
-    "problem": "line D A, line A B, line C B, line D C, line D B, line D A, line A B, line C B, line D C, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3874.jpg"
-  },
-  {
-    "id": 3967,
-    "problem_id": 3875,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3875.jpg"
-  },
-  {
-    "id": 3968,
-    "problem_id": 3876,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3876.jpg"
-  },
-  {
-    "id": 3969,
-    "problem_id": 3877,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3877.jpg"
-  },
-  {
-    "id": 3970,
-    "problem_id": 3878,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle C?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3878.jpg"
-  },
-  {
-    "id": 3971,
-    "problem_id": 3879,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3879.jpg"
-  },
-  {
-    "id": 3972,
-    "problem_id": 3880,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3880.jpg"
-  },
-  {
-    "id": 3973,
-    "problem_id": 3881,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3881.jpg"
-  },
-  {
-    "id": 3974,
-    "problem_id": 3882,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3882.jpg"
-  },
-  {
-    "id": 3975,
-    "problem_id": 3883,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find KL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3883.jpg"
-  },
-  {
-    "id": 3976,
-    "problem_id": 3884,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nSolve for w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3884.jpg"
-  },
-  {
-    "id": 3977,
-    "problem_id": 3885,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nSolve for w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3885.jpg"
-  },
-  {
-    "id": 3978,
-    "problem_id": 3886,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nSolve for w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3886.jpg"
-  },
-  {
-    "id": 3979,
-    "problem_id": 3887,
-    "problem": "line G F E, line C A E, line B D E, line D A, line A F, line G F E, line C A E, line B D E, line D A, line A F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3887.jpg"
-  },
-  {
-    "id": 3980,
-    "problem_id": 3888,
-    "problem": "line G F E, line C A E, line B D E, line D A, line A F, line G F E, line C A E, line B D E, line D A, line A F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3888.jpg"
-  },
-  {
-    "id": 3981,
-    "problem_id": 3889,
-    "problem": "line G F E, line C A E, line B D E, line D A, line A F, line G F E, line C A E, line B D E, line D A, line A F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3889.jpg"
-  },
-  {
-    "id": 3982,
-    "problem_id": 3890,
-    "problem": "line G F E, line C A E, line B D E, line D A, line A F, line G F E, line C A E, line B D E, line D A, line A F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3890.jpg"
-  },
-  {
-    "id": 3983,
-    "problem_id": 3891,
-    "problem": "line G F E, line C A E, line B D E, line D A, line A F, line G F E, line C A E, line B D E, line D A, line A F\nFind EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3891.jpg"
-  },
-  {
-    "id": 3984,
-    "problem_id": 3892,
-    "problem": "line K L, line N L, line K N, line N M, line M L, line J L, line K J, line K L, line N L, line K N, line N M, line M L, line J L, line K J\n\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle LKN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3892.jpg"
-  },
-  {
-    "id": 3985,
-    "problem_id": 3893,
-    "problem": "line K L, line N L, line K N, line N M, line M L, line J L, line K J, line K L, line N L, line K N, line N M, line M L, line J L, line K J\n\\triangle KLN and \\triangle LMN are isosceles and m \\angle JKN = 130. Find the measure of \\angle LKN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3893.jpg"
-  },
-  {
-    "id": 3986,
-    "problem_id": 3894,
-    "problem": "line Y G, line Y L, line L G, line A G, line Y A, line L A, line Y G, line Y L, line L G, line A G, line Y A, line L A\nPoint A is the incenter of \\triangle YLG. Find the measure of \\angle YAL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3894.jpg"
-  },
-  {
-    "id": 3987,
-    "problem_id": 3895,
-    "problem": "line Y G, line Y L, line L G, line A G, line Y A, line L A, line Y G, line Y L, line L G, line A G, line Y A, line L A\nPoint A is the incenter of \\triangle YLG. Find the measure of \\angle YAL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3895.jpg"
-  },
-  {
-    "id": 3988,
-    "problem_id": 3896,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3896.jpg"
-  },
-  {
-    "id": 3989,
-    "problem_id": 3897,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3897.jpg"
-  },
-  {
-    "id": 3990,
-    "problem_id": 3898,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3898.jpg"
-  },
-  {
-    "id": 3991,
-    "problem_id": 3899,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3899.jpg"
-  },
-  {
-    "id": 3992,
-    "problem_id": 3900,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3900.jpg"
-  },
-  {
-    "id": 3993,
-    "problem_id": 3901,
-    "problem": "line C R S D, line B R Q F, line A S E, line C R S D, line B R Q F, line A S E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3901.jpg"
-  },
-  {
-    "id": 3994,
-    "problem_id": 3902,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3902.jpg"
-  },
-  {
-    "id": 3995,
-    "problem_id": 3903,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3903.jpg"
-  },
-  {
-    "id": 3996,
-    "problem_id": 3904,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3904.jpg"
-  },
-  {
-    "id": 3997,
-    "problem_id": 3905,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3905.jpg"
-  },
-  {
-    "id": 3998,
-    "problem_id": 3906,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3906.jpg"
-  },
-  {
-    "id": 3999,
-    "problem_id": 3907,
-    "problem": "line Q T, line Q S, \\odot Q lieson T S, line Q T, line Q S, \\odot Q lieson T S\nFind the circumference of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3907.jpg"
-  },
-  {
-    "id": 4000,
-    "problem_id": 3908,
-    "problem": "line Q T, line Q S, \\odot Q lieson T S, line Q T, line Q S, \\odot Q lieson T S\nFind the circumference of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3908.jpg"
-  },
-  {
-    "id": 4001,
-    "problem_id": 3909,
-    "problem": "line T U V, line T U V\nU is the midpoint of TV. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3909.jpg"
-  },
-  {
-    "id": 4002,
-    "problem_id": 3910,
-    "problem": "line T U V, line T U V\nU is the midpoint of TV. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3910.jpg"
-  },
-  {
-    "id": 4003,
-    "problem_id": 3911,
-    "problem": "line A G B, line G E, line E F, line C F D, \\odot E lieson A B C D, line A G B, line G E, line E F, line C F D, \\odot E lieson A B C D\nIn \\odot E, EG = EF. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3911.jpg"
-  },
-  {
-    "id": 4004,
-    "problem_id": 3912,
-    "problem": "line A G B, line G E, line E F, line C F D, \\odot E lieson A B C D, line A G B, line G E, line E F, line C F D, \\odot E lieson A B C D\nIn \\odot E, EG = EF. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3912.jpg"
-  },
-  {
-    "id": 4005,
-    "problem_id": 3913,
-    "problem": "line A G B, line G E, line E F, line C F D, \\odot E lieson A B C D, line A G B, line G E, line E F, line C F D, \\odot E lieson A B C D\nIn \\odot E, EG = EF. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3913.jpg"
-  },
-  {
-    "id": 4006,
-    "problem_id": 3914,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3914.jpg"
-  },
-  {
-    "id": 4007,
-    "problem_id": 3915,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3915.jpg"
-  },
-  {
-    "id": 4008,
-    "problem_id": 3916,
-    "problem": "line B C, line B D, line C D, line A C, line A B, line B C, line B D, line C D, line A C, line A B\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3916.jpg"
-  },
-  {
-    "id": 4009,
-    "problem_id": 3917,
-    "problem": "line W Y B, line W Z C, line W X A, line Y X, line Z Y, line W Y B, line W Z C, line W X A, line Y X, line Z Y\nFind XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3917.jpg"
-  },
-  {
-    "id": 4010,
-    "problem_id": 3918,
-    "problem": "line W Y B, line W Z C, line W X A, line Y X, line Z Y, line W Y B, line W Z C, line W X A, line Y X, line Z Y\nFind XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3918.jpg"
-  },
-  {
-    "id": 4011,
-    "problem_id": 3919,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 3 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3919.jpg"
-  },
-  {
-    "id": 4012,
-    "problem_id": 3920,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 3 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3920.jpg"
-  },
-  {
-    "id": 4013,
-    "problem_id": 3921,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 3 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3921.jpg"
-  },
-  {
-    "id": 4014,
-    "problem_id": 3922,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 3 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3922.jpg"
-  },
-  {
-    "id": 4015,
-    "problem_id": 3923,
-    "problem": "line B C, line C D, line A D, line B A, line B C, line C D, line A D, line B A\nFind the measure of \\angle 3 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3923.jpg"
-  },
-  {
-    "id": 4016,
-    "problem_id": 3924,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3924.jpg"
-  },
-  {
-    "id": 4017,
-    "problem_id": 3925,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3925.jpg"
-  },
-  {
-    "id": 4018,
-    "problem_id": 3926,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3926.jpg"
-  },
-  {
-    "id": 4019,
-    "problem_id": 3927,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3927.jpg"
-  },
-  {
-    "id": 4020,
-    "problem_id": 3928,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3928.jpg"
-  },
-  {
-    "id": 4021,
-    "problem_id": 3929,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3929.jpg"
-  },
-  {
-    "id": 4022,
-    "problem_id": 3930,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3930.jpg"
-  },
-  {
-    "id": 4023,
-    "problem_id": 3931,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nGiven JK = JL. Solve for the length of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3931.jpg"
-  },
-  {
-    "id": 4024,
-    "problem_id": 3932,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nGiven JK = JL. Solve for the length of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3932.jpg"
-  },
-  {
-    "id": 4025,
-    "problem_id": 3933,
-    "problem": "line K J, line J L, line K L, line K J, line J L, line K L\nGiven JK = JL. Solve for the length of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3933.jpg"
-  },
-  {
-    "id": 4026,
-    "problem_id": 3934,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the measure of \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3934.jpg"
-  },
-  {
-    "id": 4027,
-    "problem_id": 3935,
-    "problem": "line F E, line E D, line F D, line F E, line E D, line F D\nSolve for the measure of \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3935.jpg"
-  },
-  {
-    "id": 4028,
-    "problem_id": 3936,
-    "problem": "line B E A, line B C, line A D, line C D, \\odot E lieson A B, line B E A, line B C, line A D, line C D, \\odot E lieson A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3936.jpg"
-  },
-  {
-    "id": 4029,
-    "problem_id": 3937,
-    "problem": "line B E A, line B C, line A D, line C D, \\odot E lieson A B, line B E A, line B C, line A D, line C D, \\odot E lieson A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3937.jpg"
-  },
-  {
-    "id": 4030,
-    "problem_id": 3938,
-    "problem": "line B E A, line B C, line A D, line C D, \\odot E lieson A B, line B E A, line B C, line A D, line C D, \\odot E lieson A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3938.jpg"
-  },
-  {
-    "id": 4031,
-    "problem_id": 3939,
-    "problem": "line B E A, line B C, line A D, line C D, \\odot E lieson A B, line B E A, line B C, line A D, line C D, \\odot E lieson A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3939.jpg"
-  },
-  {
-    "id": 4032,
-    "problem_id": 3940,
-    "problem": "line B E A, line B C, line A D, line C D, \\odot E lieson A B, line B E A, line B C, line A D, line C D, \\odot E lieson A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3940.jpg"
-  },
-  {
-    "id": 4033,
-    "problem_id": 3941,
-    "problem": "line P R, line S U, line Q R, line T U, line Q P, line T S, line P R, line S U, line Q R, line T U, line Q P, line T S\n\\triangle PQR \\cong \\triangle STU. Find m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3941.jpg"
-  },
-  {
-    "id": 4034,
-    "problem_id": 3942,
-    "problem": "line A B, line B D, line A C, line C D, line A B, line B D, line A C, line C D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3942.jpg"
-  },
-  {
-    "id": 4035,
-    "problem_id": 3943,
-    "problem": "line A B, line B D, line A C, line C D, line A B, line B D, line A C, line C D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3943.jpg"
-  },
-  {
-    "id": 4036,
-    "problem_id": 3944,
-    "problem": "line A B, line B D, line A C, line C D, line A B, line B D, line A C, line C D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3944.jpg"
-  },
-  {
-    "id": 4037,
-    "problem_id": 3945,
-    "problem": "line A B, line B D, line A C, line C D, line A B, line B D, line A C, line C D\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3945.jpg"
-  },
-  {
-    "id": 4038,
-    "problem_id": 3946,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3946.jpg"
-  },
-  {
-    "id": 4039,
-    "problem_id": 3947,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3947.jpg"
-  },
-  {
-    "id": 4040,
-    "problem_id": 3948,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3948.jpg"
-  },
-  {
-    "id": 4041,
-    "problem_id": 3949,
-    "problem": "line F G, line G H, \\odot G lieson F H, line F G, line G H, \\odot G lieson F H\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3949.jpg"
-  },
-  {
-    "id": 4042,
-    "problem_id": 3950,
-    "problem": "line E F, line C D, line A C E, line B D F, line A B, line E F, line C D, line A C E, line B D F, line A B\nDetermine n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3950.jpg"
-  },
-  {
-    "id": 4043,
-    "problem_id": 3951,
-    "problem": "line E F, line C D, line A C E, line B D F, line A B, line E F, line C D, line A C E, line B D F, line A B\nDetermine n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3951.jpg"
-  },
-  {
-    "id": 4044,
-    "problem_id": 3952,
-    "problem": "line E F, line C D, line A C E, line B D F, line A B, line E F, line C D, line A C E, line B D F, line A B\nDetermine n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3952.jpg"
-  },
-  {
-    "id": 4045,
-    "problem_id": 3953,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3953.jpg"
-  },
-  {
-    "id": 4046,
-    "problem_id": 3954,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3954.jpg"
-  },
-  {
-    "id": 4048,
-    "problem_id": 3955,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3955.jpg"
-  },
-  {
-    "id": 4049,
-    "problem_id": 3956,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3956.jpg"
-  },
-  {
-    "id": 4050,
-    "problem_id": 3957,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3957.jpg"
-  },
-  {
-    "id": 4051,
-    "problem_id": 3958,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3958.jpg"
-  },
-  {
-    "id": 4052,
-    "problem_id": 3959,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3959.jpg"
-  },
-  {
-    "id": 4053,
-    "problem_id": 3960,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3960.jpg"
-  },
-  {
-    "id": 4054,
-    "problem_id": 3961,
-    "problem": "line B A, line A D, line E D, line B E, line B C D, line A C E, line B A, line A D, line E D, line B E, line B C D, line A C E\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3961.jpg"
-  },
-  {
-    "id": 4055,
-    "problem_id": 3962,
-    "problem": "line B C D, line D E, line A C E, line A B, line B C D, line D E, line A C E, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3962.jpg"
-  },
-  {
-    "id": 4056,
-    "problem_id": 3963,
-    "problem": "line B C D, line D E, line A C E, line A B, line B C D, line D E, line A C E, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3963.jpg"
-  },
-  {
-    "id": 4057,
-    "problem_id": 3964,
-    "problem": "line B C D, line D E, line A C E, line A B, line B C D, line D E, line A C E, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3964.jpg"
-  },
-  {
-    "id": 4058,
-    "problem_id": 3965,
-    "problem": "line B C D, line D E, line A C E, line A B, line B C D, line D E, line A C E, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3965.jpg"
-  },
-  {
-    "id": 4059,
-    "problem_id": 3966,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3966.jpg"
-  },
-  {
-    "id": 4060,
-    "problem_id": 3967,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3967.jpg"
-  },
-  {
-    "id": 4061,
-    "problem_id": 3968,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3968.jpg"
-  },
-  {
-    "id": 4062,
-    "problem_id": 3969,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3969.jpg"
-  },
-  {
-    "id": 4063,
-    "problem_id": 3970,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3970.jpg"
-  },
-  {
-    "id": 4064,
-    "problem_id": 3971,
-    "problem": "line A D, line B F, line A B, line D E F, line C F, line C E, line A D, line B F, line A B, line D E F, line C F, line C E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3971.jpg"
-  },
-  {
-    "id": 4065,
-    "problem_id": 3972,
-    "problem": "line L J, line J K, line L K, line L J, line J K, line L K\nFind the measurement of \\angle LJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3972.jpg"
-  },
-  {
-    "id": 4066,
-    "problem_id": 3973,
-    "problem": "line L J, line J K, line L K, line L J, line J K, line L K\nFind the measurement of \\angle LJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3973.jpg"
-  },
-  {
-    "id": 4067,
-    "problem_id": 3974,
-    "problem": "line L J, line J K, line L K, line L J, line J K, line L K\nFind the measurement of \\angle LJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3974.jpg"
-  },
-  {
-    "id": 4068,
-    "problem_id": 3975,
-    "problem": "line L J, line J K, line L K, line L J, line J K, line L K\nFind the measurement of \\angle LJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3975.jpg"
-  },
-  {
-    "id": 4069,
-    "problem_id": 3976,
-    "problem": "line L J, line J K, line L K, line L J, line J K, line L K\nFind the measurement of \\angle LJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3976.jpg"
-  },
-  {
-    "id": 4070,
-    "problem_id": 3977,
-    "problem": "line L J, line J K, line L K, line L J, line J K, line L K\nFind the measurement of \\angle LJK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3977.jpg"
-  },
-  {
-    "id": 4071,
-    "problem_id": 3978,
-    "problem": "line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C, line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3978.jpg"
-  },
-  {
-    "id": 4072,
-    "problem_id": 3979,
-    "problem": "line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C, line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3979.jpg"
-  },
-  {
-    "id": 4073,
-    "problem_id": 3980,
-    "problem": "line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C, line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3980.jpg"
-  },
-  {
-    "id": 4074,
-    "problem_id": 3981,
-    "problem": "line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C, line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3981.jpg"
-  },
-  {
-    "id": 4075,
-    "problem_id": 3982,
-    "problem": "line R S, line S T, line R Q, line Q T, line R S, line S T, line R Q, line Q T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3982.jpg"
-  },
-  {
-    "id": 4076,
-    "problem_id": 3983,
-    "problem": "line R S, line S T, line R Q, line Q T, line R S, line S T, line R Q, line Q T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3983.jpg"
-  },
-  {
-    "id": 4078,
-    "problem_id": 3984,
-    "problem": "line G H, line F G A, line A B, line B C, line D C, line E D, line F E, line G H, line F G A, line A B, line B C, line D C, line E D, line F E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3984.jpg"
-  },
-  {
-    "id": 4079,
-    "problem_id": 3985,
-    "problem": "line B A E, line C A F, line A D, \\odot A lieson F E D C B, line B A E, line C A F, line A D, \\odot A lieson F E D C B\nWhat is m \\widehat DEB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3985.jpg"
-  },
-  {
-    "id": 4080,
-    "problem_id": 3986,
-    "problem": "line C T F, line P C, line C K R, line P R F, line P K T, line R T, line C T F, line P C, line C K R, line P R F, line P K T, line R T\nIf TK = 5, what is KP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3986.jpg"
-  },
-  {
-    "id": 4081,
-    "problem_id": 3987,
-    "problem": "line M H L, line K J L, line K P M, line P H, line J H, line P J, line M H L, line K J L, line K P M, line P H, line J H, line P J\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3987.jpg"
-  },
-  {
-    "id": 4082,
-    "problem_id": 3988,
-    "problem": "line M H L, line K J L, line K P M, line P H, line J H, line P J, line M H L, line K J L, line K P M, line P H, line J H, line P J\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3988.jpg"
-  },
-  {
-    "id": 4083,
-    "problem_id": 3989,
-    "problem": "line M H L, line K J L, line K P M, line P H, line J H, line P J, line M H L, line K J L, line K P M, line P H, line J H, line P J\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3989.jpg"
-  },
-  {
-    "id": 4084,
-    "problem_id": 3990,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3990.jpg"
-  },
-  {
-    "id": 4085,
-    "problem_id": 3991,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3991.jpg"
-  },
-  {
-    "id": 4086,
-    "problem_id": 3992,
-    "problem": "line E F G, line E F G\nIf EG = 59, what is EF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3992.jpg"
-  },
-  {
-    "id": 4087,
-    "problem_id": 3993,
-    "problem": "line G A P C H, line F B P D I, line P R E, line G A P C H, line F B P D I, line P R E\nFind the value of x so that AC and BD are perpendicular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3993.jpg"
-  },
-  {
-    "id": 4088,
-    "problem_id": 3994,
-    "problem": "line G A P C H, line F B P D I, line P R E, line G A P C H, line F B P D I, line P R E\nFind the value of x so that AC and BD are perpendicular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3994.jpg"
-  },
-  {
-    "id": 4089,
-    "problem_id": 3995,
-    "problem": "line G A P C H, line F B P D I, line P R E, line G A P C H, line F B P D I, line P R E\nFind the value of x so that AC and BD are perpendicular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3995.jpg"
-  },
-  {
-    "id": 4090,
-    "problem_id": 3996,
-    "problem": "line G A P C H, line F B P D I, line P R E, line G A P C H, line F B P D I, line P R E\nFind the value of x so that AC and BD are perpendicular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3996.jpg"
-  },
-  {
-    "id": 4091,
-    "problem_id": 3997,
-    "problem": "line G A P C H, line F B P D I, line P R E, line G A P C H, line F B P D I, line P R E\nFind the value of x so that AC and BD are perpendicular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3997.jpg"
-  },
-  {
-    "id": 4092,
-    "problem_id": 3998,
-    "problem": "line N M A, line N Q B, line N P C, line M Q, line Q P, line N M A, line N Q B, line N P C, line M Q, line Q P\nFind m \\angle PNM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3998.jpg"
-  },
-  {
-    "id": 4093,
-    "problem_id": 3999,
-    "problem": "line V T U A, line R S, line R V, line S T, line V T U A, line R S, line R V, line S T\nm \\angle RST = x+50, and m \\angle STU = 3x+20. Find m \\angle SRV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/3999.jpg"
-  },
-  {
-    "id": 4094,
-    "problem_id": 4000,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4000.jpg"
-  },
-  {
-    "id": 4095,
-    "problem_id": 4001,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4001.jpg"
-  },
-  {
-    "id": 4096,
-    "problem_id": 4002,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4002.jpg"
-  },
-  {
-    "id": 4097,
-    "problem_id": 4003,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4003.jpg"
-  },
-  {
-    "id": 4098,
-    "problem_id": 4004,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4004.jpg"
-  },
-  {
-    "id": 4099,
-    "problem_id": 4005,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4005.jpg"
-  },
-  {
-    "id": 4100,
-    "problem_id": 4006,
-    "problem": "line K M, line L M, line L K, line K M, line L M, line L K\nSolve for m \\angle L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4006.jpg"
-  },
-  {
-    "id": 4101,
-    "problem_id": 4007,
-    "problem": "line W S, line S R V, line W R T, line V T, line W S, line S R V, line W R T, line V T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4007.jpg"
-  },
-  {
-    "id": 4102,
-    "problem_id": 4008,
-    "problem": "line W S, line S R V, line W R T, line V T, line W S, line S R V, line W R T, line V T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4008.jpg"
-  },
-  {
-    "id": 4103,
-    "problem_id": 4009,
-    "problem": "line W S, line S R V, line W R T, line V T, line W S, line S R V, line W R T, line V T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4009.jpg"
-  },
-  {
-    "id": 4104,
-    "problem_id": 4010,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find BE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4010.jpg"
-  },
-  {
-    "id": 4105,
-    "problem_id": 4011,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find BE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4011.jpg"
-  },
-  {
-    "id": 4106,
-    "problem_id": 4012,
-    "problem": "line B C D, line A C, line A D, line B C D, line A C, line A D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4012.jpg"
-  },
-  {
-    "id": 4107,
-    "problem_id": 4013,
-    "problem": "line B C D, line A C, line A D, line B C D, line A C, line A D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4013.jpg"
-  },
-  {
-    "id": 4108,
-    "problem_id": 4014,
-    "problem": "line B C D, line A C, line A D, line B C D, line A C, line A D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4014.jpg"
-  },
-  {
-    "id": 4110,
-    "problem_id": 4015,
-    "problem": "line B C D, line A C, line A D, line B C D, line A C, line A D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4015.jpg"
-  },
-  {
-    "id": 4111,
-    "problem_id": 4016,
-    "problem": "line B C D, line A C, line A D, line B C D, line A C, line A D\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4016.jpg"
-  },
-  {
-    "id": 4112,
-    "problem_id": 4017,
-    "problem": "line P N, line N M, line L M, line R L, line R S, line K S L, line K R, line J K, line J P, \\odot R lieson J P N M L K, line P N, line N M, line L M, line R L, line R S, line K S L, line K R, line J K, line J P, \\odot R lieson J P N M L K\nA regular polygon is inscribed in a circle. What is the measure of \\angle SRL?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4017.jpg"
-  },
-  {
-    "id": 4113,
-    "problem_id": 4018,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4018.jpg"
-  },
-  {
-    "id": 4114,
-    "problem_id": 4019,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4019.jpg"
-  },
-  {
-    "id": 4115,
-    "problem_id": 4020,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4020.jpg"
-  },
-  {
-    "id": 4116,
-    "problem_id": 4021,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4021.jpg"
-  },
-  {
-    "id": 4117,
-    "problem_id": 4022,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4022.jpg"
-  },
-  {
-    "id": 4118,
-    "problem_id": 4023,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4023.jpg"
-  },
-  {
-    "id": 4119,
-    "problem_id": 4024,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4024.jpg"
-  },
-  {
-    "id": 4120,
-    "problem_id": 4025,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4025.jpg"
-  },
-  {
-    "id": 4121,
-    "problem_id": 4026,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4026.jpg"
-  },
-  {
-    "id": 4122,
-    "problem_id": 4027,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4027.jpg"
-  },
-  {
-    "id": 4123,
-    "problem_id": 4028,
-    "problem": "line V Z, line V W X, line Z W Y, line Y X, line V Z, line V W X, line Z W Y, line Y X\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4028.jpg"
-  },
-  {
-    "id": 4124,
-    "problem_id": 4029,
-    "problem": "line K L H, line G L J, \\odot A lieson G K J H, line K L H, line G L J, \\odot A lieson G K J H\nFind the measure of \\angle KLG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4029.jpg"
-  },
-  {
-    "id": 4125,
-    "problem_id": 4030,
-    "problem": "line K L H, line G L J, \\odot A lieson G K J H, line K L H, line G L J, \\odot A lieson G K J H\nFind the measure of \\angle KLG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4030.jpg"
-  },
-  {
-    "id": 4126,
-    "problem_id": 4031,
-    "problem": "line L Q, line M P, line M L, line P Q, line L Q, line M P, line M L, line P Q\nFind m \\angle MLQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4031.jpg"
-  },
-  {
-    "id": 4127,
-    "problem_id": 4032,
-    "problem": "line A B C, line A B C\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4032.jpg"
-  },
-  {
-    "id": 4128,
-    "problem_id": 4033,
-    "problem": "line A B C, line A B C\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4033.jpg"
-  },
-  {
-    "id": 4129,
-    "problem_id": 4034,
-    "problem": "line A B C, line A B C\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4034.jpg"
-  },
-  {
-    "id": 4130,
-    "problem_id": 4035,
-    "problem": "line A B C, line A B C\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4035.jpg"
-  },
-  {
-    "id": 4131,
-    "problem_id": 4036,
-    "problem": "line A B C, line A B C\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4036.jpg"
-  },
-  {
-    "id": 4132,
-    "problem_id": 4037,
-    "problem": "line B D, line C D, line A B C, line B D, line C D, line A B C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4037.jpg"
-  },
-  {
-    "id": 4133,
-    "problem_id": 4038,
-    "problem": "line B D, line C D, line A B C, line B D, line C D, line A B C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4038.jpg"
-  },
-  {
-    "id": 4134,
-    "problem_id": 4039,
-    "problem": "line B D, line C D, line A B C, line B D, line C D, line A B C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4039.jpg"
-  },
-  {
-    "id": 4135,
-    "problem_id": 4040,
-    "problem": "line B D, line C D, line A B C, line B D, line C D, line A B C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4040.jpg"
-  },
-  {
-    "id": 4136,
-    "problem_id": 4041,
-    "problem": "line A C D, line B C, \\odot C lieson B D A, line A C D, line B C, \\odot C lieson B D A\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4041.jpg"
-  },
-  {
-    "id": 4137,
-    "problem_id": 4042,
-    "problem": "line H F C A, line G F E, line B C D, line H F C A, line G F E, line B C D\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4042.jpg"
-  },
-  {
-    "id": 4138,
-    "problem_id": 4043,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nWhat is the measurement of \\angle BED?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4043.jpg"
-  },
-  {
-    "id": 4139,
-    "problem_id": 4044,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nWhat is the measurement of \\angle BED?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4044.jpg"
-  },
-  {
-    "id": 4140,
-    "problem_id": 4045,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nWhat is the measurement of \\angle BED?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4045.jpg"
-  },
-  {
-    "id": 4141,
-    "problem_id": 4046,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nWhat is the measurement of \\angle BED?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4046.jpg"
-  },
-  {
-    "id": 4142,
-    "problem_id": 4047,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nWhat is the measurement of \\angle BED?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4047.jpg"
-  },
-  {
-    "id": 4143,
-    "problem_id": 4048,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4048.jpg"
-  },
-  {
-    "id": 4144,
-    "problem_id": 4049,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4049.jpg"
-  },
-  {
-    "id": 4145,
-    "problem_id": 4050,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4050.jpg"
-  },
-  {
-    "id": 4146,
-    "problem_id": 4051,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4051.jpg"
-  },
-  {
-    "id": 4147,
-    "problem_id": 4052,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4052.jpg"
-  },
-  {
-    "id": 4148,
-    "problem_id": 4053,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4053.jpg"
-  },
-  {
-    "id": 4149,
-    "problem_id": 4054,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4054.jpg"
-  },
-  {
-    "id": 4150,
-    "problem_id": 4055,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4055.jpg"
-  },
-  {
-    "id": 4151,
-    "problem_id": 4056,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4056.jpg"
-  },
-  {
-    "id": 4152,
-    "problem_id": 4057,
-    "problem": "line J L, line J K, line L K, line J L, line J K, line L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4057.jpg"
-  },
-  {
-    "id": 4153,
-    "problem_id": 4058,
-    "problem": "line N Q K, line J N, line N M, line K M, line J Q M, line J K, line N Q K, line J N, line N M, line K M, line J Q M, line J K\nJKMN is a rectangle. If m \\angle JKN = 2x^{2}+2 and m \\angle NKM = 14x, find m \\angle KNJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4058.jpg"
-  },
-  {
-    "id": 4154,
-    "problem_id": 4059,
-    "problem": "line N Q K, line J N, line N M, line K M, line J Q M, line J K, line N Q K, line J N, line N M, line K M, line J Q M, line J K\nJKMN is a rectangle. If m \\angle JKN = 2x^{2}+2 and m \\angle NKM = 14x, find m \\angle KNJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4059.jpg"
-  },
-  {
-    "id": 4155,
-    "problem_id": 4060,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4060.jpg"
-  },
-  {
-    "id": 4156,
-    "problem_id": 4061,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4061.jpg"
-  },
-  {
-    "id": 4157,
-    "problem_id": 4062,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4062.jpg"
-  },
-  {
-    "id": 4158,
-    "problem_id": 4063,
-    "problem": "line C D E, line B D F, line A D, line C D E, line B D F, line A D\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4063.jpg"
-  },
-  {
-    "id": 4159,
-    "problem_id": 4064,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4064.jpg"
-  },
-  {
-    "id": 4160,
-    "problem_id": 4065,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4065.jpg"
-  },
-  {
-    "id": 4161,
-    "problem_id": 4066,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4066.jpg"
-  },
-  {
-    "id": 4162,
-    "problem_id": 4067,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4067.jpg"
-  },
-  {
-    "id": 4163,
-    "problem_id": 4068,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4068.jpg"
-  },
-  {
-    "id": 4164,
-    "problem_id": 4069,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4069.jpg"
-  },
-  {
-    "id": 4165,
-    "problem_id": 4070,
-    "problem": "line C Q R D, line B R S F, line A Q E, line C Q R D, line B R S F, line A Q E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4070.jpg"
-  },
-  {
-    "id": 4166,
-    "problem_id": 4071,
-    "problem": "line C Q R D, line B R S F, line A Q E, line C Q R D, line B R S F, line A Q E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4071.jpg"
-  },
-  {
-    "id": 4167,
-    "problem_id": 4072,
-    "problem": "line C Q R D, line B R S F, line A Q E, line C Q R D, line B R S F, line A Q E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4072.jpg"
-  },
-  {
-    "id": 4168,
-    "problem_id": 4073,
-    "problem": "line C Q R D, line B R S F, line A Q E, line C Q R D, line B R S F, line A Q E\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4073.jpg"
-  },
-  {
-    "id": 4169,
-    "problem_id": 4074,
-    "problem": "line B A, line B E, line E D C, line A C, line A D, line B A, line B E, line E D C, line A C, line A D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4074.jpg"
-  },
-  {
-    "id": 4170,
-    "problem_id": 4075,
-    "problem": "line B A, line B E, line E D C, line A C, line A D, line B A, line B E, line E D C, line A C, line A D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4075.jpg"
-  },
-  {
-    "id": 4171,
-    "problem_id": 4076,
-    "problem": "line B A, line B E, line E D C, line A C, line A D, line B A, line B E, line E D C, line A C, line A D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4076.jpg"
-  },
-  {
-    "id": 4172,
-    "problem_id": 4077,
-    "problem": "line B A, line B E, line E D C, line A C, line A D, line B A, line B E, line E D C, line A C, line A D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4077.jpg"
-  },
-  {
-    "id": 4173,
-    "problem_id": 4078,
-    "problem": "line B A, line B E, line E D C, line A C, line A D, line B A, line B E, line E D C, line A C, line A D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4078.jpg"
-  },
-  {
-    "id": 4174,
-    "problem_id": 4079,
-    "problem": "line C D E, line A B, line A C, line B D, line B E, line C D E, line A B, line A C, line B D, line B E\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4079.jpg"
-  },
-  {
-    "id": 4175,
-    "problem_id": 4080,
-    "problem": "line C D E, line A B, line A C, line B D, line B E, line C D E, line A B, line A C, line B D, line B E\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4080.jpg"
-  },
-  {
-    "id": 4176,
-    "problem_id": 4081,
-    "problem": "line Q R, line P Q, line P S, line P A, line S A R, line Q R, line P Q, line P S, line P A, line S A R\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4081.jpg"
-  },
-  {
-    "id": 4177,
-    "problem_id": 4082,
-    "problem": "line Q R, line P Q, line P S, line P A, line S A R, line Q R, line P Q, line P S, line P A, line S A R\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4082.jpg"
-  },
-  {
-    "id": 4178,
-    "problem_id": 4083,
-    "problem": "line C E D, line B E A, \\odot A lieson C D B, line C E D, line B E A, \\odot A lieson C D B\nFind m \\widehat CBD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4083.jpg"
-  },
-  {
-    "id": 4179,
-    "problem_id": 4084,
-    "problem": "line A D, line B A, line C D, line B C, line A D, line B A, line C D, line B C\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4084.jpg"
-  },
-  {
-    "id": 4180,
-    "problem_id": 4085,
-    "problem": "line A D, line B A, line C D, line B C, line A D, line B A, line C D, line B C\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4085.jpg"
-  },
-  {
-    "id": 4181,
-    "problem_id": 4086,
-    "problem": "line T Y, line A Y, line D A, line O D, line O T, line T Y, line A Y, line D A, line O D, line O T\nWhat is m \\angle Y in pentagon TODAY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4086.jpg"
-  },
-  {
-    "id": 4182,
-    "problem_id": 4087,
-    "problem": "line T Y, line A Y, line D A, line O D, line O T, line T Y, line A Y, line D A, line O D, line O T\nWhat is m \\angle Y in pentagon TODAY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4087.jpg"
-  },
-  {
-    "id": 4183,
-    "problem_id": 4088,
-    "problem": "line T Y, line A Y, line D A, line O D, line O T, line T Y, line A Y, line D A, line O D, line O T\nWhat is m \\angle Y in pentagon TODAY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4088.jpg"
-  },
-  {
-    "id": 4184,
-    "problem_id": 4089,
-    "problem": "line T Y, line A Y, line D A, line O D, line O T, line T Y, line A Y, line D A, line O D, line O T\nWhat is m \\angle Y in pentagon TODAY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4089.jpg"
-  },
-  {
-    "id": 4185,
-    "problem_id": 4090,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4090.jpg"
-  },
-  {
-    "id": 4186,
-    "problem_id": 4091,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4091.jpg"
-  },
-  {
-    "id": 4187,
-    "problem_id": 4092,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4092.jpg"
-  },
-  {
-    "id": 4188,
-    "problem_id": 4093,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4093.jpg"
-  },
-  {
-    "id": 4189,
-    "problem_id": 4094,
-    "problem": "line D G, line F G, line E D, line E F, line D G, line F G, line E D, line E F\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4094.jpg"
-  },
-  {
-    "id": 4190,
-    "problem_id": 4095,
-    "problem": "line A D, line C D, line A E C, line B E D, line B A, line B C, line A D, line C D, line A E C, line B E D, line B A, line B C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4095.jpg"
-  },
-  {
-    "id": 4191,
-    "problem_id": 4096,
-    "problem": "line A D, line C D, line A E C, line B E D, line B A, line B C, line A D, line C D, line A E C, line B E D, line B A, line B C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4096.jpg"
-  },
-  {
-    "id": 4192,
-    "problem_id": 4097,
-    "problem": "line A D, line C D, line A E C, line B E D, line B A, line B C, line A D, line C D, line A E C, line B E D, line B A, line B C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4097.jpg"
-  },
-  {
-    "id": 4193,
-    "problem_id": 4098,
-    "problem": "line A D, line C D, line A E C, line B E D, line B A, line B C, line A D, line C D, line A E C, line B E D, line B A, line B C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4098.jpg"
-  },
-  {
-    "id": 4194,
-    "problem_id": 4099,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4099.jpg"
-  },
-  {
-    "id": 4195,
-    "problem_id": 4100,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4100.jpg"
-  },
-  {
-    "id": 4196,
-    "problem_id": 4101,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4101.jpg"
-  },
-  {
-    "id": 4197,
-    "problem_id": 4102,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4102.jpg"
-  },
-  {
-    "id": 4198,
-    "problem_id": 4103,
-    "problem": "line A B C, line C D, line E A, line E D, line E B, line A B C, line C D, line E A, line E D, line E B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4103.jpg"
-  },
-  {
-    "id": 4200,
-    "problem_id": 4104,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4104.jpg"
-  },
-  {
-    "id": 4201,
-    "problem_id": 4105,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4105.jpg"
-  },
-  {
-    "id": 4202,
-    "problem_id": 4106,
-    "problem": "line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P, line P M L, line Q S L, line J K L, line J S M, line P S K, line J Q P\nPoint S is the incenter of \\triangle JPL. Find PQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4106.jpg"
-  },
-  {
-    "id": 4203,
-    "problem_id": 4107,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nSolve for the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4107.jpg"
-  },
-  {
-    "id": 4204,
-    "problem_id": 4108,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nSolve for the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4108.jpg"
-  },
-  {
-    "id": 4205,
-    "problem_id": 4109,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4109.jpg"
-  },
-  {
-    "id": 4206,
-    "problem_id": 4110,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4110.jpg"
-  },
-  {
-    "id": 4207,
-    "problem_id": 4111,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4111.jpg"
-  },
-  {
-    "id": 4208,
-    "problem_id": 4112,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4112.jpg"
-  },
-  {
-    "id": 4209,
-    "problem_id": 4113,
-    "problem": "line B C, line D C, line A B, line A D, line A C, line B C, line D C, line A B, line A D, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4113.jpg"
-  },
-  {
-    "id": 4210,
-    "problem_id": 4114,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4114.jpg"
-  },
-  {
-    "id": 4211,
-    "problem_id": 4115,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4115.jpg"
-  },
-  {
-    "id": 4212,
-    "problem_id": 4116,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4116.jpg"
-  },
-  {
-    "id": 4213,
-    "problem_id": 4117,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4117.jpg"
-  },
-  {
-    "id": 4214,
-    "problem_id": 4118,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4118.jpg"
-  },
-  {
-    "id": 4215,
-    "problem_id": 4119,
-    "problem": "line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B, line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4119.jpg"
-  },
-  {
-    "id": 4216,
-    "problem_id": 4120,
-    "problem": "line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B, line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4120.jpg"
-  },
-  {
-    "id": 4217,
-    "problem_id": 4121,
-    "problem": "line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B, line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4121.jpg"
-  },
-  {
-    "id": 4218,
-    "problem_id": 4122,
-    "problem": "line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B, line D C B, line A B, line A C E, line D E, \\odot F lieson A D E B\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4122.jpg"
-  },
-  {
-    "id": 4219,
-    "problem_id": 4123,
-    "problem": "line S T, line S U, \\odot A lieson U T S, line S T, line S U, \\odot A lieson U T S\nFind the measure of \\widehat US.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4123.jpg"
-  },
-  {
-    "id": 4220,
-    "problem_id": 4124,
-    "problem": "line S T, line S U, \\odot A lieson U T S, line S T, line S U, \\odot A lieson U T S\nFind the measure of \\widehat US.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4124.jpg"
-  },
-  {
-    "id": 4221,
-    "problem_id": 4125,
-    "problem": "line S T, line S U, \\odot A lieson U T S, line S T, line S U, \\odot A lieson U T S\nFind the measure of \\widehat US.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4125.jpg"
-  },
-  {
-    "id": 4222,
-    "problem_id": 4126,
-    "problem": "line D F C, line B G C, line B E D, line G F, line E G, line E F, line D F C, line B G C, line B E D, line G F, line E G, line E F\nFind the perimeter of \\triangle BCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4126.jpg"
-  },
-  {
-    "id": 4223,
-    "problem_id": 4127,
-    "problem": "line A C D, line B C, line B A, line B D, line A C D, line B C, line B A, line B D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4127.jpg"
-  },
-  {
-    "id": 4224,
-    "problem_id": 4128,
-    "problem": "line A C D, line B C, line B A, line B D, line A C D, line B C, line B A, line B D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4128.jpg"
-  },
-  {
-    "id": 4225,
-    "problem_id": 4129,
-    "problem": "line B D E F, line m lieson G D A, line l lieson H E C, line B D E F, line m lieson G D A, line l lieson H E C\nFind the value of x for which line l \\parallel line m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4129.jpg"
-  },
-  {
-    "id": 4226,
-    "problem_id": 4130,
-    "problem": "line B D E F, line m lieson G D A, line l lieson H E C, line B D E F, line m lieson G D A, line l lieson H E C\nFind the value of x for which line l \\parallel line m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4130.jpg"
-  },
-  {
-    "id": 4227,
-    "problem_id": 4131,
-    "problem": "line B D E F, line m lieson G D A, line l lieson H E C, line B D E F, line m lieson G D A, line l lieson H E C\nFind the value of x for which line l \\parallel line m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4131.jpg"
-  },
-  {
-    "id": 4228,
-    "problem_id": 4132,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat HMK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4132.jpg"
-  },
-  {
-    "id": 4229,
-    "problem_id": 4133,
-    "problem": "line J K, line J M, line M L, line K L, line J K, line J M, line M L, line K L\nFind the measurement of \\angle J of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4133.jpg"
-  },
-  {
-    "id": 4230,
-    "problem_id": 4134,
-    "problem": "line J K, line J M, line M L, line K L, line J K, line J M, line M L, line K L\nFind the measurement of \\angle J of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4134.jpg"
-  },
-  {
-    "id": 4231,
-    "problem_id": 4135,
-    "problem": "line J K, line J M, line M L, line K L, line J K, line J M, line M L, line K L\nFind the measurement of \\angle J of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4135.jpg"
-  },
-  {
-    "id": 4232,
-    "problem_id": 4136,
-    "problem": "line J K, line J M, line M L, line K L, line J K, line J M, line M L, line K L\nFind the measurement of \\angle J of JKLM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4136.jpg"
-  },
-  {
-    "id": 4233,
-    "problem_id": 4137,
-    "problem": "line U S, line A S B, \\odot C lieson U T S, line U S, line A S B, \\odot C lieson U T S\nFind m \\widehat STU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4137.jpg"
-  },
-  {
-    "id": 4234,
-    "problem_id": 4138,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind FH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4138.jpg"
-  },
-  {
-    "id": 4235,
-    "problem_id": 4139,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind FH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4139.jpg"
-  },
-  {
-    "id": 4236,
-    "problem_id": 4140,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind FH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4140.jpg"
-  },
-  {
-    "id": 4237,
-    "problem_id": 4141,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind FH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4141.jpg"
-  },
-  {
-    "id": 4238,
-    "problem_id": 4142,
-    "problem": "line C B A, line C D, line D E F, line A F, line B E, line C B A, line C D, line D E F, line A F, line B E\nRefer to trapezoid ACDF. Find BE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4142.jpg"
-  },
-  {
-    "id": 4239,
-    "problem_id": 4143,
-    "problem": "line A B D, line C A, line C B, line C D, line A B D, line C A, line C B, line C D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4143.jpg"
-  },
-  {
-    "id": 4240,
-    "problem_id": 4144,
-    "problem": "line T Y Z, line T W, line W Z, line Y W, line T Y Z, line T W, line W Z, line Y W\nFind TW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4144.jpg"
-  },
-  {
-    "id": 4241,
-    "problem_id": 4145,
-    "problem": "line H G, line D E, line D I, line F G, line E F, line I H, line H G, line D E, line D I, line F G, line E F, line I H\nDetermine the measure of \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4145.jpg"
-  },
-  {
-    "id": 4242,
-    "problem_id": 4146,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4146.jpg"
-  },
-  {
-    "id": 4243,
-    "problem_id": 4147,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4147.jpg"
-  },
-  {
-    "id": 4244,
-    "problem_id": 4148,
-    "problem": "line A C D, line A B, line B D, \\odot C lieson A D B, line A C D, line A B, line B D, \\odot C lieson A D B\nFind the exact area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4148.jpg"
-  },
-  {
-    "id": 4245,
-    "problem_id": 4149,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4149.jpg"
-  },
-  {
-    "id": 4246,
-    "problem_id": 4150,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4150.jpg"
-  },
-  {
-    "id": 4247,
-    "problem_id": 4151,
-    "problem": "line F D, line A B, line F E, line A C, line D E, line C B, line F D, line A B, line F E, line A C, line D E, line C B\n\\triangle ABC \\cong \\triangle FDE. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4151.jpg"
-  },
-  {
-    "id": 4248,
-    "problem_id": 4152,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the regular polygon. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4152.jpg"
-  },
-  {
-    "id": 4249,
-    "problem_id": 4153,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the regular polygon. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4153.jpg"
-  },
-  {
-    "id": 4250,
-    "problem_id": 4154,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the regular polygon. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4154.jpg"
-  },
-  {
-    "id": 4251,
-    "problem_id": 4155,
-    "problem": "line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J, line A G H, line B I A, line B J C, line C K D, line D L E, line F M E, line A N F, \\odot H lieson I G N M L K J\nFind the area of the regular polygon. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4155.jpg"
-  },
-  {
-    "id": 4252,
-    "problem_id": 4156,
-    "problem": "line J K L, line J K L\nIn the diagram, JL = 120. What is JK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4156.jpg"
-  },
-  {
-    "id": 4253,
-    "problem_id": 4157,
-    "problem": "line J K L, line J K L\nIn the diagram, JL = 120. What is JK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4157.jpg"
-  },
-  {
-    "id": 4254,
-    "problem_id": 4158,
-    "problem": "line J K L, line J K L\nIn the diagram, JL = 120. What is JK?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4158.jpg"
-  },
-  {
-    "id": 4255,
-    "problem_id": 4159,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4159.jpg"
-  },
-  {
-    "id": 4256,
-    "problem_id": 4160,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4160.jpg"
-  },
-  {
-    "id": 4257,
-    "problem_id": 4161,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4161.jpg"
-  },
-  {
-    "id": 4258,
-    "problem_id": 4162,
-    "problem": "line B A, line A C, line C D, line B D, line B A, line A C, line C D, line B D\nSolve for m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4162.jpg"
-  },
-  {
-    "id": 4259,
-    "problem_id": 4163,
-    "problem": "line Q S R, line Q P, line P S, line P R, line Q S R, line Q P, line P S, line P R\nFind x if PS is a median of \\triangle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4163.jpg"
-  },
-  {
-    "id": 4260,
-    "problem_id": 4164,
-    "problem": "line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C, line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C\nIn \\triangle DEF, DB = 24.6, and EZ = 11.6. What is CE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4164.jpg"
-  },
-  {
-    "id": 4261,
-    "problem_id": 4165,
-    "problem": "line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C, line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C\nIn \\triangle DEF, DB = 24.6, and EZ = 11.6. What is CE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4165.jpg"
-  },
-  {
-    "id": 4262,
-    "problem_id": 4166,
-    "problem": "line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C, line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C\nIn \\triangle DEF, DB = 24.6, and EZ = 11.6. What is CE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4166.jpg"
-  },
-  {
-    "id": 4263,
-    "problem_id": 4167,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4167.jpg"
-  },
-  {
-    "id": 4264,
-    "problem_id": 4168,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4168.jpg"
-  },
-  {
-    "id": 4265,
-    "problem_id": 4169,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 15.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4169.jpg"
-  },
-  {
-    "id": 4266,
-    "problem_id": 4170,
-    "problem": "line P Q, line B A, line D A, line P S, line C D, line Q R, line S R, line C B, line P Q, line B A, line D A, line P S, line C D, line Q R, line S R, line C B\nEach pair of polygons is similar. What is the measure of BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4170.jpg"
-  },
-  {
-    "id": 4267,
-    "problem_id": 4171,
-    "problem": "line P Q, line B A, line D A, line P S, line C D, line Q R, line S R, line C B, line P Q, line B A, line D A, line P S, line C D, line Q R, line S R, line C B\nEach pair of polygons is similar. What is the measure of BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4171.jpg"
-  },
-  {
-    "id": 4268,
-    "problem_id": 4172,
-    "problem": "line P Q, line B A, line D A, line P S, line C D, line Q R, line S R, line C B, line P Q, line B A, line D A, line P S, line C D, line Q R, line S R, line C B\nEach pair of polygons is similar. What is the measure of BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4172.jpg"
-  },
-  {
-    "id": 4269,
-    "problem_id": 4173,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4173.jpg"
-  },
-  {
-    "id": 4270,
-    "problem_id": 4174,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4174.jpg"
-  },
-  {
-    "id": 4271,
-    "problem_id": 4175,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4175.jpg"
-  },
-  {
-    "id": 4272,
-    "problem_id": 4176,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4176.jpg"
-  },
-  {
-    "id": 4273,
-    "problem_id": 4177,
-    "problem": "line N P, line N M, line M P, line N P, line N M, line M P\nWhat is the measure of NP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4177.jpg"
-  },
-  {
-    "id": 4274,
-    "problem_id": 4178,
-    "problem": "line N P, line N M, line M P, line N P, line N M, line M P\nWhat is the measure of NP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4178.jpg"
-  },
-  {
-    "id": 4275,
-    "problem_id": 4179,
-    "problem": "line N P, line N M, line M P, line N P, line N M, line M P\nWhat is the measure of NP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4179.jpg"
-  },
-  {
-    "id": 4276,
-    "problem_id": 4180,
-    "problem": "line N P, line N M, line M P, line N P, line N M, line M P\nWhat is the measure of NP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4180.jpg"
-  },
-  {
-    "id": 4277,
-    "problem_id": 4181,
-    "problem": "line N P, line N M, line M P, line N P, line N M, line M P\nWhat is the measure of NP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4181.jpg"
-  },
-  {
-    "id": 4278,
-    "problem_id": 4182,
-    "problem": "line N P, line N M, line M P, line N P, line N M, line M P\nWhat is the measure of NP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4182.jpg"
-  },
-  {
-    "id": 4279,
-    "problem_id": 4183,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4183.jpg"
-  },
-  {
-    "id": 4280,
-    "problem_id": 4184,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4184.jpg"
-  },
-  {
-    "id": 4281,
-    "problem_id": 4185,
-    "problem": "line A C, line B D, line C D, line A B, line A C, line B D, line C D, line A B\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4185.jpg"
-  },
-  {
-    "id": 4282,
-    "problem_id": 4186,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4186.jpg"
-  },
-  {
-    "id": 4283,
-    "problem_id": 4187,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4187.jpg"
-  },
-  {
-    "id": 4284,
-    "problem_id": 4188,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4188.jpg"
-  },
-  {
-    "id": 4285,
-    "problem_id": 4189,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4189.jpg"
-  },
-  {
-    "id": 4286,
-    "problem_id": 4190,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4190.jpg"
-  },
-  {
-    "id": 4287,
-    "problem_id": 4191,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4191.jpg"
-  },
-  {
-    "id": 4288,
-    "problem_id": 4192,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind GF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4192.jpg"
-  },
-  {
-    "id": 4289,
-    "problem_id": 4193,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the circumference of \\odot D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4193.jpg"
-  },
-  {
-    "id": 4290,
-    "problem_id": 4194,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the circumference of \\odot D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4194.jpg"
-  },
-  {
-    "id": 4291,
-    "problem_id": 4195,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the circumference of \\odot D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4195.jpg"
-  },
-  {
-    "id": 4292,
-    "problem_id": 4196,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the circumference of \\odot D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4196.jpg"
-  },
-  {
-    "id": 4293,
-    "problem_id": 4197,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the measure of \\angle BCA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4197.jpg"
-  },
-  {
-    "id": 4294,
-    "problem_id": 4198,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the measure of \\angle BCA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4198.jpg"
-  },
-  {
-    "id": 4295,
-    "problem_id": 4199,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the measure of \\angle BCA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4199.jpg"
-  },
-  {
-    "id": 4296,
-    "problem_id": 4200,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the measure of \\angle BCA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4200.jpg"
-  },
-  {
-    "id": 4297,
-    "problem_id": 4201,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the measure of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4201.jpg"
-  },
-  {
-    "id": 4298,
-    "problem_id": 4202,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the measure of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4202.jpg"
-  },
-  {
-    "id": 4299,
-    "problem_id": 4203,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the measure of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4203.jpg"
-  },
-  {
-    "id": 4300,
-    "problem_id": 4204,
-    "problem": "line D B, line B C, line D C, line A D, line A B, line D B, line B C, line D C, line A D, line A B\nFind the measure of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4204.jpg"
-  },
-  {
-    "id": 4301,
-    "problem_id": 4205,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4205.jpg"
-  },
-  {
-    "id": 4302,
-    "problem_id": 4206,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4206.jpg"
-  },
-  {
-    "id": 4303,
-    "problem_id": 4207,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4207.jpg"
-  },
-  {
-    "id": 4305,
-    "problem_id": 4208,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 8?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4208.jpg"
-  },
-  {
-    "id": 4306,
-    "problem_id": 4209,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 8?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4209.jpg"
-  },
-  {
-    "id": 4307,
-    "problem_id": 4210,
-    "problem": "line D E, line E F, line D F, line D E, line E F, line D F\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4210.jpg"
-  },
-  {
-    "id": 4308,
-    "problem_id": 4211,
-    "problem": "line D E, line E F, line D F, line D E, line E F, line D F\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4211.jpg"
-  },
-  {
-    "id": 4309,
-    "problem_id": 4212,
-    "problem": "line D E, line E F, line D F, line D E, line E F, line D F\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4212.jpg"
-  },
-  {
-    "id": 4310,
-    "problem_id": 4213,
-    "problem": "line D E, line E F, line D F, line D E, line E F, line D F\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4213.jpg"
-  },
-  {
-    "id": 4311,
-    "problem_id": 4214,
-    "problem": "line D E, line E F, line D F, line D E, line E F, line D F\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4214.jpg"
-  },
-  {
-    "id": 4312,
-    "problem_id": 4215,
-    "problem": "line D E, line E F, line D F, line D E, line E F, line D F\nSolve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4215.jpg"
-  },
-  {
-    "id": 4313,
-    "problem_id": 4216,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable y for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4216.jpg"
-  },
-  {
-    "id": 4314,
-    "problem_id": 4217,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable y for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4217.jpg"
-  },
-  {
-    "id": 4315,
-    "problem_id": 4218,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable y for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4218.jpg"
-  },
-  {
-    "id": 4316,
-    "problem_id": 4219,
-    "problem": "line B C, line A D, line A B, line D C, line B C, line A D, line A B, line D C\nFind the value of the variable y for which ABCD is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4219.jpg"
-  },
-  {
-    "id": 4317,
-    "problem_id": 4220,
-    "problem": "line Y Z, line X B Z, line Y A X, line A B, line Y Z, line X B Z, line Y A X, line A B\nAX = 26 and BZ = 36. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4220.jpg"
-  },
-  {
-    "id": 4318,
-    "problem_id": 4221,
-    "problem": "line Y Z, line X B Z, line Y A X, line A B, line Y Z, line X B Z, line Y A X, line A B\nAX = 26 and BZ = 36. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4221.jpg"
-  },
-  {
-    "id": 4319,
-    "problem_id": 4222,
-    "problem": "line Y Z, line X B Z, line Y A X, line A B, line Y Z, line X B Z, line Y A X, line A B\nAX = 26 and BZ = 36. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4222.jpg"
-  },
-  {
-    "id": 4320,
-    "problem_id": 4223,
-    "problem": "line Y Z, line X B Z, line Y A X, line A B, line Y Z, line X B Z, line Y A X, line A B\nAX = 26 and BZ = 36. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4223.jpg"
-  },
-  {
-    "id": 4321,
-    "problem_id": 4224,
-    "problem": "line Y Z, line X B Z, line Y A X, line A B, line Y Z, line X B Z, line Y A X, line A B\nAX = 26 and BZ = 36. Find the perimeter of \\triangle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4224.jpg"
-  },
-  {
-    "id": 4322,
-    "problem_id": 4225,
-    "problem": "line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R, line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R\nIn \\odot A, m \\widehat PQ = m \\widehat RS. Find m \\angle 3 if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4225.jpg"
-  },
-  {
-    "id": 4323,
-    "problem_id": 4226,
-    "problem": "line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R, line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R\nIn \\odot A, m \\widehat PQ = m \\widehat RS. Find m \\angle 3 if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4226.jpg"
-  },
-  {
-    "id": 4324,
-    "problem_id": 4227,
-    "problem": "line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R, line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R\nIn \\odot A, m \\widehat PQ = m \\widehat RS. Find m \\angle 3 if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4227.jpg"
-  },
-  {
-    "id": 4325,
-    "problem_id": 4228,
-    "problem": "line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R, line S T, line P A S, line P T, line P B R, line Q B S, \\odot A lieson Q P T S R\nIn \\odot A, m \\widehat PQ = m \\widehat RS. Find m \\angle 3 if m \\angle 1 = 6x+11, m \\angle 2 = 9x+19, m \\angle 3 = 4y-25, and m \\angle 4 = 3y-9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4228.jpg"
-  },
-  {
-    "id": 4326,
-    "problem_id": 4229,
-    "problem": "line A C, line A B D, \\odot E lieson B C D, line A C, line A B D, \\odot E lieson B C D\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4229.jpg"
-  },
-  {
-    "id": 4327,
-    "problem_id": 4230,
-    "problem": "line A C, line A B D, \\odot E lieson B C D, line A C, line A B D, \\odot E lieson B C D\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4230.jpg"
-  },
-  {
-    "id": 4328,
-    "problem_id": 4231,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the measure of \\angle 2 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4231.jpg"
-  },
-  {
-    "id": 4329,
-    "problem_id": 4232,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the measure of \\angle 2 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4232.jpg"
-  },
-  {
-    "id": 4330,
-    "problem_id": 4233,
-    "problem": "line D A, line A B, line C B, line D C, line A E C, line D E B, line D A, line A B, line C B, line D C, line A E C, line D E B\nFind x in the rhombus. Area = 96 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4233.jpg"
-  },
-  {
-    "id": 4331,
-    "problem_id": 4234,
-    "problem": "line D A, line A B, line C B, line D C, line A E C, line D E B, line D A, line A B, line C B, line D C, line A E C, line D E B\nFind x in the rhombus. Area = 96 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4234.jpg"
-  },
-  {
-    "id": 4332,
-    "problem_id": 4235,
-    "problem": "line D A, line A B, line C B, line D C, line A E C, line D E B, line D A, line A B, line C B, line D C, line A E C, line D E B\nFind x in the rhombus. Area = 96 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4235.jpg"
-  },
-  {
-    "id": 4333,
-    "problem_id": 4236,
-    "problem": "line D A, line A B, line C B, line D C, line A E C, line D E B, line D A, line A B, line C B, line D C, line A E C, line D E B\nFind x in the rhombus. Area = 96 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4236.jpg"
-  },
-  {
-    "id": 4334,
-    "problem_id": 4237,
-    "problem": "line D A, line A B, line C B, line D C, line A E C, line D E B, line D A, line A B, line C B, line D C, line A E C, line D E B\nFind x in the rhombus. Area = 96 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4237.jpg"
-  },
-  {
-    "id": 4335,
-    "problem_id": 4238,
-    "problem": "line B C D, line E D, line B A, line B E, line A D, line A C E, line B C D, line E D, line B A, line B E, line A D, line A C E\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4238.jpg"
-  },
-  {
-    "id": 4336,
-    "problem_id": 4239,
-    "problem": "line B C D, line E D, line B A, line B E, line A D, line A C E, line B C D, line E D, line B A, line B E, line A D, line A C E\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4239.jpg"
-  },
-  {
-    "id": 4337,
-    "problem_id": 4240,
-    "problem": "line B C D, line E D, line B A, line B E, line A D, line A C E, line B C D, line E D, line B A, line B E, line A D, line A C E\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4240.jpg"
-  },
-  {
-    "id": 4338,
-    "problem_id": 4241,
-    "problem": "line B C D, line E D, line B A, line B E, line A D, line A C E, line B C D, line E D, line B A, line B E, line A D, line A C E\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4241.jpg"
-  },
-  {
-    "id": 4339,
-    "problem_id": 4242,
-    "problem": "line B C D, line E D, line B A, line B E, line A D, line A C E, line B C D, line E D, line B A, line B E, line A D, line A C E\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4242.jpg"
-  },
-  {
-    "id": 4340,
-    "problem_id": 4243,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4243.jpg"
-  },
-  {
-    "id": 4341,
-    "problem_id": 4244,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x. Area = 165 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4244.jpg"
-  },
-  {
-    "id": 4342,
-    "problem_id": 4245,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x. Area = 165 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4245.jpg"
-  },
-  {
-    "id": 4343,
-    "problem_id": 4246,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind x. Area = 165 cm^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4246.jpg"
-  },
-  {
-    "id": 4344,
-    "problem_id": 4247,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4247.jpg"
-  },
-  {
-    "id": 4345,
-    "problem_id": 4248,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4248.jpg"
-  },
-  {
-    "id": 4347,
-    "problem_id": 4249,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4249.jpg"
-  },
-  {
-    "id": 4348,
-    "problem_id": 4250,
-    "problem": "line A C, line A B, line B D, line C D, line A E D, line B E C, line A C, line A B, line B D, line C D, line A E D, line B E C\nQuadrilateral ABDC is a rectangle. Find m \\angle 5 if m \\angle 1 = 38.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4250.jpg"
-  },
-  {
-    "id": 4349,
-    "problem_id": 4251,
-    "problem": "line G R, line F R, line H R, line R E, \\odot R lieson F E H G, line G R, line F R, line H R, line R E, \\odot R lieson F E H G\nWhat is m \\widehat GF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4251.jpg"
-  },
-  {
-    "id": 4350,
-    "problem_id": 4252,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4252.jpg"
-  },
-  {
-    "id": 4351,
-    "problem_id": 4253,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4253.jpg"
-  },
-  {
-    "id": 4352,
-    "problem_id": 4254,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4254.jpg"
-  },
-  {
-    "id": 4353,
-    "problem_id": 4255,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4255.jpg"
-  },
-  {
-    "id": 4354,
-    "problem_id": 4256,
-    "problem": "line C D, \\odot D lieson C A B, line C D, \\odot D lieson C A B\nFind the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4256.jpg"
-  },
-  {
-    "id": 4355,
-    "problem_id": 4257,
-    "problem": "line C D, \\odot D lieson C A B, line C D, \\odot D lieson C A B\nFind the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4257.jpg"
-  },
-  {
-    "id": 4356,
-    "problem_id": 4258,
-    "problem": "line E F, line A E, line A F, line C D, line B C, line B D, line E F, line A E, line A F, line C D, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4258.jpg"
-  },
-  {
-    "id": 4357,
-    "problem_id": 4259,
-    "problem": "line E F, line A E, line A F, line C D, line B C, line B D, line E F, line A E, line A F, line C D, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4259.jpg"
-  },
-  {
-    "id": 4358,
-    "problem_id": 4260,
-    "problem": "line E F, line A E, line A F, line C D, line B C, line B D, line E F, line A E, line A F, line C D, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4260.jpg"
-  },
-  {
-    "id": 4359,
-    "problem_id": 4261,
-    "problem": "line E F, line A E, line A F, line C D, line B C, line B D, line E F, line A E, line A F, line C D, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4261.jpg"
-  },
-  {
-    "id": 4360,
-    "problem_id": 4262,
-    "problem": "line E F, line A E, line A F, line C D, line B C, line B D, line E F, line A E, line A F, line C D, line B C, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4262.jpg"
-  },
-  {
-    "id": 4361,
-    "problem_id": 4263,
-    "problem": "line D G H A, line l lieson F H B, line m lieson E G C, line D G H A, line l lieson F H B, line m lieson E G C\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4263.jpg"
-  },
-  {
-    "id": 4363,
-    "problem_id": 4264,
-    "problem": "line A B C D, line J H G E D, line B G I, \\odot F lieson B H I E C, line A B C D, line J H G E D, line B G I, \\odot F lieson B H I E C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4264.jpg"
-  },
-  {
-    "id": 4364,
-    "problem_id": 4265,
-    "problem": "line K B M, line J B L, \\odot A lieson J M L K, line K B M, line J B L, \\odot A lieson J M L K\nFind MK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4265.jpg"
-  },
-  {
-    "id": 4365,
-    "problem_id": 4266,
-    "problem": "line T S, line A B, line Q R, line T A Q, line S B R, line T S, line A B, line Q R, line T A Q, line S B R\nFor trapezoid QRST, A and B are midpoints of the legs. Find m \\angle SBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4266.jpg"
-  },
-  {
-    "id": 4366,
-    "problem_id": 4267,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nWhat is the perimeter of \\triangle CXY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4267.jpg"
-  },
-  {
-    "id": 4367,
-    "problem_id": 4268,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nWhat is the perimeter of \\triangle CXY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4268.jpg"
-  },
-  {
-    "id": 4368,
-    "problem_id": 4269,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nWhat is the perimeter of \\triangle CXY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4269.jpg"
-  },
-  {
-    "id": 4369,
-    "problem_id": 4270,
-    "problem": "line C Y B, line C X A, line A B, line X W Y, line C Y B, line C X A, line A B, line X W Y\nWhat is the perimeter of \\triangle CXY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4270.jpg"
-  },
-  {
-    "id": 4370,
-    "problem_id": 4271,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4271.jpg"
-  },
-  {
-    "id": 4371,
-    "problem_id": 4272,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4272.jpg"
-  },
-  {
-    "id": 4372,
-    "problem_id": 4273,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4273.jpg"
-  },
-  {
-    "id": 4373,
-    "problem_id": 4274,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4274.jpg"
-  },
-  {
-    "id": 4374,
-    "problem_id": 4275,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4275.jpg"
-  },
-  {
-    "id": 4375,
-    "problem_id": 4276,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4276.jpg"
-  },
-  {
-    "id": 4376,
-    "problem_id": 4277,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4277.jpg"
-  },
-  {
-    "id": 4377,
-    "problem_id": 4278,
-    "problem": "line A B, line E C B, line A D E, line D C, line A B, line E C B, line A D E, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4278.jpg"
-  },
-  {
-    "id": 4378,
-    "problem_id": 4279,
-    "problem": "line A B, line E C B, line A D E, line D C, line A B, line E C B, line A D E, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4279.jpg"
-  },
-  {
-    "id": 4379,
-    "problem_id": 4280,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4280.jpg"
-  },
-  {
-    "id": 4380,
-    "problem_id": 4281,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4281.jpg"
-  },
-  {
-    "id": 4381,
-    "problem_id": 4282,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4282.jpg"
-  },
-  {
-    "id": 4382,
-    "problem_id": 4283,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4283.jpg"
-  },
-  {
-    "id": 4383,
-    "problem_id": 4284,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4284.jpg"
-  },
-  {
-    "id": 4384,
-    "problem_id": 4285,
-    "problem": "line S T, line R S, line R T, line S T, line R S, line R T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4285.jpg"
-  },
-  {
-    "id": 4385,
-    "problem_id": 4286,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find SK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4286.jpg"
-  },
-  {
-    "id": 4386,
-    "problem_id": 4287,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find SK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4287.jpg"
-  },
-  {
-    "id": 4387,
-    "problem_id": 4288,
-    "problem": "line C D E, line A C, line B D, line B E, line A B, line C D E, line A C, line B D, line B E, line A B\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4288.jpg"
-  },
-  {
-    "id": 4388,
-    "problem_id": 4289,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram PQRS to find QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4289.jpg"
-  },
-  {
-    "id": 4389,
-    "problem_id": 4290,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram PQRS to find QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4290.jpg"
-  },
-  {
-    "id": 4390,
-    "problem_id": 4291,
-    "problem": "line A B, line C D E, line A E, line A C, line B E, line A D, line A B, line C D E, line A E, line A C, line B E, line A D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4291.jpg"
-  },
-  {
-    "id": 4391,
-    "problem_id": 4292,
-    "problem": "line P G, line P H, \\odot P lieson G H, line P G, line P H, \\odot P lieson G H\nWhat is the measure of \\angle GPH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4292.jpg"
-  },
-  {
-    "id": 4392,
-    "problem_id": 4293,
-    "problem": "line C A B D, line D G L P, line M N O P, line C F K M, \\odot Q lieson B E I G, \\odot R lieson A F H E, \\odot S lieson K N J H, \\odot T lieson I J O L, line C A B D, line D G L P, line M N O P, line C F K M, \\odot Q lieson B E I G, \\odot R lieson A F H E, \\odot S lieson K N J H, \\odot T lieson I J O L\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4293.jpg"
-  },
-  {
-    "id": 4393,
-    "problem_id": 4294,
-    "problem": "line C A B D, line D G L P, line M N O P, line C F K M, \\odot Q lieson B E I G, \\odot R lieson A F H E, \\odot S lieson K N J H, \\odot T lieson I J O L, line C A B D, line D G L P, line M N O P, line C F K M, \\odot Q lieson B E I G, \\odot R lieson A F H E, \\odot S lieson K N J H, \\odot T lieson I J O L\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4294.jpg"
-  },
-  {
-    "id": 4394,
-    "problem_id": 4295,
-    "problem": "line C A B D, line D G L P, line M N O P, line C F K M, \\odot Q lieson B E I G, \\odot R lieson A F H E, \\odot S lieson K N J H, \\odot T lieson I J O L, line C A B D, line D G L P, line M N O P, line C F K M, \\odot Q lieson B E I G, \\odot R lieson A F H E, \\odot S lieson K N J H, \\odot T lieson I J O L\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4295.jpg"
-  },
-  {
-    "id": 4395,
-    "problem_id": 4296,
-    "problem": "line A D, line A B C, line D C, line B D, line A D, line A B C, line D C, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4296.jpg"
-  },
-  {
-    "id": 4396,
-    "problem_id": 4297,
-    "problem": "line A D, line A B C, line D C, line B D, line A D, line A B C, line D C, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4297.jpg"
-  },
-  {
-    "id": 4397,
-    "problem_id": 4298,
-    "problem": "line B C D, line B E, line E D, line A B, line A D, line A C E, line B C D, line B E, line E D, line A B, line A D, line A C E\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4298.jpg"
-  },
-  {
-    "id": 4398,
-    "problem_id": 4299,
-    "problem": "line R T A, line R S, line S T, line R T A, line R S, line S T\nWhat is the length of SR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4299.jpg"
-  },
-  {
-    "id": 4399,
-    "problem_id": 4300,
-    "problem": "line R T A, line R S, line S T, line R T A, line R S, line S T\nWhat is the length of SR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4300.jpg"
-  },
-  {
-    "id": 4400,
-    "problem_id": 4301,
-    "problem": "line R T A, line R S, line S T, line R T A, line R S, line S T\nWhat is the length of SR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4301.jpg"
-  },
-  {
-    "id": 4401,
-    "problem_id": 4302,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4302.jpg"
-  },
-  {
-    "id": 4402,
-    "problem_id": 4303,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4303.jpg"
-  },
-  {
-    "id": 4403,
-    "problem_id": 4304,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4304.jpg"
-  },
-  {
-    "id": 4404,
-    "problem_id": 4305,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4305.jpg"
-  },
-  {
-    "id": 4405,
-    "problem_id": 4306,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4306.jpg"
-  },
-  {
-    "id": 4406,
-    "problem_id": 4307,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4307.jpg"
-  },
-  {
-    "id": 4407,
-    "problem_id": 4308,
-    "problem": "line A B, line C A, line C B, line D E, line F D, line F E, line A B, line C A, line C B, line D E, line F D, line F E\nIf \\triangle CAB \\sim \\triangle FDE, find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4308.jpg"
-  },
-  {
-    "id": 4408,
-    "problem_id": 4309,
-    "problem": "line A B, line C A, line C B, line D E, line F D, line F E, line A B, line C A, line C B, line D E, line F D, line F E\nIf \\triangle CAB \\sim \\triangle FDE, find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4309.jpg"
-  },
-  {
-    "id": 4409,
-    "problem_id": 4310,
-    "problem": "line L M, line M A K, line L K, \\odot A lieson L K M, line L M, line M A K, line L K, \\odot A lieson L K M\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4310.jpg"
-  },
-  {
-    "id": 4410,
-    "problem_id": 4311,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find the scale factor of TRAP to EZYD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4311.jpg"
-  },
-  {
-    "id": 4411,
-    "problem_id": 4312,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find the scale factor of TRAP to EZYD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4312.jpg"
-  },
-  {
-    "id": 4412,
-    "problem_id": 4313,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find the scale factor of TRAP to EZYD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4313.jpg"
-  },
-  {
-    "id": 4413,
-    "problem_id": 4314,
-    "problem": "line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R, line Y D, line P A, line Y Z, line D E, line Z E, line R A, line T P, line T R\nTRAP \\sim EZYD. Find the scale factor of TRAP to EZYD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4314.jpg"
-  },
-  {
-    "id": 4415,
-    "problem_id": 4315,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4315.jpg"
-  },
-  {
-    "id": 4416,
-    "problem_id": 4316,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4316.jpg"
-  },
-  {
-    "id": 4417,
-    "problem_id": 4317,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4317.jpg"
-  },
-  {
-    "id": 4418,
-    "problem_id": 4318,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4318.jpg"
-  },
-  {
-    "id": 4419,
-    "problem_id": 4319,
-    "problem": "line A E F J, line H F G I, line B E D C, line A E F J, line H F G I, line B E D C\nFind m \\angle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4319.jpg"
-  },
-  {
-    "id": 4420,
-    "problem_id": 4320,
-    "problem": "line A E F J, line H F G I, line B E D C, line A E F J, line H F G I, line B E D C\nFind m \\angle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4320.jpg"
-  },
-  {
-    "id": 4421,
-    "problem_id": 4321,
-    "problem": "line A E F J, line H F G I, line B E D C, line A E F J, line H F G I, line B E D C\nFind m \\angle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4321.jpg"
-  },
-  {
-    "id": 4422,
-    "problem_id": 4322,
-    "problem": "line A E F J, line H F G I, line B E D C, line A E F J, line H F G I, line B E D C\nFind m \\angle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4322.jpg"
-  },
-  {
-    "id": 4423,
-    "problem_id": 4323,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable y for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4323.jpg"
-  },
-  {
-    "id": 4424,
-    "problem_id": 4324,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable y for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4324.jpg"
-  },
-  {
-    "id": 4425,
-    "problem_id": 4325,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable y for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4325.jpg"
-  },
-  {
-    "id": 4426,
-    "problem_id": 4326,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable y for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4326.jpg"
-  },
-  {
-    "id": 4427,
-    "problem_id": 4327,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable y for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4327.jpg"
-  },
-  {
-    "id": 4428,
-    "problem_id": 4328,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable y for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4328.jpg"
-  },
-  {
-    "id": 4429,
-    "problem_id": 4329,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4329.jpg"
-  },
-  {
-    "id": 4430,
-    "problem_id": 4330,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4330.jpg"
-  },
-  {
-    "id": 4431,
-    "problem_id": 4331,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4331.jpg"
-  },
-  {
-    "id": 4432,
-    "problem_id": 4332,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4332.jpg"
-  },
-  {
-    "id": 4433,
-    "problem_id": 4333,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4333.jpg"
-  },
-  {
-    "id": 4434,
-    "problem_id": 4334,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4334.jpg"
-  },
-  {
-    "id": 4435,
-    "problem_id": 4335,
-    "problem": "line T P, line T S, line V U, line V S, line P S U, line T P, line T S, line V U, line V S, line P S U\nDetermine m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4335.jpg"
-  },
-  {
-    "id": 4436,
-    "problem_id": 4336,
-    "problem": "line C J L, line L M B, line L K A, line J M, line M K, line C J L, line L M B, line L K A, line J M, line M K\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4336.jpg"
-  },
-  {
-    "id": 4438,
-    "problem_id": 4337,
-    "problem": "line C J L, line L M B, line L K A, line J M, line M K, line C J L, line L M B, line L K A, line J M, line M K\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4337.jpg"
-  },
-  {
-    "id": 4439,
-    "problem_id": 4338,
-    "problem": "line C J L, line L M B, line L K A, line J M, line M K, line C J L, line L M B, line L K A, line J M, line M K\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4338.jpg"
-  },
-  {
-    "id": 4440,
-    "problem_id": 4339,
-    "problem": "line C J L, line L M B, line L K A, line J M, line M K, line C J L, line L M B, line L K A, line J M, line M K\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4339.jpg"
-  },
-  {
-    "id": 4441,
-    "problem_id": 4340,
-    "problem": "line D C, line A B C, line A E D, line E B, line D C, line A B C, line A E D, line E B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4340.jpg"
-  },
-  {
-    "id": 4442,
-    "problem_id": 4341,
-    "problem": "line D C, line A B C, line A E D, line E B, line D C, line A B C, line A E D, line E B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4341.jpg"
-  },
-  {
-    "id": 4443,
-    "problem_id": 4342,
-    "problem": "line D C, line A B C, line A E D, line E B, line D C, line A B C, line A E D, line E B\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4342.jpg"
-  },
-  {
-    "id": 4444,
-    "problem_id": 4343,
-    "problem": "line R S, line S T, line U T, line R U, \\odot P lieson R U T S, line R S, line S T, line U T, line R U, \\odot P lieson R U T S\nQuadrilateral RSTU is inscribed in circle P. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4343.jpg"
-  },
-  {
-    "id": 4445,
-    "problem_id": 4344,
-    "problem": "line R S, line S T, line U T, line R U, \\odot P lieson R U T S, line R S, line S T, line U T, line R U, \\odot P lieson R U T S\nQuadrilateral RSTU is inscribed in circle P. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4344.jpg"
-  },
-  {
-    "id": 4446,
-    "problem_id": 4345,
-    "problem": "line R S, line S T, line U T, line R U, \\odot P lieson R U T S, line R S, line S T, line U T, line R U, \\odot P lieson R U T S\nQuadrilateral RSTU is inscribed in circle P. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4345.jpg"
-  },
-  {
-    "id": 4447,
-    "problem_id": 4346,
-    "problem": "line R S, line S T, line U T, line R U, \\odot P lieson R U T S, line R S, line S T, line U T, line R U, \\odot P lieson R U T S\nQuadrilateral RSTU is inscribed in circle P. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4346.jpg"
-  },
-  {
-    "id": 4448,
-    "problem_id": 4347,
-    "problem": "line C O A, line B O, line D O, \\odot O lieson C B A D, line C O A, line B O, line D O, \\odot O lieson C B A D\nWhat is the measure of \\widehat AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4347.jpg"
-  },
-  {
-    "id": 4449,
-    "problem_id": 4348,
-    "problem": "line S T, line T R, line S R, line S T, line T R, line S R\nFind \\cos R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4348.jpg"
-  },
-  {
-    "id": 4450,
-    "problem_id": 4349,
-    "problem": "line S T, line T R, line S R, line S T, line T R, line S R\nFind \\cos R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4349.jpg"
-  },
-  {
-    "id": 4451,
-    "problem_id": 4350,
-    "problem": "line A C D, line E C B, line A B, line B D, line E A, line E D, line A C D, line E C B, line A B, line B D, line E A, line E D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4350.jpg"
-  },
-  {
-    "id": 4452,
-    "problem_id": 4351,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4351.jpg"
-  },
-  {
-    "id": 4453,
-    "problem_id": 4352,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4352.jpg"
-  },
-  {
-    "id": 4454,
-    "problem_id": 4353,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4353.jpg"
-  },
-  {
-    "id": 4455,
-    "problem_id": 4354,
-    "problem": "line W Z, line Y Z, line X Y, line X W, line W Z, line Y Z, line X Y, line X W\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4354.jpg"
-  },
-  {
-    "id": 4456,
-    "problem_id": 4355,
-    "problem": "line R T, line U V, line R U S, line S V T, line R T, line U V, line R U S, line S V T\n\\triangle SUV \\sim \\triangle SRT. Find the length of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4355.jpg"
-  },
-  {
-    "id": 4457,
-    "problem_id": 4356,
-    "problem": "line R T, line U V, line R U S, line S V T, line R T, line U V, line R U S, line S V T\n\\triangle SUV \\sim \\triangle SRT. Find the length of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4356.jpg"
-  },
-  {
-    "id": 4458,
-    "problem_id": 4357,
-    "problem": "line R T, line U V, line R U S, line S V T, line R T, line U V, line R U S, line S V T\n\\triangle SUV \\sim \\triangle SRT. Find the length of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4357.jpg"
-  },
-  {
-    "id": 4459,
-    "problem_id": 4358,
-    "problem": "line I B G E L, line J F G C K, line H A G D M, line I B G E L, line J F G C K, line H A G D M\nIf m \\angle BGC = 4x+7 and m \\angle FGE = 71, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4358.jpg"
-  },
-  {
-    "id": 4460,
-    "problem_id": 4359,
-    "problem": "line I B G E L, line J F G C K, line H A G D M, line I B G E L, line J F G C K, line H A G D M\nIf m \\angle BGC = 4x+7 and m \\angle FGE = 71, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4359.jpg"
-  },
-  {
-    "id": 4461,
-    "problem_id": 4360,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find the measure of \\angle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4360.jpg"
-  },
-  {
-    "id": 4462,
-    "problem_id": 4361,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find the measure of \\angle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4361.jpg"
-  },
-  {
-    "id": 4463,
-    "problem_id": 4362,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find the measure of \\angle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4362.jpg"
-  },
-  {
-    "id": 4464,
-    "problem_id": 4363,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find the measure of \\angle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4363.jpg"
-  },
-  {
-    "id": 4465,
-    "problem_id": 4364,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find the measure of \\angle XYZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4364.jpg"
-  },
-  {
-    "id": 4466,
-    "problem_id": 4365,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4365.jpg"
-  },
-  {
-    "id": 4467,
-    "problem_id": 4366,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4366.jpg"
-  },
-  {
-    "id": 4469,
-    "problem_id": 4367,
-    "problem": "line A C D, line B C, \\odot E lieson B, line A C D, line B C, \\odot E lieson B\nFind the value of variable w. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4367.jpg"
-  },
-  {
-    "id": 4470,
-    "problem_id": 4368,
-    "problem": "line A C D, line B C, \\odot E lieson B, line A C D, line B C, \\odot E lieson B\nFind the value of variable w. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4368.jpg"
-  },
-  {
-    "id": 4471,
-    "problem_id": 4369,
-    "problem": "line B A, line B C, line A D C, \\odot A lieson D B, line B A, line B C, line A D C, \\odot A lieson D B\nThe segment is tangent to the circle. Find AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4369.jpg"
-  },
-  {
-    "id": 4472,
-    "problem_id": 4370,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4370.jpg"
-  },
-  {
-    "id": 4473,
-    "problem_id": 4371,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4371.jpg"
-  },
-  {
-    "id": 4474,
-    "problem_id": 4372,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4372.jpg"
-  },
-  {
-    "id": 4475,
-    "problem_id": 4373,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4373.jpg"
-  },
-  {
-    "id": 4476,
-    "problem_id": 4374,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4374.jpg"
-  },
-  {
-    "id": 4477,
-    "problem_id": 4375,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4375.jpg"
-  },
-  {
-    "id": 4478,
-    "problem_id": 4376,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4376.jpg"
-  },
-  {
-    "id": 4479,
-    "problem_id": 4377,
-    "problem": "line A B, line C A, line C B, line A B, line C A, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4377.jpg"
-  },
-  {
-    "id": 4480,
-    "problem_id": 4378,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4378.jpg"
-  },
-  {
-    "id": 4481,
-    "problem_id": 4379,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4379.jpg"
-  },
-  {
-    "id": 4482,
-    "problem_id": 4380,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4380.jpg"
-  },
-  {
-    "id": 4483,
-    "problem_id": 4381,
-    "problem": "line S V T, line W X T, line W V, line S U W, line V X, line U V, line S V T, line W X T, line W V, line S U W, line V X, line U V\nDetermine m \\angle VWX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4381.jpg"
-  },
-  {
-    "id": 4484,
-    "problem_id": 4382,
-    "problem": "line S V T, line W X T, line W V, line S U W, line V X, line U V, line S V T, line W X T, line W V, line S U W, line V X, line U V\nDetermine m \\angle VWX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4382.jpg"
-  },
-  {
-    "id": 4485,
-    "problem_id": 4383,
-    "problem": "line S V T, line W X T, line W V, line S U W, line V X, line U V, line S V T, line W X T, line W V, line S U W, line V X, line U V\nDetermine m \\angle VWX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4383.jpg"
-  },
-  {
-    "id": 4487,
-    "problem_id": 4384,
-    "problem": "line A B, line B C, line A D, line D C, line A B, line B C, line A D, line D C\nFind y in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4384.jpg"
-  },
-  {
-    "id": 4488,
-    "problem_id": 4385,
-    "problem": "line A B, line B C, line A D, line D C, line A B, line B C, line A D, line D C\nFind y in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4385.jpg"
-  },
-  {
-    "id": 4489,
-    "problem_id": 4386,
-    "problem": "line A B, line B C, line A D, line D C, line A B, line B C, line A D, line D C\nFind y in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4386.jpg"
-  },
-  {
-    "id": 4490,
-    "problem_id": 4387,
-    "problem": "line A B, line B C, line A D, line D C, line A B, line B C, line A D, line D C\nFind y in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4387.jpg"
-  },
-  {
-    "id": 4491,
-    "problem_id": 4388,
-    "problem": "line A B, line B C, line A D, line D C, line A B, line B C, line A D, line D C\nFind y in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4388.jpg"
-  },
-  {
-    "id": 4492,
-    "problem_id": 4389,
-    "problem": "line A F B, line B G D, line E H D, line C I E, line A J C, \\odot K lieson J I H G F, line A F B, line B G D, line E H D, line C I E, line A J C, \\odot K lieson J I H G F\nThe polygon below circumscribes the circle. Find the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4389.jpg"
-  },
-  {
-    "id": 4493,
-    "problem_id": 4390,
-    "problem": "line A B, line B C, line A C, \\odot C lieson A B, line A B, line B C, line A C, \\odot C lieson A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4390.jpg"
-  },
-  {
-    "id": 4494,
-    "problem_id": 4391,
-    "problem": "line A B, line B C, line A C, \\odot C lieson A B, line A B, line B C, line A C, \\odot C lieson A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4391.jpg"
-  },
-  {
-    "id": 4495,
-    "problem_id": 4392,
-    "problem": "line A B, line B C, line A C, \\odot C lieson A B, line A B, line B C, line A C, \\odot C lieson A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4392.jpg"
-  },
-  {
-    "id": 4496,
-    "problem_id": 4393,
-    "problem": "line A B, line B C, line A C, \\odot C lieson A B, line A B, line B C, line A C, \\odot C lieson A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4393.jpg"
-  },
-  {
-    "id": 4497,
-    "problem_id": 4394,
-    "problem": "line S T U, line V U, line T V, line R T, line R S, line S T U, line V U, line T V, line R T, line R S\n\\triangle RST \\cong \\triangle VUT. What is the area of \\triangle RST?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4394.jpg"
-  },
-  {
-    "id": 4498,
-    "problem_id": 4395,
-    "problem": "line S T U, line V U, line T V, line R T, line R S, line S T U, line V U, line T V, line R T, line R S\n\\triangle RST \\cong \\triangle VUT. What is the area of \\triangle RST?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4395.jpg"
-  },
-  {
-    "id": 4499,
-    "problem_id": 4396,
-    "problem": "line C B E, line D B A, line C B E, line D B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4396.jpg"
-  },
-  {
-    "id": 4500,
-    "problem_id": 4397,
-    "problem": "line C B E, line D B A, line C B E, line D B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4397.jpg"
-  },
-  {
-    "id": 4501,
-    "problem_id": 4398,
-    "problem": "line C B E, line D B A, line C B E, line D B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4398.jpg"
-  },
-  {
-    "id": 4502,
-    "problem_id": 4399,
-    "problem": "line A B, line D C, line F E, line A D F, line B C E, line A B, line D C, line F E, line A D F, line B C E\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4399.jpg"
-  },
-  {
-    "id": 4503,
-    "problem_id": 4400,
-    "problem": "line A B, line D C, line F E, line A D F, line B C E, line A B, line D C, line F E, line A D F, line B C E\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4400.jpg"
-  },
-  {
-    "id": 4504,
-    "problem_id": 4401,
-    "problem": "line A B, line D C, line F E, line A D F, line B C E, line A B, line D C, line F E, line A D F, line B C E\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4401.jpg"
-  },
-  {
-    "id": 4505,
-    "problem_id": 4402,
-    "problem": "line A B, line D C, line F E, line A D F, line B C E, line A B, line D C, line F E, line A D F, line B C E\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4402.jpg"
-  },
-  {
-    "id": 4506,
-    "problem_id": 4403,
-    "problem": "line C F, line A C E, line D C, line B C, line C F, line A C E, line D C, line B C\nSuppose \\angle 4 and \\angle 5 form a linear pair. If m \\angle 1 = 2x, m \\angle 2 = 3x-20, and m \\angle 3 = x-4, what is m \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4403.jpg"
-  },
-  {
-    "id": 4507,
-    "problem_id": 4404,
-    "problem": "line A D, line A B C, line D C, line B D, line A D, line A B C, line D C, line B D\nFind the value of n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4404.jpg"
-  },
-  {
-    "id": 4508,
-    "problem_id": 4405,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nWhat is the value of y in the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4405.jpg"
-  },
-  {
-    "id": 4509,
-    "problem_id": 4406,
-    "problem": "line C D, line A B, line A C, line B D, line C D, line A B, line A C, line B D\nWhat is the value of y in the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4406.jpg"
-  },
-  {
-    "id": 4510,
-    "problem_id": 4407,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4407.jpg"
-  },
-  {
-    "id": 4511,
-    "problem_id": 4408,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4408.jpg"
-  },
-  {
-    "id": 4512,
-    "problem_id": 4409,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4409.jpg"
-  },
-  {
-    "id": 4513,
-    "problem_id": 4410,
-    "problem": "line J H, line H K, line J K, line P N, line P Q, line N Q, line J H, line H K, line J K, line P N, line P Q, line N Q\nFind HK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4410.jpg"
-  },
-  {
-    "id": 4515,
-    "problem_id": 4411,
-    "problem": "line A B C, line A B C\nWhat is the measure of BC if B is the midpoint of AC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4411.jpg"
-  },
-  {
-    "id": 4516,
-    "problem_id": 4412,
-    "problem": "line A B C, line A B C\nWhat is the measure of BC if B is the midpoint of AC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4412.jpg"
-  },
-  {
-    "id": 4517,
-    "problem_id": 4413,
-    "problem": "line A B C, line A B C\nWhat is the measure of BC if B is the midpoint of AC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4413.jpg"
-  },
-  {
-    "id": 4519,
-    "problem_id": 4414,
-    "problem": "line P M, line J L M, line P L K, line J K, line P M, line J L M, line P L K, line J K\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4414.jpg"
-  },
-  {
-    "id": 4520,
-    "problem_id": 4415,
-    "problem": "line P M, line J L M, line P L K, line J K, line P M, line J L M, line P L K, line J K\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4415.jpg"
-  },
-  {
-    "id": 4521,
-    "problem_id": 4416,
-    "problem": "line P M, line J L M, line P L K, line J K, line P M, line J L M, line P L K, line J K\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4416.jpg"
-  },
-  {
-    "id": 4522,
-    "problem_id": 4417,
-    "problem": "line P M, line J L M, line P L K, line J K, line P M, line J L M, line P L K, line J K\nFind JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4417.jpg"
-  },
-  {
-    "id": 4523,
-    "problem_id": 4418,
-    "problem": "line D P, line C P B, line A P, \\odot P lieson A D C B, line D P, line C P B, line A P, \\odot P lieson A D C B\nWhat is m \\widehat ABD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4418.jpg"
-  },
-  {
-    "id": 4525,
-    "problem_id": 4419,
-    "problem": "line D P, line C P B, line A P, \\odot P lieson A D C B, line D P, line C P B, line A P, \\odot P lieson A D C B\nWhat is m \\widehat ABD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4419.jpg"
-  },
-  {
-    "id": 4526,
-    "problem_id": 4420,
-    "problem": "line D P, line C P B, line A P, \\odot P lieson A D C B, line D P, line C P B, line A P, \\odot P lieson A D C B\nWhat is m \\widehat ABD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4420.jpg"
-  },
-  {
-    "id": 4527,
-    "problem_id": 4421,
-    "problem": "line D P, line C P B, line A P, \\odot P lieson A D C B, line D P, line C P B, line A P, \\odot P lieson A D C B\nWhat is m \\widehat ABD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4421.jpg"
-  },
-  {
-    "id": 4528,
-    "problem_id": 4422,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4422.jpg"
-  },
-  {
-    "id": 4529,
-    "problem_id": 4423,
-    "problem": "line J G M, line H G L, line G K, \\odot G lieson J H M L K, line J G M, line H G L, line G K, \\odot G lieson J H M L K\nFind m \\widehat JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4423.jpg"
-  },
-  {
-    "id": 4530,
-    "problem_id": 4424,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4424.jpg"
-  },
-  {
-    "id": 4531,
-    "problem_id": 4425,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4425.jpg"
-  },
-  {
-    "id": 4532,
-    "problem_id": 4426,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4426.jpg"
-  },
-  {
-    "id": 4533,
-    "problem_id": 4427,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4427.jpg"
-  },
-  {
-    "id": 4534,
-    "problem_id": 4428,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4428.jpg"
-  },
-  {
-    "id": 4535,
-    "problem_id": 4429,
-    "problem": "line D C, line C B, line A B, line D A, line D C, line C B, line A B, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4429.jpg"
-  },
-  {
-    "id": 4536,
-    "problem_id": 4430,
-    "problem": "line E F, line E H, line H G, line F G, line E F, line E H, line H G, line F G\nFind the measure of \\angle EHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4430.jpg"
-  },
-  {
-    "id": 4537,
-    "problem_id": 4431,
-    "problem": "line E F, line E H, line H G, line F G, line E F, line E H, line H G, line F G\nFind the measure of \\angle EHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4431.jpg"
-  },
-  {
-    "id": 4538,
-    "problem_id": 4432,
-    "problem": "line M L, line J M, line J K, line K L, line M L, line J M, line J K, line K L\nUse parallelogram JKLM to find m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4432.jpg"
-  },
-  {
-    "id": 4539,
-    "problem_id": 4433,
-    "problem": "line M L, line J M, line J K, line K L, line M L, line J M, line J K, line K L\nUse parallelogram JKLM to find m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4433.jpg"
-  },
-  {
-    "id": 4540,
-    "problem_id": 4434,
-    "problem": "line S M P N R, line S M P N R\nFind the length of MS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4434.jpg"
-  },
-  {
-    "id": 4541,
-    "problem_id": 4435,
-    "problem": "line S M P N R, line S M P N R\nFind the length of MS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4435.jpg"
-  },
-  {
-    "id": 4542,
-    "problem_id": 4436,
-    "problem": "line S M P N R, line S M P N R\nFind the length of MS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4436.jpg"
-  },
-  {
-    "id": 4543,
-    "problem_id": 4437,
-    "problem": "line S M P N R, line S M P N R\nFind the length of MS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4437.jpg"
-  },
-  {
-    "id": 4544,
-    "problem_id": 4438,
-    "problem": "line S M P N R, line S M P N R\nFind the length of MS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4438.jpg"
-  },
-  {
-    "id": 4545,
-    "problem_id": 4439,
-    "problem": "line A C, line A B, \\odot A lieson C B, line A C, line A B, \\odot A lieson C B\nFind the area of the shaded region of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4439.jpg"
-  },
-  {
-    "id": 4546,
-    "problem_id": 4440,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4440.jpg"
-  },
-  {
-    "id": 4547,
-    "problem_id": 4441,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4441.jpg"
-  },
-  {
-    "id": 4548,
-    "problem_id": 4442,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4442.jpg"
-  },
-  {
-    "id": 4549,
-    "problem_id": 4443,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4443.jpg"
-  },
-  {
-    "id": 4551,
-    "problem_id": 4444,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4444.jpg"
-  },
-  {
-    "id": 4553,
-    "problem_id": 4445,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4445.jpg"
-  },
-  {
-    "id": 4554,
-    "problem_id": 4446,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4446.jpg"
-  },
-  {
-    "id": 4555,
-    "problem_id": 4447,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4447.jpg"
-  },
-  {
-    "id": 4556,
-    "problem_id": 4448,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4448.jpg"
-  },
-  {
-    "id": 4557,
-    "problem_id": 4449,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4449.jpg"
-  },
-  {
-    "id": 4558,
-    "problem_id": 4450,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4450.jpg"
-  },
-  {
-    "id": 4561,
-    "problem_id": 4451,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4451.jpg"
-  },
-  {
-    "id": 4562,
-    "problem_id": 4452,
-    "problem": "line C B, line A B, line D A, line D C, line C B, line A B, line D A, line D C\nIf the perimeter of rectangle ABCD is 44 centimeters, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4452.jpg"
-  },
-  {
-    "id": 4563,
-    "problem_id": 4453,
-    "problem": "line C B, line A B, line D A, line D C, line C B, line A B, line D A, line D C\nIf the perimeter of rectangle ABCD is 44 centimeters, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4453.jpg"
-  },
-  {
-    "id": 4564,
-    "problem_id": 4454,
-    "problem": "line C B, line A B, line D A, line D C, line C B, line A B, line D A, line D C\nIf the perimeter of rectangle ABCD is 44 centimeters, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4454.jpg"
-  },
-  {
-    "id": 4565,
-    "problem_id": 4455,
-    "problem": "line B D A, line C D, line C A, line B C, line B D A, line C D, line C A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4455.jpg"
-  },
-  {
-    "id": 4566,
-    "problem_id": 4456,
-    "problem": "line B D A, line C D, line C A, line B C, line B D A, line C D, line C A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4456.jpg"
-  },
-  {
-    "id": 4567,
-    "problem_id": 4457,
-    "problem": "line B D A, line C D, line C A, line B C, line B D A, line C D, line C A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4457.jpg"
-  },
-  {
-    "id": 4569,
-    "problem_id": 4458,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the radius of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4458.jpg"
-  },
-  {
-    "id": 4570,
-    "problem_id": 4459,
-    "problem": "line A C F, line D E F, line A B D, line B C, line C E, line A C F, line D E F, line A B D, line B C, line C E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4459.jpg"
-  },
-  {
-    "id": 4571,
-    "problem_id": 4460,
-    "problem": "line A C F, line D E F, line A B D, line B C, line C E, line A C F, line D E F, line A B D, line B C, line C E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4460.jpg"
-  },
-  {
-    "id": 4572,
-    "problem_id": 4461,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4461.jpg"
-  },
-  {
-    "id": 4573,
-    "problem_id": 4462,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4462.jpg"
-  },
-  {
-    "id": 4574,
-    "problem_id": 4463,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4463.jpg"
-  },
-  {
-    "id": 4575,
-    "problem_id": 4464,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4464.jpg"
-  },
-  {
-    "id": 4576,
-    "problem_id": 4465,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4465.jpg"
-  },
-  {
-    "id": 4577,
-    "problem_id": 4466,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4466.jpg"
-  },
-  {
-    "id": 4578,
-    "problem_id": 4467,
-    "problem": "line P T R, line Q T S, line P S, line Q R, line Q P, line R S, line P T R, line Q T S, line P S, line Q R, line Q P, line R S\nIn PQRS, m \\angle RSP = 99, PQ = 19.8, and RT = 12.3. Find SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4467.jpg"
-  },
-  {
-    "id": 4579,
-    "problem_id": 4468,
-    "problem": "line A D, line A C, line A E, line B G, line B F, line C D E, line B H, line F G H, line A D, line A C, line A E, line B G, line B F, line C D E, line B H, line F G H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4468.jpg"
-  },
-  {
-    "id": 4580,
-    "problem_id": 4469,
-    "problem": "line A D, line A C, line A E, line B G, line B F, line C D E, line B H, line F G H, line A D, line A C, line A E, line B G, line B F, line C D E, line B H, line F G H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4469.jpg"
-  },
-  {
-    "id": 4581,
-    "problem_id": 4470,
-    "problem": "line A D, line A C, line A E, line B G, line B F, line C D E, line B H, line F G H, line A D, line A C, line A E, line B G, line B F, line C D E, line B H, line F G H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4470.jpg"
-  },
-  {
-    "id": 4583,
-    "problem_id": 4471,
-    "problem": "line E C A, line F B A, \\odot G lieson D B C, line E C A, line F B A, \\odot G lieson D B C\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4471.jpg"
-  },
-  {
-    "id": 4584,
-    "problem_id": 4472,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle GJH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4472.jpg"
-  },
-  {
-    "id": 4585,
-    "problem_id": 4473,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle GJH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4473.jpg"
-  },
-  {
-    "id": 4586,
-    "problem_id": 4474,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle GJH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4474.jpg"
-  },
-  {
-    "id": 4587,
-    "problem_id": 4475,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle GJH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4475.jpg"
-  },
-  {
-    "id": 4588,
-    "problem_id": 4476,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle GJH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4476.jpg"
-  },
-  {
-    "id": 4589,
-    "problem_id": 4477,
-    "problem": "line K D J H I, line B E J, line J G C, line A F J, line K D J H I, line B E J, line J G C, line A F J\nFind the measure of \\angle GJH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4477.jpg"
-  },
-  {
-    "id": 4590,
-    "problem_id": 4478,
-    "problem": "line A B, line C D E, line A D, line A C, line B E, \\odot F lieson E B, line A B, line C D E, line A D, line A C, line B E, \\odot F lieson E B\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4478.jpg"
-  },
-  {
-    "id": 4591,
-    "problem_id": 4479,
-    "problem": "line A B, line C D E, line A D, line A C, line B E, \\odot F lieson E B, line A B, line C D E, line A D, line A C, line B E, \\odot F lieson E B\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4479.jpg"
-  },
-  {
-    "id": 4592,
-    "problem_id": 4480,
-    "problem": "line C B, line A B, line E D, line E F, line A C, line D F, line C B, line A B, line E D, line E F, line A C, line D F\n\\triangle ABC \\sim \\triangle FED. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4480.jpg"
-  },
-  {
-    "id": 4593,
-    "problem_id": 4481,
-    "problem": "line C B, line A B, line E D, line E F, line A C, line D F, line C B, line A B, line E D, line E F, line A C, line D F\n\\triangle ABC \\sim \\triangle FED. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4481.jpg"
-  },
-  {
-    "id": 4594,
-    "problem_id": 4482,
-    "problem": "line C B, line A B, line E D, line E F, line A C, line D F, line C B, line A B, line E D, line E F, line A C, line D F\n\\triangle ABC \\sim \\triangle FED. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4482.jpg"
-  },
-  {
-    "id": 4595,
-    "problem_id": 4483,
-    "problem": "line C B, line A B, line E D, line E F, line A C, line D F, line C B, line A B, line E D, line E F, line A C, line D F\n\\triangle ABC \\sim \\triangle FED. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4483.jpg"
-  },
-  {
-    "id": 4596,
-    "problem_id": 4484,
-    "problem": "line C B, line A B, line E D, line E F, line A C, line D F, line C B, line A B, line E D, line E F, line A C, line D F\n\\triangle ABC \\sim \\triangle FED. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4484.jpg"
-  },
-  {
-    "id": 4597,
-    "problem_id": 4485,
-    "problem": "line C B, line A B, line E D, line E F, line A C, line D F, line C B, line A B, line E D, line E F, line A C, line D F\n\\triangle ABC \\sim \\triangle FED. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4485.jpg"
-  },
-  {
-    "id": 4598,
-    "problem_id": 4486,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4486.jpg"
-  },
-  {
-    "id": 4599,
-    "problem_id": 4487,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4487.jpg"
-  },
-  {
-    "id": 4600,
-    "problem_id": 4488,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4488.jpg"
-  },
-  {
-    "id": 4601,
-    "problem_id": 4489,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4489.jpg"
-  },
-  {
-    "id": 4602,
-    "problem_id": 4490,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4490.jpg"
-  },
-  {
-    "id": 4603,
-    "problem_id": 4491,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4491.jpg"
-  },
-  {
-    "id": 4604,
-    "problem_id": 4492,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4492.jpg"
-  },
-  {
-    "id": 4605,
-    "problem_id": 4493,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4493.jpg"
-  },
-  {
-    "id": 4606,
-    "problem_id": 4494,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4494.jpg"
-  },
-  {
-    "id": 4607,
-    "problem_id": 4495,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4495.jpg"
-  },
-  {
-    "id": 4608,
-    "problem_id": 4496,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4496.jpg"
-  },
-  {
-    "id": 4609,
-    "problem_id": 4497,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4497.jpg"
-  },
-  {
-    "id": 4610,
-    "problem_id": 4498,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4498.jpg"
-  },
-  {
-    "id": 4611,
-    "problem_id": 4499,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\sin V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4499.jpg"
-  },
-  {
-    "id": 4612,
-    "problem_id": 4500,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4500.jpg"
-  },
-  {
-    "id": 4613,
-    "problem_id": 4501,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4501.jpg"
-  },
-  {
-    "id": 4614,
-    "problem_id": 4502,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4502.jpg"
-  },
-  {
-    "id": 4615,
-    "problem_id": 4503,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4503.jpg"
-  },
-  {
-    "id": 4617,
-    "problem_id": 4504,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4504.jpg"
-  },
-  {
-    "id": 4618,
-    "problem_id": 4505,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4505.jpg"
-  },
-  {
-    "id": 4619,
-    "problem_id": 4506,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4506.jpg"
-  },
-  {
-    "id": 4620,
-    "problem_id": 4507,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4507.jpg"
-  },
-  {
-    "id": 4621,
-    "problem_id": 4508,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4508.jpg"
-  },
-  {
-    "id": 4622,
-    "problem_id": 4509,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4509.jpg"
-  },
-  {
-    "id": 4623,
-    "problem_id": 4510,
-    "problem": "line G H, line F H, line F G, line G H, line F H, line F G\nFind FH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4510.jpg"
-  },
-  {
-    "id": 4624,
-    "problem_id": 4511,
-    "problem": "line X W, line X Y, line W Y, line X W, line X Y, line W Y\nFind the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4511.jpg"
-  },
-  {
-    "id": 4625,
-    "problem_id": 4512,
-    "problem": "line X W, line X Y, line W Y, line X W, line X Y, line W Y\nFind the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4512.jpg"
-  },
-  {
-    "id": 4626,
-    "problem_id": 4513,
-    "problem": "line X W, line X Y, line W Y, line X W, line X Y, line W Y\nFind the length of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4513.jpg"
-  },
-  {
-    "id": 4627,
-    "problem_id": 4514,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4514.jpg"
-  },
-  {
-    "id": 4628,
-    "problem_id": 4515,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4515.jpg"
-  },
-  {
-    "id": 4629,
-    "problem_id": 4516,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4516.jpg"
-  },
-  {
-    "id": 4630,
-    "problem_id": 4517,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4517.jpg"
-  },
-  {
-    "id": 4631,
-    "problem_id": 4518,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4518.jpg"
-  },
-  {
-    "id": 4632,
-    "problem_id": 4519,
-    "problem": "line J N C, line J Z B, line A I J, line N Z, line I N, line J N C, line J Z B, line A I J, line N Z, line I N\nFind the measure of \\angle NJZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4519.jpg"
-  },
-  {
-    "id": 4633,
-    "problem_id": 4520,
-    "problem": "line A C, line B C, \\odot C lieson A B, line A C, line B C, \\odot C lieson A B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4520.jpg"
-  },
-  {
-    "id": 4634,
-    "problem_id": 4521,
-    "problem": "line R V, line V U T, line R S T, line S U, line R V, line V U T, line R S T, line S U\nFind the length of VR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4521.jpg"
-  },
-  {
-    "id": 4635,
-    "problem_id": 4522,
-    "problem": "line R V, line V U T, line R S T, line S U, line R V, line V U T, line R S T, line S U\nFind the length of VR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4522.jpg"
-  },
-  {
-    "id": 4636,
-    "problem_id": 4523,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind m \\angle UTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4523.jpg"
-  },
-  {
-    "id": 4637,
-    "problem_id": 4524,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind m \\angle UTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4524.jpg"
-  },
-  {
-    "id": 4638,
-    "problem_id": 4525,
-    "problem": "line C D T U E, line A D F, line B T S G, line C D T U E, line A D F, line B T S G\nFind m \\angle UTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4525.jpg"
-  },
-  {
-    "id": 4639,
-    "problem_id": 4526,
-    "problem": "line A E H, line A B C, line H I J, line C G J, line D F, \\odot F lieson E I G D B, line A E H, line A B C, line H I J, line C G J, line D F, \\odot F lieson E I G D B\nFind x. Assume that any segment that appears to be tangent is tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4526.jpg"
-  },
-  {
-    "id": 4640,
-    "problem_id": 4527,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4527.jpg"
-  },
-  {
-    "id": 4642,
-    "problem_id": 4528,
-    "problem": "line A B C, line D B, line D C, line A D, line A B C, line D B, line D C, line A D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4528.jpg"
-  },
-  {
-    "id": 4643,
-    "problem_id": 4529,
-    "problem": "line B D A, line D C, \\odot D lieson A C B, line B D A, line D C, \\odot D lieson A C B\nDetermine the measure of \\widehat BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4529.jpg"
-  },
-  {
-    "id": 4644,
-    "problem_id": 4530,
-    "problem": "line B D A, line D C, \\odot D lieson A C B, line B D A, line D C, \\odot D lieson A C B\nDetermine the measure of \\widehat BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4530.jpg"
-  },
-  {
-    "id": 4645,
-    "problem_id": 4531,
-    "problem": "line R P T, line Q T, line Q R, line T S, line Q P S, line R S, line R P T, line Q T, line Q R, line T S, line Q P S, line R S\nIn rhombus QRST, what is RT?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4531.jpg"
-  },
-  {
-    "id": 4646,
-    "problem_id": 4532,
-    "problem": "line R P T, line Q T, line Q R, line T S, line Q P S, line R S, line R P T, line Q T, line Q R, line T S, line Q P S, line R S\nIn rhombus QRST, what is RT?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4532.jpg"
-  },
-  {
-    "id": 4647,
-    "problem_id": 4533,
-    "problem": "line R P T, line Q T, line Q R, line T S, line Q P S, line R S, line R P T, line Q T, line Q R, line T S, line Q P S, line R S\nIn rhombus QRST, what is RT?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4533.jpg"
-  },
-  {
-    "id": 4648,
-    "problem_id": 4534,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4534.jpg"
-  },
-  {
-    "id": 4649,
-    "problem_id": 4535,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4535.jpg"
-  },
-  {
-    "id": 4650,
-    "problem_id": 4536,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4536.jpg"
-  },
-  {
-    "id": 4651,
-    "problem_id": 4537,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4537.jpg"
-  },
-  {
-    "id": 4652,
-    "problem_id": 4538,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable x for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4538.jpg"
-  },
-  {
-    "id": 4653,
-    "problem_id": 4539,
-    "problem": "line F H D, line D G, line E H G, line E D, line E F, line F G, line F H D, line D G, line E H G, line E D, line E F, line F G\nUse parallelogram DEFG. Find the perimeter of \\parallelogram DEFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4539.jpg"
-  },
-  {
-    "id": 4654,
-    "problem_id": 4540,
-    "problem": "line F H D, line D G, line E H G, line E D, line E F, line F G, line F H D, line D G, line E H G, line E D, line E F, line F G\nUse parallelogram DEFG. Find the perimeter of \\parallelogram DEFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4540.jpg"
-  },
-  {
-    "id": 4655,
-    "problem_id": 4541,
-    "problem": "line F H D, line D G, line E H G, line E D, line E F, line F G, line F H D, line D G, line E H G, line E D, line E F, line F G\nUse parallelogram DEFG. Find the perimeter of \\parallelogram DEFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4541.jpg"
-  },
-  {
-    "id": 4656,
-    "problem_id": 4542,
-    "problem": "line F H D, line D G, line E H G, line E D, line E F, line F G, line F H D, line D G, line E H G, line E D, line E F, line F G\nUse parallelogram DEFG. Find the perimeter of \\parallelogram DEFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4542.jpg"
-  },
-  {
-    "id": 4657,
-    "problem_id": 4543,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4543.jpg"
-  },
-  {
-    "id": 4658,
-    "problem_id": 4544,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4544.jpg"
-  },
-  {
-    "id": 4659,
-    "problem_id": 4545,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4545.jpg"
-  },
-  {
-    "id": 4660,
-    "problem_id": 4546,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4546.jpg"
-  },
-  {
-    "id": 4661,
-    "problem_id": 4547,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4547.jpg"
-  },
-  {
-    "id": 4662,
-    "problem_id": 4548,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4548.jpg"
-  },
-  {
-    "id": 4663,
-    "problem_id": 4549,
-    "problem": "line B A, line B C, line D C, line A D, \\odot E lieson B A D C, line B A, line B C, line D C, line A D, \\odot E lieson B A D C\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4549.jpg"
-  },
-  {
-    "id": 4664,
-    "problem_id": 4550,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4550.jpg"
-  },
-  {
-    "id": 4665,
-    "problem_id": 4551,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4551.jpg"
-  },
-  {
-    "id": 4666,
-    "problem_id": 4552,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4552.jpg"
-  },
-  {
-    "id": 4667,
-    "problem_id": 4553,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4553.jpg"
-  },
-  {
-    "id": 4668,
-    "problem_id": 4554,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4554.jpg"
-  },
-  {
-    "id": 4669,
-    "problem_id": 4555,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4555.jpg"
-  },
-  {
-    "id": 4670,
-    "problem_id": 4556,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4556.jpg"
-  },
-  {
-    "id": 4671,
-    "problem_id": 4557,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4557.jpg"
-  },
-  {
-    "id": 4672,
-    "problem_id": 4558,
-    "problem": "line B C D, line A D, line B A, line A C, line B C D, line A D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4558.jpg"
-  },
-  {
-    "id": 4673,
-    "problem_id": 4559,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4559.jpg"
-  },
-  {
-    "id": 4674,
-    "problem_id": 4560,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4560.jpg"
-  },
-  {
-    "id": 4675,
-    "problem_id": 4561,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4561.jpg"
-  },
-  {
-    "id": 4677,
-    "problem_id": 4562,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4562.jpg"
-  },
-  {
-    "id": 4678,
-    "problem_id": 4563,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable y for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4563.jpg"
-  },
-  {
-    "id": 4679,
-    "problem_id": 4564,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable y for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4564.jpg"
-  },
-  {
-    "id": 4680,
-    "problem_id": 4565,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of the variable y for the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4565.jpg"
-  },
-  {
-    "id": 4681,
-    "problem_id": 4566,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4566.jpg"
-  },
-  {
-    "id": 4682,
-    "problem_id": 4567,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4567.jpg"
-  },
-  {
-    "id": 4683,
-    "problem_id": 4568,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4568.jpg"
-  },
-  {
-    "id": 4684,
-    "problem_id": 4569,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4569.jpg"
-  },
-  {
-    "id": 4685,
-    "problem_id": 4570,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4570.jpg"
-  },
-  {
-    "id": 4686,
-    "problem_id": 4571,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4571.jpg"
-  },
-  {
-    "id": 4687,
-    "problem_id": 4572,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4572.jpg"
-  },
-  {
-    "id": 4688,
-    "problem_id": 4573,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind x if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4573.jpg"
-  },
-  {
-    "id": 4689,
-    "problem_id": 4574,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind x if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4574.jpg"
-  },
-  {
-    "id": 4690,
-    "problem_id": 4575,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind x if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4575.jpg"
-  },
-  {
-    "id": 4691,
-    "problem_id": 4576,
-    "problem": "line B C, line D C, line A D, line A B, line D E B, line A E C, line B C, line D C, line A D, line A B, line D E B, line A E C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4576.jpg"
-  },
-  {
-    "id": 4692,
-    "problem_id": 4577,
-    "problem": "line B C, line D C, line A D, line A B, line D E B, line A E C, line B C, line D C, line A D, line A B, line D E B, line A E C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4577.jpg"
-  },
-  {
-    "id": 4693,
-    "problem_id": 4578,
-    "problem": "line B C, line D C, line A D, line A B, line D E B, line A E C, line B C, line D C, line A D, line A B, line D E B, line A E C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4578.jpg"
-  },
-  {
-    "id": 4694,
-    "problem_id": 4579,
-    "problem": "line B C, line D C, line A D, line A B, line D E B, line A E C, line B C, line D C, line A D, line A B, line D E B, line A E C\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4579.jpg"
-  },
-  {
-    "id": 4695,
-    "problem_id": 4580,
-    "problem": "line T S, line R T, line R S, line T S, line R T, line R S\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4580.jpg"
-  },
-  {
-    "id": 4696,
-    "problem_id": 4581,
-    "problem": "line T S, line R T, line R S, line T S, line R T, line R S\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4581.jpg"
-  },
-  {
-    "id": 4697,
-    "problem_id": 4582,
-    "problem": "line T S, line R T, line R S, line T S, line R T, line R S\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4582.jpg"
-  },
-  {
-    "id": 4698,
-    "problem_id": 4583,
-    "problem": "line T S, line R T, line R S, line T S, line R T, line R S\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4583.jpg"
-  },
-  {
-    "id": 4699,
-    "problem_id": 4584,
-    "problem": "line T S, line R T, line R S, line T S, line R T, line R S\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4584.jpg"
-  },
-  {
-    "id": 4700,
-    "problem_id": 4585,
-    "problem": "line T S, line R T, line R S, line T S, line R T, line R S\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4585.jpg"
-  },
-  {
-    "id": 4701,
-    "problem_id": 4586,
-    "problem": "line A B C, line D C, line F D, line F E B, line F A, line E D, line A B C, line D C, line F D, line F E B, line F A, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4586.jpg"
-  },
-  {
-    "id": 4702,
-    "problem_id": 4587,
-    "problem": "line A B C, line D C, line F D, line F E B, line F A, line E D, line A B C, line D C, line F D, line F E B, line F A, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4587.jpg"
-  },
-  {
-    "id": 4703,
-    "problem_id": 4588,
-    "problem": "line A B C, line D C, line F D, line F E B, line F A, line E D, line A B C, line D C, line F D, line F E B, line F A, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4588.jpg"
-  },
-  {
-    "id": 4704,
-    "problem_id": 4589,
-    "problem": "line C J I H, line D K L G, line B J K E, line A I L F, line C J I H, line D K L G, line B J K E, line A I L F\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4589.jpg"
-  },
-  {
-    "id": 4705,
-    "problem_id": 4590,
-    "problem": "line C J I H, line D K L G, line B J K E, line A I L F, line C J I H, line D K L G, line B J K E, line A I L F\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4590.jpg"
-  },
-  {
-    "id": 4706,
-    "problem_id": 4591,
-    "problem": "line C J I H, line D K L G, line B J K E, line A I L F, line C J I H, line D K L G, line B J K E, line A I L F\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4591.jpg"
-  },
-  {
-    "id": 4707,
-    "problem_id": 4592,
-    "problem": "line G P H, line G R J, line H Q J, line P Q, line P R, line G P H, line G R J, line H Q J, line P Q, line P R\nFind m \\angle RPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4592.jpg"
-  },
-  {
-    "id": 4708,
-    "problem_id": 4593,
-    "problem": "line J H D F, line A C H K, line l lieson I H G, line m lieson B C D E, line J H D F, line A C H K, line l lieson I H G, line m lieson B C D E\nFind the value of x for which line l \\parallel line m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4593.jpg"
-  },
-  {
-    "id": 4709,
-    "problem_id": 4594,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4594.jpg"
-  },
-  {
-    "id": 4710,
-    "problem_id": 4595,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4595.jpg"
-  },
-  {
-    "id": 4711,
-    "problem_id": 4596,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4596.jpg"
-  },
-  {
-    "id": 4712,
-    "problem_id": 4597,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4597.jpg"
-  },
-  {
-    "id": 4713,
-    "problem_id": 4598,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4598.jpg"
-  },
-  {
-    "id": 4714,
-    "problem_id": 4599,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4599.jpg"
-  },
-  {
-    "id": 4715,
-    "problem_id": 4600,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nFind m \\angle D of quadrilateral ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4600.jpg"
-  },
-  {
-    "id": 4716,
-    "problem_id": 4601,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nFind m \\angle D of quadrilateral ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4601.jpg"
-  },
-  {
-    "id": 4717,
-    "problem_id": 4602,
-    "problem": "line Q T, line Q S, \\odot Q lieson T S, line Q T, line Q S, \\odot Q lieson T S\nFind the diameter of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4602.jpg"
-  },
-  {
-    "id": 4718,
-    "problem_id": 4603,
-    "problem": "line A C, line C B, \\odot C lieson B A, line A C, line C B, \\odot C lieson B A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4603.jpg"
-  },
-  {
-    "id": 4719,
-    "problem_id": 4604,
-    "problem": "line A C, line C B, \\odot C lieson B A, line A C, line C B, \\odot C lieson B A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4604.jpg"
-  },
-  {
-    "id": 4720,
-    "problem_id": 4605,
-    "problem": "line A C, line C B, \\odot C lieson B A, line A C, line C B, \\odot C lieson B A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4605.jpg"
-  },
-  {
-    "id": 4721,
-    "problem_id": 4606,
-    "problem": "line A C, line C B, \\odot C lieson B A, line A C, line C B, \\odot C lieson B A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4606.jpg"
-  },
-  {
-    "id": 4722,
-    "problem_id": 4607,
-    "problem": "line A C, line C B, \\odot C lieson B A, line A C, line C B, \\odot C lieson B A\nFind the length of \\widehat AB shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4607.jpg"
-  },
-  {
-    "id": 4723,
-    "problem_id": 4608,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. What is FE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4608.jpg"
-  },
-  {
-    "id": 4724,
-    "problem_id": 4609,
-    "problem": "line H A F, line H D I, line I C G, line F E G, \\odot B lieson D A E C, line H A F, line H D I, line I C G, line F E G, \\odot B lieson D A E C\nThe square is circumscribed to the circle. Find the exact area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4609.jpg"
-  },
-  {
-    "id": 4725,
-    "problem_id": 4610,
-    "problem": "line B C D, line B A, line B E, line A C E, line E D, line A D, line B C D, line B A, line B E, line A C E, line E D, line A D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4610.jpg"
-  },
-  {
-    "id": 4726,
-    "problem_id": 4611,
-    "problem": "line B C D, line B A, line B E, line A C E, line E D, line A D, line B C D, line B A, line B E, line A C E, line E D, line A D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4611.jpg"
-  },
-  {
-    "id": 4727,
-    "problem_id": 4612,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the radius of \\odot T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4612.jpg"
-  },
-  {
-    "id": 4728,
-    "problem_id": 4613,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the radius of \\odot T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4613.jpg"
-  },
-  {
-    "id": 4729,
-    "problem_id": 4614,
-    "problem": "line E D, line F D, \\odot D lieson E F, line E D, line F D, \\odot D lieson E F\nFind the radius of \\odot T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4614.jpg"
-  },
-  {
-    "id": 4730,
-    "problem_id": 4615,
-    "problem": "line A P, line B P, line P C, \\odot P lieson A D C B, line A P, line B P, line P C, \\odot P lieson A D C B\nFind the measure of \\widehat AB for \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4615.jpg"
-  },
-  {
-    "id": 4731,
-    "problem_id": 4616,
-    "problem": "line A C, line A B D, line C D, line C B, line A C, line A B D, line C D, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4616.jpg"
-  },
-  {
-    "id": 4732,
-    "problem_id": 4617,
-    "problem": "line A C, line A B D, line C D, line C B, line A C, line A B D, line C D, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4617.jpg"
-  },
-  {
-    "id": 4733,
-    "problem_id": 4618,
-    "problem": "line A C, line A B D, line C D, line C B, line A C, line A B D, line C D, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4618.jpg"
-  },
-  {
-    "id": 4734,
-    "problem_id": 4619,
-    "problem": "line A C, line A B D, line C D, line C B, line A C, line A B D, line C D, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4619.jpg"
-  },
-  {
-    "id": 4735,
-    "problem_id": 4620,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4620.jpg"
-  },
-  {
-    "id": 4736,
-    "problem_id": 4621,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4621.jpg"
-  },
-  {
-    "id": 4737,
-    "problem_id": 4622,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4622.jpg"
-  },
-  {
-    "id": 4738,
-    "problem_id": 4623,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4623.jpg"
-  },
-  {
-    "id": 4739,
-    "problem_id": 4624,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4624.jpg"
-  },
-  {
-    "id": 4740,
-    "problem_id": 4625,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4625.jpg"
-  },
-  {
-    "id": 4741,
-    "problem_id": 4626,
-    "problem": "line D C B, line A D, line B E, line A C E, line A B, line D E, line D C B, line A D, line B E, line A C E, line A B, line D E\nFind m \\angle 1 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4626.jpg"
-  },
-  {
-    "id": 4742,
-    "problem_id": 4627,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4627.jpg"
-  },
-  {
-    "id": 4743,
-    "problem_id": 4628,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4628.jpg"
-  },
-  {
-    "id": 4744,
-    "problem_id": 4629,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4629.jpg"
-  },
-  {
-    "id": 4745,
-    "problem_id": 4630,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4630.jpg"
-  },
-  {
-    "id": 4746,
-    "problem_id": 4631,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4631.jpg"
-  },
-  {
-    "id": 4747,
-    "problem_id": 4632,
-    "problem": "line A B, line B E, line D E, line A D, line A C E, line D C B, line A B, line B E, line D E, line A D, line A C E, line D C B\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4632.jpg"
-  },
-  {
-    "id": 4748,
-    "problem_id": 4633,
-    "problem": "line B Q D, line A Q C, \\odot Q lieson B A D C, line B Q D, line A Q C, \\odot Q lieson B A D C\nFind m \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4633.jpg"
-  },
-  {
-    "id": 4750,
-    "problem_id": 4634,
-    "problem": "line C D, line D E, \\odot D lieson C E, line C D, line D E, \\odot D lieson C E\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4634.jpg"
-  },
-  {
-    "id": 4751,
-    "problem_id": 4635,
-    "problem": "line A B, line B D, line E D, line C E, line A C, line A B, line B D, line E D, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4635.jpg"
-  },
-  {
-    "id": 4752,
-    "problem_id": 4636,
-    "problem": "line A B, line B D, line E D, line C E, line A C, line A B, line B D, line E D, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4636.jpg"
-  },
-  {
-    "id": 4753,
-    "problem_id": 4637,
-    "problem": "line A B, line B D, line E D, line C E, line A C, line A B, line B D, line E D, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4637.jpg"
-  },
-  {
-    "id": 4754,
-    "problem_id": 4638,
-    "problem": "line A B, line B D, line E D, line C E, line A C, line A B, line B D, line E D, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4638.jpg"
-  },
-  {
-    "id": 4755,
-    "problem_id": 4639,
-    "problem": "line R S, line R Q, \\odot T lieson Q S, line R S, line R Q, \\odot T lieson Q S\nThe segment is tangent to the circle. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4639.jpg"
-  },
-  {
-    "id": 4756,
-    "problem_id": 4640,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4640.jpg"
-  },
-  {
-    "id": 4757,
-    "problem_id": 4641,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4641.jpg"
-  },
-  {
-    "id": 4758,
-    "problem_id": 4642,
-    "problem": "line K G, line H G, line J H, line J K, \\odot A lieson J H G K, line K G, line H G, line J H, line J K, \\odot A lieson J H G K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4642.jpg"
-  },
-  {
-    "id": 4759,
-    "problem_id": 4643,
-    "problem": "line G F, line D A, line D C, line A B, line C B, line E F, line H G, line H E, line G F, line D A, line D C, line A B, line C B, line E F, line H G, line H E\n\\parallelogram ABCD \\sim \\parallelogram EFGH. Find the length of EH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4643.jpg"
-  },
-  {
-    "id": 4760,
-    "problem_id": 4644,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. Solve for b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4644.jpg"
-  },
-  {
-    "id": 4761,
-    "problem_id": 4645,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. Solve for b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4645.jpg"
-  },
-  {
-    "id": 4762,
-    "problem_id": 4646,
-    "problem": "line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W, line X V Z, line X Y, line W Z, line W V Y, line Y Z, line X W\nWXYZ is a parallelogram. Solve for b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4646.jpg"
-  },
-  {
-    "id": 4763,
-    "problem_id": 4647,
-    "problem": "line J L, line J P N, line H P L, line J H, line L N, line H N, line J L, line J P N, line H P L, line J H, line L N, line H N\nIn trapezoid HJLN, JP = 32.5, and HL = 50. Find PN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4647.jpg"
-  },
-  {
-    "id": 4764,
-    "problem_id": 4648,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4648.jpg"
-  },
-  {
-    "id": 4765,
-    "problem_id": 4649,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4649.jpg"
-  },
-  {
-    "id": 4766,
-    "problem_id": 4650,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4650.jpg"
-  },
-  {
-    "id": 4767,
-    "problem_id": 4651,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nWhat is m \\angle A?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4651.jpg"
-  },
-  {
-    "id": 4768,
-    "problem_id": 4652,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nSolve for the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4652.jpg"
-  },
-  {
-    "id": 4769,
-    "problem_id": 4653,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nSolve for the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4653.jpg"
-  },
-  {
-    "id": 4770,
-    "problem_id": 4654,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nSolve for the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4654.jpg"
-  },
-  {
-    "id": 4771,
-    "problem_id": 4655,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nSolve for the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4655.jpg"
-  },
-  {
-    "id": 4772,
-    "problem_id": 4656,
-    "problem": "line C B, line A C, \\odot C lieson B A, line C B, line A C, \\odot C lieson B A\nSolve for the length of \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4656.jpg"
-  },
-  {
-    "id": 4773,
-    "problem_id": 4657,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4657.jpg"
-  },
-  {
-    "id": 4774,
-    "problem_id": 4658,
-    "problem": "line D E I K, line A C H L, line B C E F, line G H I J, line D E I K, line A C H L, line B C E F, line G H I J\nm \\angle 1 = 123. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4658.jpg"
-  },
-  {
-    "id": 4775,
-    "problem_id": 4659,
-    "problem": "line H F C A, line G F E, line B C D, line H F C A, line G F E, line B C D\nFind the value of the variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4659.jpg"
-  },
-  {
-    "id": 4776,
-    "problem_id": 4660,
-    "problem": "line H F C A, line G F E, line B C D, line H F C A, line G F E, line B C D\nFind the value of the variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4660.jpg"
-  },
-  {
-    "id": 4777,
-    "problem_id": 4661,
-    "problem": "line H F C A, line G F E, line B C D, line H F C A, line G F E, line B C D\nFind the value of the variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4661.jpg"
-  },
-  {
-    "id": 4778,
-    "problem_id": 4662,
-    "problem": "line H F C A, line G F E, line B C D, line H F C A, line G F E, line B C D\nFind the value of the variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4662.jpg"
-  },
-  {
-    "id": 4779,
-    "problem_id": 4663,
-    "problem": "line H F C A, line G F E, line B C D, line H F C A, line G F E, line B C D\nFind the value of the variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4663.jpg"
-  },
-  {
-    "id": 4780,
-    "problem_id": 4664,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. Find the measure of \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4664.jpg"
-  },
-  {
-    "id": 4781,
-    "problem_id": 4665,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. Find the measure of \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4665.jpg"
-  },
-  {
-    "id": 4782,
-    "problem_id": 4666,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4666.jpg"
-  },
-  {
-    "id": 4783,
-    "problem_id": 4667,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4667.jpg"
-  },
-  {
-    "id": 4784,
-    "problem_id": 4668,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4668.jpg"
-  },
-  {
-    "id": 4785,
-    "problem_id": 4669,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4669.jpg"
-  },
-  {
-    "id": 4786,
-    "problem_id": 4670,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4670.jpg"
-  },
-  {
-    "id": 4787,
-    "problem_id": 4671,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4671.jpg"
-  },
-  {
-    "id": 4788,
-    "problem_id": 4672,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4672.jpg"
-  },
-  {
-    "id": 4790,
-    "problem_id": 4673,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4673.jpg"
-  },
-  {
-    "id": 4791,
-    "problem_id": 4674,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4674.jpg"
-  },
-  {
-    "id": 4792,
-    "problem_id": 4675,
-    "problem": "line P S, line R S, line Q R, line Q P, line P S, line R S, line Q R, line Q P\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4675.jpg"
-  },
-  {
-    "id": 4793,
-    "problem_id": 4676,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4676.jpg"
-  },
-  {
-    "id": 4794,
-    "problem_id": 4677,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4677.jpg"
-  },
-  {
-    "id": 4795,
-    "problem_id": 4678,
-    "problem": "line A C, line B C, line B A, line A C, line B C, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4678.jpg"
-  },
-  {
-    "id": 4796,
-    "problem_id": 4679,
-    "problem": "line R Q, line R P, line P Q, line R Q, line R P, line P Q\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4679.jpg"
-  },
-  {
-    "id": 4797,
-    "problem_id": 4680,
-    "problem": "line R Q, line R P, line P Q, line R Q, line R P, line P Q\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4680.jpg"
-  },
-  {
-    "id": 4798,
-    "problem_id": 4681,
-    "problem": "line R Q, line R P, line P Q, line R Q, line R P, line P Q\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4681.jpg"
-  },
-  {
-    "id": 4799,
-    "problem_id": 4682,
-    "problem": "line R Q, line R P, line P Q, line R Q, line R P, line P Q\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4682.jpg"
-  },
-  {
-    "id": 4800,
-    "problem_id": 4683,
-    "problem": "line R Q, line R P, line P Q, line R Q, line R P, line P Q\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4683.jpg"
-  },
-  {
-    "id": 4801,
-    "problem_id": 4684,
-    "problem": "line A E F B, line A D, line D E, line C F, line D C, line C B, line A E F B, line A D, line D E, line C F, line D C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4684.jpg"
-  },
-  {
-    "id": 4802,
-    "problem_id": 4685,
-    "problem": "line A E F B, line A D, line D E, line C F, line D C, line C B, line A E F B, line A D, line D E, line C F, line D C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4685.jpg"
-  },
-  {
-    "id": 4803,
-    "problem_id": 4686,
-    "problem": "line A E F B, line A D, line D E, line C F, line D C, line C B, line A E F B, line A D, line D E, line C F, line D C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4686.jpg"
-  },
-  {
-    "id": 4804,
-    "problem_id": 4687,
-    "problem": "line A E F B, line A D, line D E, line C F, line D C, line C B, line A E F B, line A D, line D E, line C F, line D C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4687.jpg"
-  },
-  {
-    "id": 4805,
-    "problem_id": 4688,
-    "problem": "line A E F B, line A D, line D E, line C F, line D C, line C B, line A E F B, line A D, line D E, line C F, line D C, line C B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4688.jpg"
-  },
-  {
-    "id": 4806,
-    "problem_id": 4689,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4689.jpg"
-  },
-  {
-    "id": 4807,
-    "problem_id": 4690,
-    "problem": "line A S X, line R X T, line S R, line S T, line A S X, line R X T, line S R, line S T\nFind the measure of XT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4690.jpg"
-  },
-  {
-    "id": 4808,
-    "problem_id": 4691,
-    "problem": "line A S X, line R X T, line S R, line S T, line A S X, line R X T, line S R, line S T\nFind the measure of XT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4691.jpg"
-  },
-  {
-    "id": 4809,
-    "problem_id": 4692,
-    "problem": "line A S X, line R X T, line S R, line S T, line A S X, line R X T, line S R, line S T\nFind the measure of XT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4692.jpg"
-  },
-  {
-    "id": 4810,
-    "problem_id": 4693,
-    "problem": "line A S X, line R X T, line S R, line S T, line A S X, line R X T, line S R, line S T\nFind the measure of XT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4693.jpg"
-  },
-  {
-    "id": 4811,
-    "problem_id": 4694,
-    "problem": "line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R, line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R\nPolygon BCDE \\cong polygon RSTU. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4694.jpg"
-  },
-  {
-    "id": 4812,
-    "problem_id": 4695,
-    "problem": "line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R, line B C, line C D, line E D, line B E, line R S, line T S, line U T, line U R\nPolygon BCDE \\cong polygon RSTU. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4695.jpg"
-  },
-  {
-    "id": 4813,
-    "problem_id": 4696,
-    "problem": "line A D C, line A B, line B C, line B D, line A D C, line A B, line B C, line B D\nWhat is the area of \\triangle ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4696.jpg"
-  },
-  {
-    "id": 4814,
-    "problem_id": 4697,
-    "problem": "line A D C, line A B, line B C, line B D, line A D C, line A B, line B C, line B D\nWhat is the area of \\triangle ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4697.jpg"
-  },
-  {
-    "id": 4815,
-    "problem_id": 4698,
-    "problem": "line A D C, line A B, line B C, line B D, line A D C, line A B, line B C, line B D\nWhat is the area of \\triangle ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4698.jpg"
-  },
-  {
-    "id": 4816,
-    "problem_id": 4699,
-    "problem": "line A D C, line A B, line B C, line B D, line A D C, line A B, line B C, line B D\nWhat is the area of \\triangle ABC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4699.jpg"
-  },
-  {
-    "id": 4817,
-    "problem_id": 4700,
-    "problem": "line J N C, line J Z B, line A I J, line N Z, line I N, line J N C, line J Z B, line A I J, line N Z, line I N\nFind the measure of \\angle INZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4700.jpg"
-  },
-  {
-    "id": 4818,
-    "problem_id": 4701,
-    "problem": "line J N C, line J Z B, line A I J, line N Z, line I N, line J N C, line J Z B, line A I J, line N Z, line I N\nFind the measure of \\angle INZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4701.jpg"
-  },
-  {
-    "id": 4819,
-    "problem_id": 4702,
-    "problem": "line J N C, line J Z B, line A I J, line N Z, line I N, line J N C, line J Z B, line A I J, line N Z, line I N\nFind the measure of \\angle INZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4702.jpg"
-  },
-  {
-    "id": 4820,
-    "problem_id": 4703,
-    "problem": "line J N C, line J Z B, line A I J, line N Z, line I N, line J N C, line J Z B, line A I J, line N Z, line I N\nFind the measure of \\angle INZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4703.jpg"
-  },
-  {
-    "id": 4822,
-    "problem_id": 4704,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4704.jpg"
-  },
-  {
-    "id": 4823,
-    "problem_id": 4705,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4705.jpg"
-  },
-  {
-    "id": 4824,
-    "problem_id": 4706,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4706.jpg"
-  },
-  {
-    "id": 4825,
-    "problem_id": 4707,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4707.jpg"
-  },
-  {
-    "id": 4826,
-    "problem_id": 4708,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4708.jpg"
-  },
-  {
-    "id": 4827,
-    "problem_id": 4709,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4709.jpg"
-  },
-  {
-    "id": 4828,
-    "problem_id": 4710,
-    "problem": "line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E, line S T, line T U, line S R, line V U, line B C, line R V, line C D, line B A, line E D, line A E\nThe two polygons are similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4710.jpg"
-  },
-  {
-    "id": 4829,
-    "problem_id": 4711,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nUse a calculator to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4711.jpg"
-  },
-  {
-    "id": 4830,
-    "problem_id": 4712,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nUse a calculator to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4712.jpg"
-  },
-  {
-    "id": 4831,
-    "problem_id": 4713,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nUse a calculator to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4713.jpg"
-  },
-  {
-    "id": 4832,
-    "problem_id": 4714,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4714.jpg"
-  },
-  {
-    "id": 4833,
-    "problem_id": 4715,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4715.jpg"
-  },
-  {
-    "id": 4834,
-    "problem_id": 4716,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4716.jpg"
-  },
-  {
-    "id": 4836,
-    "problem_id": 4717,
-    "problem": "line A C D, line B C E, line D E, line B A, line A C D, line B C E, line D E, line B A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4717.jpg"
-  },
-  {
-    "id": 4837,
-    "problem_id": 4718,
-    "problem": "line M R, line Q R, line N M, line N Q, line M L Q, line N L R, line M R, line Q R, line N M, line N Q, line M L Q, line N L R\nUse parallelogram NQRM to find MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4718.jpg"
-  },
-  {
-    "id": 4838,
-    "problem_id": 4719,
-    "problem": "line A C E, line A B D, line A F, \\odot G lieson B F D, \\odot H lieson C E F, line A C E, line A B D, line A F, \\odot G lieson B F D, \\odot H lieson C E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4719.jpg"
-  },
-  {
-    "id": 4839,
-    "problem_id": 4720,
-    "problem": "line D E, line A C D, line A B, line B E, line C E, line D E, line A C D, line A B, line B E, line C E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4720.jpg"
-  },
-  {
-    "id": 4840,
-    "problem_id": 4721,
-    "problem": "line D E, line A C D, line A B, line B E, line C E, line D E, line A C D, line A B, line B E, line C E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4721.jpg"
-  },
-  {
-    "id": 4841,
-    "problem_id": 4722,
-    "problem": "line D E, line A C D, line A B, line B E, line C E, line D E, line A C D, line A B, line B E, line C E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4722.jpg"
-  },
-  {
-    "id": 4842,
-    "problem_id": 4723,
-    "problem": "line D E, line A C D, line A B, line B E, line C E, line D E, line A C D, line A B, line B E, line C E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4723.jpg"
-  },
-  {
-    "id": 4843,
-    "problem_id": 4724,
-    "problem": "line B C, line B D, line A C, line B A, line D C, line B C, line B D, line A C, line B A, line D C\nFind the value of b that would make the quadrilateral a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4724.jpg"
-  },
-  {
-    "id": 4844,
-    "problem_id": 4725,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4725.jpg"
-  },
-  {
-    "id": 4845,
-    "problem_id": 4726,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4726.jpg"
-  },
-  {
-    "id": 4846,
-    "problem_id": 4727,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4727.jpg"
-  },
-  {
-    "id": 4847,
-    "problem_id": 4728,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4728.jpg"
-  },
-  {
-    "id": 4848,
-    "problem_id": 4729,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4729.jpg"
-  },
-  {
-    "id": 4849,
-    "problem_id": 4730,
-    "problem": "line B F, line E F G, line C D E H, line A B D, line B F, line E F G, line C D E H, line A B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4730.jpg"
-  },
-  {
-    "id": 4850,
-    "problem_id": 4731,
-    "problem": "line B F, line E F G, line C D E H, line A B D, line B F, line E F G, line C D E H, line A B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4731.jpg"
-  },
-  {
-    "id": 4851,
-    "problem_id": 4732,
-    "problem": "line B F, line E F G, line C D E H, line A B D, line B F, line E F G, line C D E H, line A B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4732.jpg"
-  },
-  {
-    "id": 4852,
-    "problem_id": 4733,
-    "problem": "line B F, line E F G, line C D E H, line A B D, line B F, line E F G, line C D E H, line A B D\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4733.jpg"
-  },
-  {
-    "id": 4853,
-    "problem_id": 4734,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4734.jpg"
-  },
-  {
-    "id": 4854,
-    "problem_id": 4735,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4735.jpg"
-  },
-  {
-    "id": 4855,
-    "problem_id": 4736,
-    "problem": "line N P, line N O, line P O, line N P, line N O, line P O\nSolve for the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4736.jpg"
-  },
-  {
-    "id": 4856,
-    "problem_id": 4737,
-    "problem": "line G H, line E F, line A G, line A B, line B H, line C E, line D F, line C D, line G H, line E F, line A G, line A B, line B H, line C E, line D F, line C D\nABHG \\sim CDFE. What is the ratio of the perimeters from the ABHG to the CDFE?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4737.jpg"
-  },
-  {
-    "id": 4857,
-    "problem_id": 4738,
-    "problem": "line R S, line S T, line R Q, line Q T, line R S, line S T, line R Q, line Q T\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4738.jpg"
-  },
-  {
-    "id": 4858,
-    "problem_id": 4739,
-    "problem": "line R S, line S T, line R Q, line Q T, line R S, line S T, line R Q, line Q T\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4739.jpg"
-  },
-  {
-    "id": 4859,
-    "problem_id": 4740,
-    "problem": "line A R, line B R, \\odot R lieson A B, line A R, line B R, \\odot R lieson A B\nFind the area of the sector ARB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4740.jpg"
-  },
-  {
-    "id": 4860,
-    "problem_id": 4741,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4741.jpg"
-  },
-  {
-    "id": 4861,
-    "problem_id": 4742,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4742.jpg"
-  },
-  {
-    "id": 4862,
-    "problem_id": 4743,
-    "problem": "line M N R, line M N R\nFind NR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4743.jpg"
-  },
-  {
-    "id": 4863,
-    "problem_id": 4744,
-    "problem": "line M N R, line M N R\nFind NR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4744.jpg"
-  },
-  {
-    "id": 4864,
-    "problem_id": 4745,
-    "problem": "line M N R, line M N R\nFind NR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4745.jpg"
-  },
-  {
-    "id": 4865,
-    "problem_id": 4746,
-    "problem": "line M N R, line M N R\nFind NR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4746.jpg"
-  },
-  {
-    "id": 4866,
-    "problem_id": 4747,
-    "problem": "line A G H D, line E H C, line F G B, line A G H D, line E H C, line F G B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4747.jpg"
-  },
-  {
-    "id": 4867,
-    "problem_id": 4748,
-    "problem": "line A G H D, line E H C, line F G B, line A G H D, line E H C, line F G B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4748.jpg"
-  },
-  {
-    "id": 4868,
-    "problem_id": 4749,
-    "problem": "line A G H D, line E H C, line F G B, line A G H D, line E H C, line F G B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4749.jpg"
-  },
-  {
-    "id": 4869,
-    "problem_id": 4750,
-    "problem": "line A B C, \\odot D lieson A C, line A B C, \\odot D lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4750.jpg"
-  },
-  {
-    "id": 4870,
-    "problem_id": 4751,
-    "problem": "line A B C, \\odot D lieson A C, line A B C, \\odot D lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4751.jpg"
-  },
-  {
-    "id": 4871,
-    "problem_id": 4752,
-    "problem": "line S R, line S T, \\odot S lieson R T, line S R, line S T, \\odot S lieson R T\nSolve for the diameter of \\odot S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4752.jpg"
-  },
-  {
-    "id": 4872,
-    "problem_id": 4753,
-    "problem": "line S R, line S T, \\odot S lieson R T, line S R, line S T, \\odot S lieson R T\nSolve for the diameter of \\odot S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4753.jpg"
-  },
-  {
-    "id": 4873,
-    "problem_id": 4754,
-    "problem": "line A D, line D B C, line A B, line A C, line A D, line D B C, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4754.jpg"
-  },
-  {
-    "id": 4874,
-    "problem_id": 4755,
-    "problem": "line A D, line D B C, line A B, line A C, line A D, line D B C, line A B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4755.jpg"
-  },
-  {
-    "id": 4875,
-    "problem_id": 4756,
-    "problem": "line A D, line E D, line B E, line A B, line A C E, line B C D, line A D, line E D, line B E, line A B, line A C E, line B C D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4756.jpg"
-  },
-  {
-    "id": 4876,
-    "problem_id": 4757,
-    "problem": "line A D, line E D, line B E, line A B, line A C E, line B C D, line A D, line E D, line B E, line A B, line A C E, line B C D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4757.jpg"
-  },
-  {
-    "id": 4877,
-    "problem_id": 4758,
-    "problem": "line A D, line E D, line B E, line A B, line A C E, line B C D, line A D, line E D, line B E, line A B, line A C E, line B C D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4758.jpg"
-  },
-  {
-    "id": 4878,
-    "problem_id": 4759,
-    "problem": "line A D, line E D, line B E, line A B, line A C E, line B C D, line A D, line E D, line B E, line A B, line A C E, line B C D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4759.jpg"
-  },
-  {
-    "id": 4879,
-    "problem_id": 4760,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4760.jpg"
-  },
-  {
-    "id": 4880,
-    "problem_id": 4761,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4761.jpg"
-  },
-  {
-    "id": 4881,
-    "problem_id": 4762,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4762.jpg"
-  },
-  {
-    "id": 4882,
-    "problem_id": 4763,
-    "problem": "line A D C, line B A, line B C, line B D, line A D C, line B A, line B C, line B D\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4763.jpg"
-  },
-  {
-    "id": 4884,
-    "problem_id": 4764,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind the measure of \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4764.jpg"
-  },
-  {
-    "id": 4885,
-    "problem_id": 4765,
-    "problem": "line A B C, line D C, line D A, line D B, line A B C, line D C, line D A, line D B\nFind the measure of \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4765.jpg"
-  },
-  {
-    "id": 4886,
-    "problem_id": 4766,
-    "problem": "line Q A R, line T B S, line A P, line P B, \\odot P lieson Q T S R, line Q A R, line T B S, line A P, line P B, \\odot P lieson Q T S R\nIn \\odot P, QR = 7x-20 and TS = 3x. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4766.jpg"
-  },
-  {
-    "id": 4887,
-    "problem_id": 4767,
-    "problem": "line Q A R, line T B S, line A P, line P B, \\odot P lieson Q T S R, line Q A R, line T B S, line A P, line P B, \\odot P lieson Q T S R\nIn \\odot P, QR = 7x-20 and TS = 3x. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4767.jpg"
-  },
-  {
-    "id": 4888,
-    "problem_id": 4768,
-    "problem": "line Q A R, line T B S, line A P, line P B, \\odot P lieson Q T S R, line Q A R, line T B S, line A P, line P B, \\odot P lieson Q T S R\nIn \\odot P, QR = 7x-20 and TS = 3x. What is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4768.jpg"
-  },
-  {
-    "id": 4889,
-    "problem_id": 4769,
-    "problem": "line A B D, line C D, line A C, line B C, line A B D, line C D, line A C, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4769.jpg"
-  },
-  {
-    "id": 4890,
-    "problem_id": 4770,
-    "problem": "line A B, line C B, line A C, line D A, line D C, line A B, line C B, line A C, line D A, line D C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4770.jpg"
-  },
-  {
-    "id": 4891,
-    "problem_id": 4771,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable r in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4771.jpg"
-  },
-  {
-    "id": 4892,
-    "problem_id": 4772,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable r in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4772.jpg"
-  },
-  {
-    "id": 4893,
-    "problem_id": 4773,
-    "problem": "line A B, line C B, line E C, line E A, line A D C, line E D B, line A B, line C B, line E C, line E A, line A D C, line E D B\nFind the value of variable r in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4773.jpg"
-  },
-  {
-    "id": 4894,
-    "problem_id": 4774,
-    "problem": "line A C, line C B, line A B, \\odot C lieson B A, line A C, line C B, line A B, \\odot C lieson B A\nFind the area of shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4774.jpg"
-  },
-  {
-    "id": 4895,
-    "problem_id": 4775,
-    "problem": "line A C, line C B, line A B, \\odot C lieson B A, line A C, line C B, line A B, \\odot C lieson B A\nFind the area of shaded segment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4775.jpg"
-  },
-  {
-    "id": 4896,
-    "problem_id": 4776,
-    "problem": "line M K, line J B K, line J M, line M B, line M K, line J B K, line J M, line M B\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4776.jpg"
-  },
-  {
-    "id": 4897,
-    "problem_id": 4777,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4777.jpg"
-  },
-  {
-    "id": 4898,
-    "problem_id": 4778,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4778.jpg"
-  },
-  {
-    "id": 4899,
-    "problem_id": 4779,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4779.jpg"
-  },
-  {
-    "id": 4900,
-    "problem_id": 4780,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4780.jpg"
-  },
-  {
-    "id": 4901,
-    "problem_id": 4781,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4781.jpg"
-  },
-  {
-    "id": 4902,
-    "problem_id": 4782,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4782.jpg"
-  },
-  {
-    "id": 4903,
-    "problem_id": 4783,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4783.jpg"
-  },
-  {
-    "id": 4904,
-    "problem_id": 4784,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4784.jpg"
-  },
-  {
-    "id": 4905,
-    "problem_id": 4785,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4785.jpg"
-  },
-  {
-    "id": 4906,
-    "problem_id": 4786,
-    "problem": "line A E C, line A B, line D E B, line D A, line C B, line D C, line A E C, line A B, line D E B, line D A, line C B, line D C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4786.jpg"
-  },
-  {
-    "id": 4907,
-    "problem_id": 4787,
-    "problem": "line A E C, line A B, line D E B, line D A, line C B, line D C, line A E C, line A B, line D E B, line D A, line C B, line D C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4787.jpg"
-  },
-  {
-    "id": 4908,
-    "problem_id": 4788,
-    "problem": "line A E C, line A B, line D E B, line D A, line C B, line D C, line A E C, line A B, line D E B, line D A, line C B, line D C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4788.jpg"
-  },
-  {
-    "id": 4909,
-    "problem_id": 4789,
-    "problem": "line A E C, line A B, line D E B, line D A, line C B, line D C, line A E C, line A B, line D E B, line D A, line C B, line D C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4789.jpg"
-  },
-  {
-    "id": 4910,
-    "problem_id": 4790,
-    "problem": "line A E C, line A B, line D E B, line D A, line C B, line D C, line A E C, line A B, line D E B, line D A, line C B, line D C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4790.jpg"
-  },
-  {
-    "id": 4911,
-    "problem_id": 4791,
-    "problem": "line A E C, line A B, line D E B, line D A, line C B, line D C, line A E C, line A B, line D E B, line D A, line C B, line D C\nFor what value of variable x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4791.jpg"
-  },
-  {
-    "id": 4912,
-    "problem_id": 4792,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind x that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4792.jpg"
-  },
-  {
-    "id": 4913,
-    "problem_id": 4793,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind x that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4793.jpg"
-  },
-  {
-    "id": 4914,
-    "problem_id": 4794,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind x that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4794.jpg"
-  },
-  {
-    "id": 4915,
-    "problem_id": 4795,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind x that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4795.jpg"
-  },
-  {
-    "id": 4916,
-    "problem_id": 4796,
-    "problem": "line C F, line C A, line A B, line B D, line E D, line F E, line C F, line C A, line A B, line B D, line E D, line F E\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4796.jpg"
-  },
-  {
-    "id": 4917,
-    "problem_id": 4797,
-    "problem": "line R V, line V U T, line R S T, line S U, line R V, line V U T, line R S T, line S U\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4797.jpg"
-  },
-  {
-    "id": 4918,
-    "problem_id": 4798,
-    "problem": "line R V, line V U T, line R S T, line S U, line R V, line V U T, line R S T, line S U\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4798.jpg"
-  },
-  {
-    "id": 4919,
-    "problem_id": 4799,
-    "problem": "line D A B, line C F B, line C A, line D E, \\odot C lieson E A F, line D A B, line C F B, line C A, line D E, \\odot C lieson E A F\nFind y. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4799.jpg"
-  },
-  {
-    "id": 4920,
-    "problem_id": 4800,
-    "problem": "line D A B, line C F B, line C A, line D E, \\odot C lieson E A F, line D A B, line C F B, line C A, line D E, \\odot C lieson E A F\nFind y. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4800.jpg"
-  },
-  {
-    "id": 4921,
-    "problem_id": 4801,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4801.jpg"
-  },
-  {
-    "id": 4922,
-    "problem_id": 4802,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4802.jpg"
-  },
-  {
-    "id": 4923,
-    "problem_id": 4803,
-    "problem": "line A B C, line C D, line A E D, line B E, line A B C, line C D, line A E D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4803.jpg"
-  },
-  {
-    "id": 4924,
-    "problem_id": 4804,
-    "problem": "line A B, line B C D, line A D, line A C, line A B, line B C D, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4804.jpg"
-  },
-  {
-    "id": 4925,
-    "problem_id": 4805,
-    "problem": "line A B, line B C D, line A D, line A C, line A B, line B C D, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4805.jpg"
-  },
-  {
-    "id": 4926,
-    "problem_id": 4806,
-    "problem": "line A B, line B C D, line A D, line A C, line A B, line B C D, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4806.jpg"
-  },
-  {
-    "id": 4927,
-    "problem_id": 4807,
-    "problem": "line A B, line B C D, line A D, line A C, line A B, line B C D, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4807.jpg"
-  },
-  {
-    "id": 4928,
-    "problem_id": 4808,
-    "problem": "line A B, line B C D, line A D, line A C, line A B, line B C D, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4808.jpg"
-  },
-  {
-    "id": 4929,
-    "problem_id": 4809,
-    "problem": "line A B, line B C D, line A D, line A C, line A B, line B C D, line A D, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4809.jpg"
-  },
-  {
-    "id": 4930,
-    "problem_id": 4810,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the perimeter of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4810.jpg"
-  },
-  {
-    "id": 4931,
-    "problem_id": 4811,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the perimeter of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4811.jpg"
-  },
-  {
-    "id": 4932,
-    "problem_id": 4812,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the perimeter of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4812.jpg"
-  },
-  {
-    "id": 4933,
-    "problem_id": 4813,
-    "problem": "line Q P, line Q T S, line S P, line R Q, line R T P, line R S, line Q P, line Q T S, line S P, line R Q, line R T P, line R S\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4813.jpg"
-  },
-  {
-    "id": 4934,
-    "problem_id": 4814,
-    "problem": "line Q P, line Q T S, line S P, line R Q, line R T P, line R S, line Q P, line Q T S, line S P, line R Q, line R T P, line R S\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4814.jpg"
-  },
-  {
-    "id": 4935,
-    "problem_id": 4815,
-    "problem": "line Q P, line Q T S, line S P, line R Q, line R T P, line R S, line Q P, line Q T S, line S P, line R Q, line R T P, line R S\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4815.jpg"
-  },
-  {
-    "id": 4936,
-    "problem_id": 4816,
-    "problem": "line Q P, line Q T S, line S P, line R Q, line R T P, line R S, line Q P, line Q T S, line S P, line R Q, line R T P, line R S\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4816.jpg"
-  },
-  {
-    "id": 4937,
-    "problem_id": 4817,
-    "problem": "line L M, line M K P, line N P, line L J N, line J K, line L M, line M K P, line N P, line L J N, line J K\nJL / NJ = MK / PK, find LJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4817.jpg"
-  },
-  {
-    "id": 4938,
-    "problem_id": 4818,
-    "problem": "line L M, line M K P, line N P, line L J N, line J K, line L M, line M K P, line N P, line L J N, line J K\nJL / NJ = MK / PK, find LJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4818.jpg"
-  },
-  {
-    "id": 4939,
-    "problem_id": 4819,
-    "problem": "line C D E, line C A, line D B, line B E, line A D, line C D E, line C A, line D B, line B E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4819.jpg"
-  },
-  {
-    "id": 4940,
-    "problem_id": 4820,
-    "problem": "line C D E, line C A, line D B, line B E, line A D, line C D E, line C A, line D B, line B E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4820.jpg"
-  },
-  {
-    "id": 4941,
-    "problem_id": 4821,
-    "problem": "line C D E, line C A, line D B, line B E, line A D, line C D E, line C A, line D B, line B E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4821.jpg"
-  },
-  {
-    "id": 4942,
-    "problem_id": 4822,
-    "problem": "line C D E, line C A, line D B, line B E, line A D, line C D E, line C A, line D B, line B E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4822.jpg"
-  },
-  {
-    "id": 4943,
-    "problem_id": 4823,
-    "problem": "line C D E, line C A, line D B, line B E, line A D, line C D E, line C A, line D B, line B E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4823.jpg"
-  },
-  {
-    "id": 4944,
-    "problem_id": 4824,
-    "problem": "line C D E, line C A, line D B, line B E, line A D, line C D E, line C A, line D B, line B E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4824.jpg"
-  },
-  {
-    "id": 4945,
-    "problem_id": 4825,
-    "problem": "line B C, line C D, line A D, line B A, line C A, line F H, line E H, line E F, line F G, line H G, line B C, line C D, line A D, line B A, line C A, line F H, line E H, line E F, line F G, line H G\nFor the pair of similar figures, the area of the blue figure is 36 yd^{2}, find the scale factor of the blue to the green figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4825.jpg"
-  },
-  {
-    "id": 4946,
-    "problem_id": 4826,
-    "problem": "line P S Q, line R U Q, line R T P, line U S, line T U, line T S, line P S Q, line R U Q, line R T P, line U S, line T U, line T S\nFind the perimeter of \\triangle STU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4826.jpg"
-  },
-  {
-    "id": 4947,
-    "problem_id": 4827,
-    "problem": "line P S Q, line R U Q, line R T P, line U S, line T U, line T S, line P S Q, line R U Q, line R T P, line U S, line T U, line T S\nFind the perimeter of \\triangle STU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4827.jpg"
-  },
-  {
-    "id": 4948,
-    "problem_id": 4828,
-    "problem": "line P S Q, line R U Q, line R T P, line U S, line T U, line T S, line P S Q, line R U Q, line R T P, line U S, line T U, line T S\nFind the perimeter of \\triangle STU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4828.jpg"
-  },
-  {
-    "id": 4949,
-    "problem_id": 4829,
-    "problem": "line C D B, line C A, line A B, line A D, line C D B, line C A, line A B, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4829.jpg"
-  },
-  {
-    "id": 4950,
-    "problem_id": 4830,
-    "problem": "line C D B, line C A, line A B, line A D, line C D B, line C A, line A B, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4830.jpg"
-  },
-  {
-    "id": 4951,
-    "problem_id": 4831,
-    "problem": "line C D B, line C A, line A B, line A D, line C D B, line C A, line A B, line A D\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4831.jpg"
-  },
-  {
-    "id": 4952,
-    "problem_id": 4832,
-    "problem": "line Q P, line P R, \\odot P lieson Q R S, line Q P, line P R, \\odot P lieson Q R S\nWhat is the length of \\widehat QR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4832.jpg"
-  },
-  {
-    "id": 4953,
-    "problem_id": 4833,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4833.jpg"
-  },
-  {
-    "id": 4954,
-    "problem_id": 4834,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nWhat is the value of h?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4834.jpg"
-  },
-  {
-    "id": 4955,
-    "problem_id": 4835,
-    "problem": "line A D C, line B C, line B A, \\odot A lieson B D, line A D C, line B C, line B A, \\odot A lieson B D\nIf BC = 8 and DC = 4, what is AD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4835.jpg"
-  },
-  {
-    "id": 4957,
-    "problem_id": 4836,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4836.jpg"
-  },
-  {
-    "id": 4958,
-    "problem_id": 4837,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4837.jpg"
-  },
-  {
-    "id": 4959,
-    "problem_id": 4838,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4838.jpg"
-  },
-  {
-    "id": 4960,
-    "problem_id": 4839,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4839.jpg"
-  },
-  {
-    "id": 4961,
-    "problem_id": 4840,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4840.jpg"
-  },
-  {
-    "id": 4962,
-    "problem_id": 4841,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4841.jpg"
-  },
-  {
-    "id": 4963,
-    "problem_id": 4842,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4842.jpg"
-  },
-  {
-    "id": 4964,
-    "problem_id": 4843,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4843.jpg"
-  },
-  {
-    "id": 4965,
-    "problem_id": 4844,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4844.jpg"
-  },
-  {
-    "id": 4966,
-    "problem_id": 4845,
-    "problem": "line C B, line C A, line A B, line C B, line C A, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4845.jpg"
-  },
-  {
-    "id": 4967,
-    "problem_id": 4846,
-    "problem": "line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D, line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4846.jpg"
-  },
-  {
-    "id": 4968,
-    "problem_id": 4847,
-    "problem": "line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D, line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4847.jpg"
-  },
-  {
-    "id": 4969,
-    "problem_id": 4848,
-    "problem": "line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D, line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4848.jpg"
-  },
-  {
-    "id": 4970,
-    "problem_id": 4849,
-    "problem": "line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D, line G H C, line A B C, line F D C, line F E A, \\odot G0 lieson F A C, \\odot G1 lieson E B H D\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4849.jpg"
-  },
-  {
-    "id": 4971,
-    "problem_id": 4850,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind y in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4850.jpg"
-  },
-  {
-    "id": 4972,
-    "problem_id": 4851,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind y in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4851.jpg"
-  },
-  {
-    "id": 4973,
-    "problem_id": 4852,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind y in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4852.jpg"
-  },
-  {
-    "id": 4974,
-    "problem_id": 4853,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind y in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4853.jpg"
-  },
-  {
-    "id": 4975,
-    "problem_id": 4854,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind y in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4854.jpg"
-  },
-  {
-    "id": 4976,
-    "problem_id": 4855,
-    "problem": "line B A, line A C, \\odot A lieson B C, line B A, line A C, \\odot A lieson B C\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4855.jpg"
-  },
-  {
-    "id": 4977,
-    "problem_id": 4856,
-    "problem": "line B A, line A C, \\odot A lieson B C, line B A, line A C, \\odot A lieson B C\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4856.jpg"
-  },
-  {
-    "id": 4978,
-    "problem_id": 4857,
-    "problem": "line B A, line A C, \\odot A lieson B C, line B A, line A C, \\odot A lieson B C\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4857.jpg"
-  },
-  {
-    "id": 4979,
-    "problem_id": 4858,
-    "problem": "line D E, line E C, line D C, line D E, line E C, line D C\nSolve for m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4858.jpg"
-  },
-  {
-    "id": 4980,
-    "problem_id": 4859,
-    "problem": "line D E, line E C, line D C, line D E, line E C, line D C\nSolve for m \\angle E.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4859.jpg"
-  },
-  {
-    "id": 4981,
-    "problem_id": 4860,
-    "problem": "line K J, line K L, line J L, line K J, line K L, line J L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4860.jpg"
-  },
-  {
-    "id": 4982,
-    "problem_id": 4861,
-    "problem": "line K J, line K L, line J L, line K J, line K L, line J L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4861.jpg"
-  },
-  {
-    "id": 4983,
-    "problem_id": 4862,
-    "problem": "line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F, line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4862.jpg"
-  },
-  {
-    "id": 4984,
-    "problem_id": 4863,
-    "problem": "line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F, line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4863.jpg"
-  },
-  {
-    "id": 4985,
-    "problem_id": 4864,
-    "problem": "line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F, line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4864.jpg"
-  },
-  {
-    "id": 4986,
-    "problem_id": 4865,
-    "problem": "line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F, line D C, line A D, line B D, line A B C, line E F, line F G, line E H G, line H F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4865.jpg"
-  },
-  {
-    "id": 4987,
-    "problem_id": 4866,
-    "problem": "line F G, line C E G, line B A, line A C, line B F, line D E, line F G, line C E G, line B A, line A C, line B F, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4866.jpg"
-  },
-  {
-    "id": 4988,
-    "problem_id": 4867,
-    "problem": "line F G, line C E G, line B A, line A C, line B F, line D E, line F G, line C E G, line B A, line A C, line B F, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4867.jpg"
-  },
-  {
-    "id": 4989,
-    "problem_id": 4868,
-    "problem": "line F G, line C E G, line B A, line A C, line B F, line D E, line F G, line C E G, line B A, line A C, line B F, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4868.jpg"
-  },
-  {
-    "id": 4990,
-    "problem_id": 4869,
-    "problem": "line F G, line C E G, line B A, line A C, line B F, line D E, line F G, line C E G, line B A, line A C, line B F, line D E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4869.jpg"
-  },
-  {
-    "id": 4991,
-    "problem_id": 4870,
-    "problem": "line A B, line B E, line A D, line A C, line C D E, line A B, line B E, line A D, line A C, line C D E\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4870.jpg"
-  },
-  {
-    "id": 4992,
-    "problem_id": 4871,
-    "problem": "line A B, line B E, line A D, line A C, line C D E, line A B, line B E, line A D, line A C, line C D E\nWhat is the area of the parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4871.jpg"
-  },
-  {
-    "id": 4993,
-    "problem_id": 4872,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4872.jpg"
-  },
-  {
-    "id": 4994,
-    "problem_id": 4873,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4873.jpg"
-  },
-  {
-    "id": 4995,
-    "problem_id": 4874,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4874.jpg"
-  },
-  {
-    "id": 4996,
-    "problem_id": 4875,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4875.jpg"
-  },
-  {
-    "id": 4997,
-    "problem_id": 4876,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of XW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4876.jpg"
-  },
-  {
-    "id": 4998,
-    "problem_id": 4877,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4877.jpg"
-  },
-  {
-    "id": 4999,
-    "problem_id": 4878,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4878.jpg"
-  },
-  {
-    "id": 5000,
-    "problem_id": 4879,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind the measure of \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4879.jpg"
-  },
-  {
-    "id": 5001,
-    "problem_id": 4880,
-    "problem": "line M L D, line A J K, line C M J, line B K L, line M L D, line A J K, line C M J, line B K L\nFind the value of r.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4880.jpg"
-  },
-  {
-    "id": 5002,
-    "problem_id": 4881,
-    "problem": "line M L D, line A J K, line C M J, line B K L, line M L D, line A J K, line C M J, line B K L\nFind the value of r.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4881.jpg"
-  },
-  {
-    "id": 5003,
-    "problem_id": 4882,
-    "problem": "line M L D, line A J K, line C M J, line B K L, line M L D, line A J K, line C M J, line B K L\nFind the value of r.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4882.jpg"
-  },
-  {
-    "id": 5004,
-    "problem_id": 4883,
-    "problem": "line M L D, line A J K, line C M J, line B K L, line M L D, line A J K, line C M J, line B K L\nFind the value of r.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4883.jpg"
-  },
-  {
-    "id": 5005,
-    "problem_id": 4884,
-    "problem": "line M L D, line A J K, line C M J, line B K L, line M L D, line A J K, line C M J, line B K L\nFind the value of r.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4884.jpg"
-  },
-  {
-    "id": 5006,
-    "problem_id": 4885,
-    "problem": "line M L D, line A J K, line C M J, line B K L, line M L D, line A J K, line C M J, line B K L\nFind the value of r.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4885.jpg"
-  },
-  {
-    "id": 5007,
-    "problem_id": 4886,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nUse parallelogram ABCD to find AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4886.jpg"
-  },
-  {
-    "id": 5008,
-    "problem_id": 4887,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nUse parallelogram ABCD to find AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4887.jpg"
-  },
-  {
-    "id": 5009,
-    "problem_id": 4888,
-    "problem": "line D C, line B C, line A B, line A D, line D C, line B C, line A B, line A D\nUse parallelogram ABCD to find AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4888.jpg"
-  },
-  {
-    "id": 5010,
-    "problem_id": 4889,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4889.jpg"
-  },
-  {
-    "id": 5011,
-    "problem_id": 4890,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4890.jpg"
-  },
-  {
-    "id": 5012,
-    "problem_id": 4891,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4891.jpg"
-  },
-  {
-    "id": 5013,
-    "problem_id": 4892,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4892.jpg"
-  },
-  {
-    "id": 5014,
-    "problem_id": 4893,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4893.jpg"
-  },
-  {
-    "id": 5015,
-    "problem_id": 4894,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4894.jpg"
-  },
-  {
-    "id": 5016,
-    "problem_id": 4895,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nFind the length of KJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4895.jpg"
-  },
-  {
-    "id": 5017,
-    "problem_id": 4896,
-    "problem": "line F E D C, line A C, line B E G, \\odot H lieson B F G D A, line F E D C, line A C, line B E G, \\odot H lieson B F G D A\nWhat is the value of z?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4896.jpg"
-  },
-  {
-    "id": 5018,
-    "problem_id": 4897,
-    "problem": "line F E D C, line A C, line B E G, \\odot H lieson B F G D A, line F E D C, line A C, line B E G, \\odot H lieson B F G D A\nWhat is the value of z?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4897.jpg"
-  },
-  {
-    "id": 5019,
-    "problem_id": 4898,
-    "problem": "line Y Z, line X Y, line X Z, line Y Z, line X Y, line X Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4898.jpg"
-  },
-  {
-    "id": 5020,
-    "problem_id": 4899,
-    "problem": "line Y Z, line X Y, line X Z, line Y Z, line X Y, line X Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4899.jpg"
-  },
-  {
-    "id": 5021,
-    "problem_id": 4900,
-    "problem": "line Y Z, line X Y, line X Z, line Y Z, line X Y, line X Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4900.jpg"
-  },
-  {
-    "id": 5022,
-    "problem_id": 4901,
-    "problem": "line Y Z, line X Y, line X Z, line Y Z, line X Y, line X Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4901.jpg"
-  },
-  {
-    "id": 5023,
-    "problem_id": 4902,
-    "problem": "line Y Z, line X Y, line X Z, line Y Z, line X Y, line X Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4902.jpg"
-  },
-  {
-    "id": 5024,
-    "problem_id": 4903,
-    "problem": "line Y Z, line X Y, line X Z, line Y Z, line X Y, line X Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4903.jpg"
-  },
-  {
-    "id": 5025,
-    "problem_id": 4904,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4904.jpg"
-  },
-  {
-    "id": 5026,
-    "problem_id": 4905,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4905.jpg"
-  },
-  {
-    "id": 5027,
-    "problem_id": 4906,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4906.jpg"
-  },
-  {
-    "id": 5029,
-    "problem_id": 4907,
-    "problem": "line C E, line B A, line A C, line F E, line D F, line B D, line C E, line B A, line A C, line F E, line D F, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4907.jpg"
-  },
-  {
-    "id": 5030,
-    "problem_id": 4908,
-    "problem": "line C E, line B A, line A C, line F E, line D F, line B D, line C E, line B A, line A C, line F E, line D F, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4908.jpg"
-  },
-  {
-    "id": 5031,
-    "problem_id": 4909,
-    "problem": "line C E, line B A, line A C, line F E, line D F, line B D, line C E, line B A, line A C, line F E, line D F, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4909.jpg"
-  },
-  {
-    "id": 5032,
-    "problem_id": 4910,
-    "problem": "line E P, line E G F, line F P, line G P, \\odot P lieson E F, line E P, line E G F, line F P, line G P, \\odot P lieson E F\nFind the area of the shaded region in the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4910.jpg"
-  },
-  {
-    "id": 5033,
-    "problem_id": 4911,
-    "problem": "line E P, line E G F, line F P, line G P, \\odot P lieson E F, line E P, line E G F, line F P, line G P, \\odot P lieson E F\nFind the area of the shaded region in the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4911.jpg"
-  },
-  {
-    "id": 5034,
-    "problem_id": 4912,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4912.jpg"
-  },
-  {
-    "id": 5035,
-    "problem_id": 4913,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4913.jpg"
-  },
-  {
-    "id": 5036,
-    "problem_id": 4914,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4914.jpg"
-  },
-  {
-    "id": 5037,
-    "problem_id": 4915,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4915.jpg"
-  },
-  {
-    "id": 5038,
-    "problem_id": 4916,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4916.jpg"
-  },
-  {
-    "id": 5039,
-    "problem_id": 4917,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4917.jpg"
-  },
-  {
-    "id": 5040,
-    "problem_id": 4918,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4918.jpg"
-  },
-  {
-    "id": 5041,
-    "problem_id": 4919,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4919.jpg"
-  },
-  {
-    "id": 5042,
-    "problem_id": 4920,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4920.jpg"
-  },
-  {
-    "id": 5043,
-    "problem_id": 4921,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4921.jpg"
-  },
-  {
-    "id": 5044,
-    "problem_id": 4922,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind ZY. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4922.jpg"
-  },
-  {
-    "id": 5045,
-    "problem_id": 4923,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind ZY. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4923.jpg"
-  },
-  {
-    "id": 5046,
-    "problem_id": 4924,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind ZY. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4924.jpg"
-  },
-  {
-    "id": 5047,
-    "problem_id": 4925,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind ZY. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4925.jpg"
-  },
-  {
-    "id": 5048,
-    "problem_id": 4926,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind ZY. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4926.jpg"
-  },
-  {
-    "id": 5049,
-    "problem_id": 4927,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is d?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4927.jpg"
-  },
-  {
-    "id": 5050,
-    "problem_id": 4928,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is d?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4928.jpg"
-  },
-  {
-    "id": 5051,
-    "problem_id": 4929,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is d?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4929.jpg"
-  },
-  {
-    "id": 5052,
-    "problem_id": 4930,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is d?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4930.jpg"
-  },
-  {
-    "id": 5053,
-    "problem_id": 4931,
-    "problem": "line A C, line B D C, line B A, line A D, line A C, line B D C, line B A, line A D\nWhat is d?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4931.jpg"
-  },
-  {
-    "id": 5054,
-    "problem_id": 4932,
-    "problem": "line A C E, line A B, line B C D, line A D, line D E, line B E, line A C E, line A B, line B C D, line A D, line D E, line B E\nWhat is the measure of \\angle 1 in the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4932.jpg"
-  },
-  {
-    "id": 5055,
-    "problem_id": 4933,
-    "problem": "line A B C D, line E C, line F B, line F A, line F E, line E D, line A B C D, line E C, line F B, line F A, line F E, line E D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4933.jpg"
-  },
-  {
-    "id": 5056,
-    "problem_id": 4934,
-    "problem": "line A B C D, line E C, line F B, line F A, line F E, line E D, line A B C D, line E C, line F B, line F A, line F E, line E D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4934.jpg"
-  },
-  {
-    "id": 5057,
-    "problem_id": 4935,
-    "problem": "line A B C D, line E C, line F B, line F A, line F E, line E D, line A B C D, line E C, line F B, line F A, line F E, line E D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4935.jpg"
-  },
-  {
-    "id": 5058,
-    "problem_id": 4936,
-    "problem": "line A B C D, line E C, line F B, line F A, line F E, line E D, line A B C D, line E C, line F B, line F A, line F E, line E D\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4936.jpg"
-  },
-  {
-    "id": 5059,
-    "problem_id": 4937,
-    "problem": "line A C D, line A E, line B A, line B C E, line A C D, line A E, line B A, line B C E\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4937.jpg"
-  },
-  {
-    "id": 5060,
-    "problem_id": 4938,
-    "problem": "line A C D, line A E, line B A, line B C E, line A C D, line A E, line B A, line B C E\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4938.jpg"
-  },
-  {
-    "id": 5061,
-    "problem_id": 4939,
-    "problem": "line A C D, line A E, line B A, line B C E, line A C D, line A E, line B A, line B C E\nFind m \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4939.jpg"
-  },
-  {
-    "id": 5062,
-    "problem_id": 4940,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4940.jpg"
-  },
-  {
-    "id": 5063,
-    "problem_id": 4941,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4941.jpg"
-  },
-  {
-    "id": 5064,
-    "problem_id": 4942,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4942.jpg"
-  },
-  {
-    "id": 5065,
-    "problem_id": 4943,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4943.jpg"
-  },
-  {
-    "id": 5066,
-    "problem_id": 4944,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4944.jpg"
-  },
-  {
-    "id": 5067,
-    "problem_id": 4945,
-    "problem": "line J K, line N M, line K M, line J N, line J K, line N M, line K M, line J N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4945.jpg"
-  },
-  {
-    "id": 5068,
-    "problem_id": 4946,
-    "problem": "line A B, line A D, line A C, \\odot R lieson B C, \\odot Q lieson D C, line A B, line A D, line A C, \\odot R lieson B C, \\odot Q lieson D C\nFind CA. Assume that segments that appear tangent to circles are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4946.jpg"
-  },
-  {
-    "id": 5069,
-    "problem_id": 4947,
-    "problem": "line A B, line A D, line A C, \\odot R lieson B C, \\odot Q lieson D C, line A B, line A D, line A C, \\odot R lieson B C, \\odot Q lieson D C\nFind CA. Assume that segments that appear tangent to circles are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4947.jpg"
-  },
-  {
-    "id": 5070,
-    "problem_id": 4948,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of variable c in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4948.jpg"
-  },
-  {
-    "id": 5071,
-    "problem_id": 4949,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of variable c in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4949.jpg"
-  },
-  {
-    "id": 5072,
-    "problem_id": 4950,
-    "problem": "line C D, line B D, line A C, line A B, line C D, line B D, line A C, line A B\nFind the value of variable c in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4950.jpg"
-  },
-  {
-    "id": 5073,
-    "problem_id": 4951,
-    "problem": "\\odot A lieson J K L, \\odot A lieson J K L\nFind m \\widehat JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4951.jpg"
-  },
-  {
-    "id": 5074,
-    "problem_id": 4952,
-    "problem": "\\odot A lieson J K L, \\odot A lieson J K L\nFind m \\widehat JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4952.jpg"
-  },
-  {
-    "id": 5075,
-    "problem_id": 4953,
-    "problem": "\\odot A lieson J K L, \\odot A lieson J K L\nFind m \\widehat JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4953.jpg"
-  },
-  {
-    "id": 5076,
-    "problem_id": 4954,
-    "problem": "line B A D, line B P E, line B C F, line A P, line C P, line B A D, line B P E, line B C F, line A P, line C P\nFind CP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4954.jpg"
-  },
-  {
-    "id": 5077,
-    "problem_id": 4955,
-    "problem": "line B A D, line B P E, line B C F, line A P, line C P, line B A D, line B P E, line B C F, line A P, line C P\nFind CP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4955.jpg"
-  },
-  {
-    "id": 5078,
-    "problem_id": 4956,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4956.jpg"
-  },
-  {
-    "id": 5079,
-    "problem_id": 4957,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4957.jpg"
-  },
-  {
-    "id": 5080,
-    "problem_id": 4958,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4958.jpg"
-  },
-  {
-    "id": 5081,
-    "problem_id": 4959,
-    "problem": "line M N, line L N, line L M, line S R, line S Q, line R Q, line M N, line L N, line L M, line S R, line S Q, line R Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4959.jpg"
-  },
-  {
-    "id": 5082,
-    "problem_id": 4960,
-    "problem": "line M N, line L N, line L M, line S R, line S Q, line R Q, line M N, line L N, line L M, line S R, line S Q, line R Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4960.jpg"
-  },
-  {
-    "id": 5083,
-    "problem_id": 4961,
-    "problem": "line M N, line L N, line L M, line S R, line S Q, line R Q, line M N, line L N, line L M, line S R, line S Q, line R Q\n\\triangle LMN \\cong \\triangle QRS. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4961.jpg"
-  },
-  {
-    "id": 5084,
-    "problem_id": 4962,
-    "problem": "line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D, line B C, line B A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4962.jpg"
-  },
-  {
-    "id": 5085,
-    "problem_id": 4963,
-    "problem": "line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D, line B C, line B A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4963.jpg"
-  },
-  {
-    "id": 5086,
-    "problem_id": 4964,
-    "problem": "line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D, line B C, line B A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4964.jpg"
-  },
-  {
-    "id": 5087,
-    "problem_id": 4965,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4965.jpg"
-  },
-  {
-    "id": 5088,
-    "problem_id": 4966,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4966.jpg"
-  },
-  {
-    "id": 5089,
-    "problem_id": 4967,
-    "problem": "line Q T, line R S T, line R Q, line S Q, line Q T, line R S T, line R Q, line S Q\nFind the length of QS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4967.jpg"
-  },
-  {
-    "id": 5090,
-    "problem_id": 4968,
-    "problem": "line A B, line B D, line C D, line A C, line A D, line A B, line B D, line C D, line A C, line A D\nFind the value of q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4968.jpg"
-  },
-  {
-    "id": 5091,
-    "problem_id": 4969,
-    "problem": "line A B, line B D, line C D, line A C, line A D, line A B, line B D, line C D, line A C, line A D\nFind the value of q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4969.jpg"
-  },
-  {
-    "id": 5092,
-    "problem_id": 4970,
-    "problem": "line A B, line B D, line C D, line A C, line A D, line A B, line B D, line C D, line A C, line A D\nFind the value of q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4970.jpg"
-  },
-  {
-    "id": 5093,
-    "problem_id": 4971,
-    "problem": "line E A, line E F, line A F, line C B, line C D, line B D, line E A, line E F, line A F, line C B, line C D, line B D\nThe figures in the pair are similar. Solve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4971.jpg"
-  },
-  {
-    "id": 5094,
-    "problem_id": 4972,
-    "problem": "line E A, line E F, line A F, line C B, line C D, line B D, line E A, line E F, line A F, line C B, line C D, line B D\nThe figures in the pair are similar. Solve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4972.jpg"
-  },
-  {
-    "id": 5095,
-    "problem_id": 4973,
-    "problem": "line E A, line E F, line A F, line C B, line C D, line B D, line E A, line E F, line A F, line C B, line C D, line B D\nThe figures in the pair are similar. Solve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4973.jpg"
-  },
-  {
-    "id": 5096,
-    "problem_id": 4974,
-    "problem": "line E A, line E F, line A F, line C B, line C D, line B D, line E A, line E F, line A F, line C B, line C D, line B D\nThe figures in the pair are similar. Solve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4974.jpg"
-  },
-  {
-    "id": 5097,
-    "problem_id": 4975,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4975.jpg"
-  },
-  {
-    "id": 5098,
-    "problem_id": 4976,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4976.jpg"
-  },
-  {
-    "id": 5099,
-    "problem_id": 4977,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4977.jpg"
-  },
-  {
-    "id": 5100,
-    "problem_id": 4978,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4978.jpg"
-  },
-  {
-    "id": 5101,
-    "problem_id": 4979,
-    "problem": "line A E, line D E, line C D, line C B, line B A, line A E, line D E, line C D, line C B, line B A\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4979.jpg"
-  },
-  {
-    "id": 5102,
-    "problem_id": 4980,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4980.jpg"
-  },
-  {
-    "id": 5103,
-    "problem_id": 4981,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4981.jpg"
-  },
-  {
-    "id": 5104,
-    "problem_id": 4982,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4982.jpg"
-  },
-  {
-    "id": 5105,
-    "problem_id": 4983,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4983.jpg"
-  },
-  {
-    "id": 5106,
-    "problem_id": 4984,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4984.jpg"
-  },
-  {
-    "id": 5107,
-    "problem_id": 4985,
-    "problem": "line M R, line Q R, line N M, line N Q, line M L Q, line N L R, line M R, line Q R, line N M, line N Q, line M L Q, line N L R\nUse parallelogram NQRM to find NQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4985.jpg"
-  },
-  {
-    "id": 5108,
-    "problem_id": 4986,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4986.jpg"
-  },
-  {
-    "id": 5109,
-    "problem_id": 4987,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4987.jpg"
-  },
-  {
-    "id": 5110,
-    "problem_id": 4988,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4988.jpg"
-  },
-  {
-    "id": 5111,
-    "problem_id": 4989,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4989.jpg"
-  },
-  {
-    "id": 5112,
-    "problem_id": 4990,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4990.jpg"
-  },
-  {
-    "id": 5113,
-    "problem_id": 4991,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4991.jpg"
-  },
-  {
-    "id": 5114,
-    "problem_id": 4992,
-    "problem": "line P N, line L M, line M N, line L P, line P N, line L M, line M N, line L P\nFind the measure of \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4992.jpg"
-  },
-  {
-    "id": 5115,
-    "problem_id": 4993,
-    "problem": "line A B E, line B D, \\odot C lieson B D, line A B E, line B D, \\odot C lieson B D\nSolve for x. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4993.jpg"
-  },
-  {
-    "id": 5116,
-    "problem_id": 4994,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable z in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4994.jpg"
-  },
-  {
-    "id": 5117,
-    "problem_id": 4995,
-    "problem": "line Q S, line Q R, line S R, line P S, line P Q, line Q S, line Q R, line S R, line P S, line P Q\nIn quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \\angle P = 58. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4995.jpg"
-  },
-  {
-    "id": 5118,
-    "problem_id": 4996,
-    "problem": "line Q S, line Q R, line S R, line P S, line P Q, line Q S, line Q R, line S R, line P S, line P Q\nIn quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \\angle P = 58. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4996.jpg"
-  },
-  {
-    "id": 5119,
-    "problem_id": 4997,
-    "problem": "line C E F, line A D F, line A B C, line B D, line D E, line C E F, line A D F, line A B C, line B D, line D E\nIf AC \\parallel DE and m \\angle 2 = 55, find m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4997.jpg"
-  },
-  {
-    "id": 5120,
-    "problem_id": 4998,
-    "problem": "line C E F, line A D F, line A B C, line B D, line D E, line C E F, line A D F, line A B C, line B D, line D E\nIf AC \\parallel DE and m \\angle 2 = 55, find m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4998.jpg"
-  },
-  {
-    "id": 5121,
-    "problem_id": 4999,
-    "problem": "line D C B, line A B, line A D, line B E, line A C E, line D E, line D C B, line A B, line A D, line B E, line A C E, line D E\nUse a Pythagorean Triple to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/4999.jpg"
-  },
-  {
-    "id": 5122,
-    "problem_id": 5000,
-    "problem": "line D C B, line A B, line A D, line B E, line A C E, line D E, line D C B, line A B, line A D, line B E, line A C E, line D E\nUse a Pythagorean Triple to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5000.jpg"
-  },
-  {
-    "id": 5123,
-    "problem_id": 5001,
-    "problem": "line D C B, line A B, line A D, line B E, line A C E, line D E, line D C B, line A B, line A D, line B E, line A C E, line D E\nUse a Pythagorean Triple to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5001.jpg"
-  },
-  {
-    "id": 5124,
-    "problem_id": 5002,
-    "problem": "line J T L, line J P S, line R P L, line K P T, line K R J, line K S L, line J T L, line J P S, line R P L, line K P T, line K R J, line K S L\nRP = 3.5 and JP = 9. Find PL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5002.jpg"
-  },
-  {
-    "id": 5125,
-    "problem_id": 5003,
-    "problem": "line K L, line K J, \\odot A lieson J L K, line K L, line K J, \\odot A lieson J L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5003.jpg"
-  },
-  {
-    "id": 5126,
-    "problem_id": 5004,
-    "problem": "line K L, line K J, \\odot A lieson J L K, line K L, line K J, \\odot A lieson J L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5004.jpg"
-  },
-  {
-    "id": 5127,
-    "problem_id": 5005,
-    "problem": "line K L, line K J, \\odot A lieson J L K, line K L, line K J, \\odot A lieson J L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5005.jpg"
-  },
-  {
-    "id": 5128,
-    "problem_id": 5006,
-    "problem": "line K L, line K J, \\odot A lieson J L K, line K L, line K J, \\odot A lieson J L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5006.jpg"
-  },
-  {
-    "id": 5129,
-    "problem_id": 5007,
-    "problem": "line K L, line K J, \\odot A lieson J L K, line K L, line K J, \\odot A lieson J L K\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5007.jpg"
-  },
-  {
-    "id": 5130,
-    "problem_id": 5008,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5008.jpg"
-  },
-  {
-    "id": 5131,
-    "problem_id": 5009,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5009.jpg"
-  },
-  {
-    "id": 5132,
-    "problem_id": 5010,
-    "problem": "line B D, line C D, line A C, line A B, line A D, line B D, line C D, line A C, line A B, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5010.jpg"
-  },
-  {
-    "id": 5133,
-    "problem_id": 5011,
-    "problem": "line B D, line C D, line A C, line A B, line A D, line B D, line C D, line A C, line A B, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5011.jpg"
-  },
-  {
-    "id": 5134,
-    "problem_id": 5012,
-    "problem": "line B D, line C D, line A C, line A B, line A D, line B D, line C D, line A C, line A B, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5012.jpg"
-  },
-  {
-    "id": 5135,
-    "problem_id": 5013,
-    "problem": "line B D, line C D, line A C, line A B, line A D, line B D, line C D, line A C, line A B, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5013.jpg"
-  },
-  {
-    "id": 5137,
-    "problem_id": 5014,
-    "problem": "line B D, line C D, line A C, line A B, line A D, line B D, line C D, line A C, line A B, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5014.jpg"
-  },
-  {
-    "id": 5138,
-    "problem_id": 5015,
-    "problem": "line B D, line C D, line A C, line A B, line A D, line B D, line C D, line A C, line A B, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5015.jpg"
-  },
-  {
-    "id": 5139,
-    "problem_id": 5016,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5016.jpg"
-  },
-  {
-    "id": 5140,
-    "problem_id": 5017,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5017.jpg"
-  },
-  {
-    "id": 5141,
-    "problem_id": 5018,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5018.jpg"
-  },
-  {
-    "id": 5142,
-    "problem_id": 5019,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5019.jpg"
-  },
-  {
-    "id": 5143,
-    "problem_id": 5020,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5020.jpg"
-  },
-  {
-    "id": 5144,
-    "problem_id": 5021,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5021.jpg"
-  },
-  {
-    "id": 5145,
-    "problem_id": 5022,
-    "problem": "line R T, line R S, line T S, line R T, line R S, line T S\nFind the measure of \\angle RTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5022.jpg"
-  },
-  {
-    "id": 5147,
-    "problem_id": 5023,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5023.jpg"
-  },
-  {
-    "id": 5148,
-    "problem_id": 5024,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5024.jpg"
-  },
-  {
-    "id": 5149,
-    "problem_id": 5025,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5025.jpg"
-  },
-  {
-    "id": 5150,
-    "problem_id": 5026,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5026.jpg"
-  },
-  {
-    "id": 5151,
-    "problem_id": 5027,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5027.jpg"
-  },
-  {
-    "id": 5152,
-    "problem_id": 5028,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5028.jpg"
-  },
-  {
-    "id": 5153,
-    "problem_id": 5029,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5029.jpg"
-  },
-  {
-    "id": 5154,
-    "problem_id": 5030,
-    "problem": "line C A E, line D A F, line D C, \\odot B lieson C F E D, line C A E, line D A F, line D C, \\odot B lieson C F E D\nFind m \\widehat CF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5030.jpg"
-  },
-  {
-    "id": 5155,
-    "problem_id": 5031,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of f?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5031.jpg"
-  },
-  {
-    "id": 5156,
-    "problem_id": 5032,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of f?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5032.jpg"
-  },
-  {
-    "id": 5157,
-    "problem_id": 5033,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nWhat is the value of f?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5033.jpg"
-  },
-  {
-    "id": 5158,
-    "problem_id": 5034,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5034.jpg"
-  },
-  {
-    "id": 5159,
-    "problem_id": 5035,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5035.jpg"
-  },
-  {
-    "id": 5160,
-    "problem_id": 5036,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5036.jpg"
-  },
-  {
-    "id": 5161,
-    "problem_id": 5037,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5037.jpg"
-  },
-  {
-    "id": 5162,
-    "problem_id": 5038,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5038.jpg"
-  },
-  {
-    "id": 5163,
-    "problem_id": 5039,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5039.jpg"
-  },
-  {
-    "id": 5164,
-    "problem_id": 5040,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nm \\angle 11 = 4x, m \\angle 12 = 2x-6. Find the measure of \\angle 12.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5040.jpg"
-  },
-  {
-    "id": 5165,
-    "problem_id": 5041,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5041.jpg"
-  },
-  {
-    "id": 5166,
-    "problem_id": 5042,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5042.jpg"
-  },
-  {
-    "id": 5167,
-    "problem_id": 5043,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5043.jpg"
-  },
-  {
-    "id": 5168,
-    "problem_id": 5044,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5044.jpg"
-  },
-  {
-    "id": 5169,
-    "problem_id": 5045,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5045.jpg"
-  },
-  {
-    "id": 5170,
-    "problem_id": 5046,
-    "problem": "line T A Q, line P T, line P Q, line P A R, line Q R, line T A Q, line P T, line P Q, line P A R, line Q R\nFind the measure of \\angle 4 if PQ \\perp QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5046.jpg"
-  },
-  {
-    "id": 5171,
-    "problem_id": 5047,
-    "problem": "line T A Q, line P T, line P Q, line P A R, line Q R, line T A Q, line P T, line P Q, line P A R, line Q R\nFind the measure of \\angle 4 if PQ \\perp QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5047.jpg"
-  },
-  {
-    "id": 5172,
-    "problem_id": 5048,
-    "problem": "line Q R, line X Y, line P S, line Q X P, line R Y S, line Q R, line X Y, line P S, line Q X P, line R Y S\nFind the measure of \\angle PXY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5048.jpg"
-  },
-  {
-    "id": 5173,
-    "problem_id": 5049,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5049.jpg"
-  },
-  {
-    "id": 5175,
-    "problem_id": 5050,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5050.jpg"
-  },
-  {
-    "id": 5176,
-    "problem_id": 5051,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5051.jpg"
-  },
-  {
-    "id": 5177,
-    "problem_id": 5052,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5052.jpg"
-  },
-  {
-    "id": 5178,
-    "problem_id": 5053,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5053.jpg"
-  },
-  {
-    "id": 5179,
-    "problem_id": 5054,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5054.jpg"
-  },
-  {
-    "id": 5180,
-    "problem_id": 5055,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5055.jpg"
-  },
-  {
-    "id": 5181,
-    "problem_id": 5056,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5056.jpg"
-  },
-  {
-    "id": 5182,
-    "problem_id": 5057,
-    "problem": "line E F G, line E F G\nIf EF = 59, what is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5057.jpg"
-  },
-  {
-    "id": 5183,
-    "problem_id": 5058,
-    "problem": "line Y Z W, line Y X, line W X, line T Y, line T W, line T Z, line Y Z W, line Y X, line W X, line T Y, line T W, line T Z\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5058.jpg"
-  },
-  {
-    "id": 5184,
-    "problem_id": 5059,
-    "problem": "line Y Z W, line Y X, line W X, line T Y, line T W, line T Z, line Y Z W, line Y X, line W X, line T Y, line T W, line T Z\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5059.jpg"
-  },
-  {
-    "id": 5185,
-    "problem_id": 5060,
-    "problem": "line Y Z W, line Y X, line W X, line T Y, line T W, line T Z, line Y Z W, line Y X, line W X, line T Y, line T W, line T Z\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5060.jpg"
-  },
-  {
-    "id": 5186,
-    "problem_id": 5061,
-    "problem": "line A C D, line A B, line B D, \\odot C lieson A D B, line A C D, line A B, line B D, \\odot C lieson A D B\nFind the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5061.jpg"
-  },
-  {
-    "id": 5187,
-    "problem_id": 5062,
-    "problem": "line A C D, line A B, line B D, \\odot C lieson A D B, line A C D, line A B, line B D, \\odot C lieson A D B\nFind the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5062.jpg"
-  },
-  {
-    "id": 5188,
-    "problem_id": 5063,
-    "problem": "line R S, line S T, line U T, line R U, \\odot P lieson R U T S, line R S, line S T, line U T, line R U, \\odot P lieson R U T S\nQuadrilateral RSTU is inscribed in circle P. Find the measure of \\widehat STU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5063.jpg"
-  },
-  {
-    "id": 5189,
-    "problem_id": 5064,
-    "problem": "line B C D, line A D, line E D, line A C E, line B E, line B A, line B C D, line A D, line E D, line A C E, line B E, line B A\nFind the measure of \\angle 1 in the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5064.jpg"
-  },
-  {
-    "id": 5190,
-    "problem_id": 5065,
-    "problem": "line X Y, line W Z X, line W T Y, line Z T, line X Y, line W Z X, line W T Y, line Z T\nFind TY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5065.jpg"
-  },
-  {
-    "id": 5191,
-    "problem_id": 5066,
-    "problem": "line X Y, line W Z X, line W T Y, line Z T, line X Y, line W Z X, line W T Y, line Z T\nFind TY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5066.jpg"
-  },
-  {
-    "id": 5192,
-    "problem_id": 5067,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nFind m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5067.jpg"
-  },
-  {
-    "id": 5193,
-    "problem_id": 5068,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nFind m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5068.jpg"
-  },
-  {
-    "id": 5194,
-    "problem_id": 5069,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nFind m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5069.jpg"
-  },
-  {
-    "id": 5195,
-    "problem_id": 5070,
-    "problem": "line M N, line N P, line L M A, line L N B, line L P C, line M N, line N P, line L M A, line L N B, line L P C\nFind m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5070.jpg"
-  },
-  {
-    "id": 5197,
-    "problem_id": 5071,
-    "problem": "line F A E D I, line H C E B G, line F A E D I, line H C E B G\nFind m \\angle AEC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5071.jpg"
-  },
-  {
-    "id": 5198,
-    "problem_id": 5072,
-    "problem": "line F A E D I, line H C E B G, line F A E D I, line H C E B G\nFind m \\angle AEC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5072.jpg"
-  },
-  {
-    "id": 5199,
-    "problem_id": 5073,
-    "problem": "line F A E D I, line H C E B G, line F A E D I, line H C E B G\nFind m \\angle AEC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5073.jpg"
-  },
-  {
-    "id": 5200,
-    "problem_id": 5074,
-    "problem": "line A C B, line O B, line O C, \\odot O lieson A B, line A C B, line O B, line O C, \\odot O lieson A B\nFind m \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5074.jpg"
-  },
-  {
-    "id": 5201,
-    "problem_id": 5075,
-    "problem": "line A C B, line O B, line O C, \\odot O lieson A B, line A C B, line O B, line O C, \\odot O lieson A B\nFind m \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5075.jpg"
-  },
-  {
-    "id": 5202,
-    "problem_id": 5076,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5076.jpg"
-  },
-  {
-    "id": 5203,
-    "problem_id": 5077,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5077.jpg"
-  },
-  {
-    "id": 5204,
-    "problem_id": 5078,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nWhat is m \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5078.jpg"
-  },
-  {
-    "id": 5205,
-    "problem_id": 5079,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the length of AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5079.jpg"
-  },
-  {
-    "id": 5206,
-    "problem_id": 5080,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the length of AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5080.jpg"
-  },
-  {
-    "id": 5207,
-    "problem_id": 5081,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the length of AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5081.jpg"
-  },
-  {
-    "id": 5208,
-    "problem_id": 5082,
-    "problem": "line B C, line C D, line A D, line B A, line B E D, line C E A, line B C, line C D, line A D, line B A, line B E D, line C E A\nFind the length of AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5082.jpg"
-  },
-  {
-    "id": 5209,
-    "problem_id": 5083,
-    "problem": "line A B E, line E D, line A C, line B C, line C D, line A B E, line E D, line A C, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5083.jpg"
-  },
-  {
-    "id": 5210,
-    "problem_id": 5084,
-    "problem": "line A B E, line E D, line A C, line B C, line C D, line A B E, line E D, line A C, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5084.jpg"
-  },
-  {
-    "id": 5211,
-    "problem_id": 5085,
-    "problem": "line A B E, line E D, line A C, line B C, line C D, line A B E, line E D, line A C, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5085.jpg"
-  },
-  {
-    "id": 5212,
-    "problem_id": 5086,
-    "problem": "line A B E, line E D, line A C, line B C, line C D, line A B E, line E D, line A C, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5086.jpg"
-  },
-  {
-    "id": 5213,
-    "problem_id": 5087,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5087.jpg"
-  },
-  {
-    "id": 5214,
-    "problem_id": 5088,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5088.jpg"
-  },
-  {
-    "id": 5215,
-    "problem_id": 5089,
-    "problem": "line R S, line T U, \\odot A lieson R U T S, line R S, line T U, \\odot A lieson R U T S\nRS = TU. Find m \\widehat RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5089.jpg"
-  },
-  {
-    "id": 5216,
-    "problem_id": 5090,
-    "problem": "line C P B, line A P, line P D, \\odot P lieson A C D B, line C P B, line A P, line P D, \\odot P lieson A C D B\nWhat is the length of \\widehat BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5090.jpg"
-  },
-  {
-    "id": 5217,
-    "problem_id": 5091,
-    "problem": "line N P, line L P, line L M N, line M P A, line N P, line L P, line L M N, line M P A\nFind NP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5091.jpg"
-  },
-  {
-    "id": 5218,
-    "problem_id": 5092,
-    "problem": "line N P, line L P, line L M N, line M P A, line N P, line L P, line L M N, line M P A\nFind NP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5092.jpg"
-  },
-  {
-    "id": 5219,
-    "problem_id": 5093,
-    "problem": "line N P, line L P, line L M N, line M P A, line N P, line L P, line L M N, line M P A\nFind NP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5093.jpg"
-  },
-  {
-    "id": 5220,
-    "problem_id": 5094,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5094.jpg"
-  },
-  {
-    "id": 5221,
-    "problem_id": 5095,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5095.jpg"
-  },
-  {
-    "id": 5222,
-    "problem_id": 5096,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5096.jpg"
-  },
-  {
-    "id": 5223,
-    "problem_id": 5097,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5097.jpg"
-  },
-  {
-    "id": 5224,
-    "problem_id": 5098,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5098.jpg"
-  },
-  {
-    "id": 5225,
-    "problem_id": 5099,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5099.jpg"
-  },
-  {
-    "id": 5226,
-    "problem_id": 5100,
-    "problem": "line D C, line B C, line A D, line A B, line D F B, line A F C, line D C, line B C, line A D, line A B, line D F B, line A F C\nUse parallelogram ABCD to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5100.jpg"
-  },
-  {
-    "id": 5227,
-    "problem_id": 5101,
-    "problem": "line B A, line A D, \\odot C lieson B D, line B A, line A D, \\odot C lieson B D\nAB and AD are tangent to \\odot C. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5101.jpg"
-  },
-  {
-    "id": 5228,
-    "problem_id": 5102,
-    "problem": "line X Y, line X W, line Y Z, line W Z, line X Y, line X W, line Y Z, line W Z\nFind m \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5102.jpg"
-  },
-  {
-    "id": 5229,
-    "problem_id": 5103,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5103.jpg"
-  },
-  {
-    "id": 5230,
-    "problem_id": 5104,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5104.jpg"
-  },
-  {
-    "id": 5231,
-    "problem_id": 5105,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5105.jpg"
-  },
-  {
-    "id": 5232,
-    "problem_id": 5106,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the value of a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5106.jpg"
-  },
-  {
-    "id": 5233,
-    "problem_id": 5107,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5107.jpg"
-  },
-  {
-    "id": 5234,
-    "problem_id": 5108,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5108.jpg"
-  },
-  {
-    "id": 5235,
-    "problem_id": 5109,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5109.jpg"
-  },
-  {
-    "id": 5236,
-    "problem_id": 5110,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5110.jpg"
-  },
-  {
-    "id": 5237,
-    "problem_id": 5111,
-    "problem": "line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L, line K S L, line J S, line R J, line H R G, \\odot J lieson H G K L\nIn \\odot J, GH = 9 and KL = 4x+1. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5111.jpg"
-  },
-  {
-    "id": 5238,
-    "problem_id": 5112,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOB = 6x+5, m \\angle BOC = 4x-2, m \\angle AOC = 8x+21. Find the measure of \\angle EOD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5112.jpg"
-  },
-  {
-    "id": 5239,
-    "problem_id": 5113,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOB = 6x+5, m \\angle BOC = 4x-2, m \\angle AOC = 8x+21. Find the measure of \\angle EOD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5113.jpg"
-  },
-  {
-    "id": 5240,
-    "problem_id": 5114,
-    "problem": "line D C E, line A C F, line B C, line D C E, line A C F, line B C\nm \\angle 11 = x+40, m \\angle 12 = x+10, m \\angle 13 = 3x+30, what is the measure of \\angle 12?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5114.jpg"
-  },
-  {
-    "id": 5241,
-    "problem_id": 5115,
-    "problem": "line X Z, line Z Y, \\odot Z lieson X Y, line X Z, line Z Y, \\odot Z lieson X Y\nWhat is m \\widehat XY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5115.jpg"
-  },
-  {
-    "id": 5242,
-    "problem_id": 5116,
-    "problem": "line S R, line U R, line T U, line T S, line S R, line U R, line T U, line T S\nSolve for x in parallelogram RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5116.jpg"
-  },
-  {
-    "id": 5243,
-    "problem_id": 5117,
-    "problem": "line S R, line U R, line T U, line T S, line S R, line U R, line T U, line T S\nSolve for x in parallelogram RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5117.jpg"
-  },
-  {
-    "id": 5244,
-    "problem_id": 5118,
-    "problem": "line S R, line U R, line T U, line T S, line S R, line U R, line T U, line T S\nSolve for x in parallelogram RSTU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5118.jpg"
-  },
-  {
-    "id": 5245,
-    "problem_id": 5119,
-    "problem": "line B C, line A D, line B A, line A F C, line C D, line B F D, line B C, line A D, line B A, line A F C, line C D, line B F D\nUse parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5119.jpg"
-  },
-  {
-    "id": 5246,
-    "problem_id": 5120,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5120.jpg"
-  },
-  {
-    "id": 5247,
-    "problem_id": 5121,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5121.jpg"
-  },
-  {
-    "id": 5248,
-    "problem_id": 5122,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5122.jpg"
-  },
-  {
-    "id": 5249,
-    "problem_id": 5123,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5123.jpg"
-  },
-  {
-    "id": 5250,
-    "problem_id": 5124,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5124.jpg"
-  },
-  {
-    "id": 5251,
-    "problem_id": 5125,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5125.jpg"
-  },
-  {
-    "id": 5252,
-    "problem_id": 5126,
-    "problem": "line B C, line D C, line A B, line A E, line E D, line B C, line D C, line A B, line A E, line E D\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5126.jpg"
-  },
-  {
-    "id": 5253,
-    "problem_id": 5127,
-    "problem": "line A B, line B E, line C E, line C A, line A D E, line C D B, line A B, line B E, line C E, line C A, line A D E, line C D B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5127.jpg"
-  },
-  {
-    "id": 5254,
-    "problem_id": 5128,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. What is EH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5128.jpg"
-  },
-  {
-    "id": 5255,
-    "problem_id": 5129,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. What is EH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5129.jpg"
-  },
-  {
-    "id": 5256,
-    "problem_id": 5130,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. What is EH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5130.jpg"
-  },
-  {
-    "id": 5257,
-    "problem_id": 5131,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5131.jpg"
-  },
-  {
-    "id": 5258,
-    "problem_id": 5132,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5132.jpg"
-  },
-  {
-    "id": 5259,
-    "problem_id": 5133,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5133.jpg"
-  },
-  {
-    "id": 5260,
-    "problem_id": 5134,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5134.jpg"
-  },
-  {
-    "id": 5261,
-    "problem_id": 5135,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5135.jpg"
-  },
-  {
-    "id": 5262,
-    "problem_id": 5136,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 7 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5136.jpg"
-  },
-  {
-    "id": 5263,
-    "problem_id": 5137,
-    "problem": "line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G, line A C, line A B, line B D, line D H, line F G H, line C F, line C E D, line A E H, line B E F, line E G\nFind the measure of \\angle 7 in the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5137.jpg"
-  },
-  {
-    "id": 5264,
-    "problem_id": 5138,
-    "problem": "line A B D, line C D, line C B, line A C, line A B D, line C D, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5138.jpg"
-  },
-  {
-    "id": 5265,
-    "problem_id": 5139,
-    "problem": "line A B D, line C D, line C B, line A C, line A B D, line C D, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5139.jpg"
-  },
-  {
-    "id": 5266,
-    "problem_id": 5140,
-    "problem": "line A B D, line C D, line C B, line A C, line A B D, line C D, line C B, line A C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5140.jpg"
-  },
-  {
-    "id": 5267,
-    "problem_id": 5141,
-    "problem": "line A B, line D A, line C A, line C B, line D C, line A B, line D A, line C A, line C B, line D C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5141.jpg"
-  },
-  {
-    "id": 5268,
-    "problem_id": 5142,
-    "problem": "line A B, line D A, line C A, line C B, line D C, line A B, line D A, line C A, line C B, line D C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5142.jpg"
-  },
-  {
-    "id": 5269,
-    "problem_id": 5143,
-    "problem": "line A B, line D A, line C A, line C B, line D C, line A B, line D A, line C A, line C B, line D C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5143.jpg"
-  },
-  {
-    "id": 5270,
-    "problem_id": 5144,
-    "problem": "line A B, line D A, line C A, line C B, line D C, line A B, line D A, line C A, line C B, line D C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5144.jpg"
-  },
-  {
-    "id": 5271,
-    "problem_id": 5145,
-    "problem": "line A B, line D A, line C A, line C B, line D C, line A B, line D A, line C A, line C B, line D C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5145.jpg"
-  },
-  {
-    "id": 5272,
-    "problem_id": 5146,
-    "problem": "line A B, line D A, line C A, line C B, line D C, line A B, line D A, line C A, line C B, line D C\nFor what value of x must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5146.jpg"
-  },
-  {
-    "id": 5273,
-    "problem_id": 5147,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5147.jpg"
-  },
-  {
-    "id": 5275,
-    "problem_id": 5148,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5148.jpg"
-  },
-  {
-    "id": 5276,
-    "problem_id": 5149,
-    "problem": "line E J, line J H, line G H, line F E, line F G, line E J, line J H, line G H, line F E, line F G\nFind m \\angle G.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5149.jpg"
-  },
-  {
-    "id": 5277,
-    "problem_id": 5150,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5150.jpg"
-  },
-  {
-    "id": 5278,
-    "problem_id": 5151,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5151.jpg"
-  },
-  {
-    "id": 5279,
-    "problem_id": 5152,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5152.jpg"
-  },
-  {
-    "id": 5280,
-    "problem_id": 5153,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5153.jpg"
-  },
-  {
-    "id": 5281,
-    "problem_id": 5154,
-    "problem": "line G A B, line E C B, line F D B, line A D, line D C, line G A B, line E C B, line F D B, line A D, line D C\nFind m \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5154.jpg"
-  },
-  {
-    "id": 5282,
-    "problem_id": 5155,
-    "problem": "line B C, line D C, line B E D, line A B, line A D, line A E C, line B C, line D C, line B E D, line A B, line A D, line A E C\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5155.jpg"
-  },
-  {
-    "id": 5283,
-    "problem_id": 5156,
-    "problem": "line B C, line D C, line B E D, line A B, line A D, line A E C, line B C, line D C, line B E D, line A B, line A D, line A E C\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5156.jpg"
-  },
-  {
-    "id": 5284,
-    "problem_id": 5157,
-    "problem": "line B C, line D C, line B E D, line A B, line A D, line A E C, line B C, line D C, line B E D, line A B, line A D, line A E C\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5157.jpg"
-  },
-  {
-    "id": 5285,
-    "problem_id": 5158,
-    "problem": "line B C, line D C, line B E D, line A B, line A D, line A E C, line B C, line D C, line B E D, line A B, line A D, line A E C\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5158.jpg"
-  },
-  {
-    "id": 5286,
-    "problem_id": 5159,
-    "problem": "line A B, line B E, line C D E, line C A, line A D, line A B, line B E, line C D E, line C A, line A D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5159.jpg"
-  },
-  {
-    "id": 5287,
-    "problem_id": 5160,
-    "problem": "line A B, line B E, line C D E, line C A, line A D, line A B, line B E, line C D E, line C A, line A D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5160.jpg"
-  },
-  {
-    "id": 5288,
-    "problem_id": 5161,
-    "problem": "line C D E, line A D F, line B D G, line C D E, line A D F, line B D G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5161.jpg"
-  },
-  {
-    "id": 5289,
-    "problem_id": 5162,
-    "problem": "line C D E, line A D F, line B D G, line C D E, line A D F, line B D G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5162.jpg"
-  },
-  {
-    "id": 5290,
-    "problem_id": 5163,
-    "problem": "line C D E, line A D F, line B D G, line C D E, line A D F, line B D G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5163.jpg"
-  },
-  {
-    "id": 5291,
-    "problem_id": 5164,
-    "problem": "line C D E, line A D F, line B D G, line C D E, line A D F, line B D G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5164.jpg"
-  },
-  {
-    "id": 5292,
-    "problem_id": 5165,
-    "problem": "line A F E, line F B C, line A B, line C D, line E D, line A F E, line F B C, line A B, line C D, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5165.jpg"
-  },
-  {
-    "id": 5293,
-    "problem_id": 5166,
-    "problem": "line A F E, line F B C, line A B, line C D, line E D, line A F E, line F B C, line A B, line C D, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5166.jpg"
-  },
-  {
-    "id": 5294,
-    "problem_id": 5167,
-    "problem": "line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C, line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C\nFind the value of variable b. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5167.jpg"
-  },
-  {
-    "id": 5295,
-    "problem_id": 5168,
-    "problem": "line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C, line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C\nFind the value of variable b. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5168.jpg"
-  },
-  {
-    "id": 5296,
-    "problem_id": 5169,
-    "problem": "line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C, line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C\nFind the value of variable b. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5169.jpg"
-  },
-  {
-    "id": 5298,
-    "problem_id": 5170,
-    "problem": "line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C, line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C\nFind the value of variable b. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5170.jpg"
-  },
-  {
-    "id": 5299,
-    "problem_id": 5171,
-    "problem": "line A B C D, line E B, line E C, line A B C D, line E B, line E C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5171.jpg"
-  },
-  {
-    "id": 5300,
-    "problem_id": 5172,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5172.jpg"
-  },
-  {
-    "id": 5301,
-    "problem_id": 5173,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5173.jpg"
-  },
-  {
-    "id": 5302,
-    "problem_id": 5174,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5174.jpg"
-  },
-  {
-    "id": 5303,
-    "problem_id": 5175,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5175.jpg"
-  },
-  {
-    "id": 5304,
-    "problem_id": 5176,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5176.jpg"
-  },
-  {
-    "id": 5305,
-    "problem_id": 5177,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5177.jpg"
-  },
-  {
-    "id": 5306,
-    "problem_id": 5178,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5178.jpg"
-  },
-  {
-    "id": 5307,
-    "problem_id": 5179,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5179.jpg"
-  },
-  {
-    "id": 5308,
-    "problem_id": 5180,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5180.jpg"
-  },
-  {
-    "id": 5309,
-    "problem_id": 5181,
-    "problem": "line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q, line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q\nABCD \\sim QSRP. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5181.jpg"
-  },
-  {
-    "id": 5310,
-    "problem_id": 5182,
-    "problem": "line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q, line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q\nABCD \\sim QSRP. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5182.jpg"
-  },
-  {
-    "id": 5311,
-    "problem_id": 5183,
-    "problem": "line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q, line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q\nABCD \\sim QSRP. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5183.jpg"
-  },
-  {
-    "id": 5312,
-    "problem_id": 5184,
-    "problem": "line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q, line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q\nABCD \\sim QSRP. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5184.jpg"
-  },
-  {
-    "id": 5313,
-    "problem_id": 5185,
-    "problem": "line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q, line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q\nABCD \\sim QSRP. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5185.jpg"
-  },
-  {
-    "id": 5314,
-    "problem_id": 5186,
-    "problem": "line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q, line D C, line B C, line A D, line A B, line R S, line S Q, line R P, line P Q\nABCD \\sim QSRP. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5186.jpg"
-  },
-  {
-    "id": 5315,
-    "problem_id": 5187,
-    "problem": "line P S, line Q R, line S R, line P Q, line P S, line Q R, line S R, line P Q\nPQRS is a rhombus. Find the length of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5187.jpg"
-  },
-  {
-    "id": 5316,
-    "problem_id": 5188,
-    "problem": "line A D, line A C E, line D E, line B C D, line B E, line A D, line A C E, line D E, line B C D, line B E\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5188.jpg"
-  },
-  {
-    "id": 5317,
-    "problem_id": 5189,
-    "problem": "line A D, line A C E, line D E, line B C D, line B E, line A D, line A C E, line D E, line B C D, line B E\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5189.jpg"
-  },
-  {
-    "id": 5318,
-    "problem_id": 5190,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5190.jpg"
-  },
-  {
-    "id": 5319,
-    "problem_id": 5191,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5191.jpg"
-  },
-  {
-    "id": 5320,
-    "problem_id": 5192,
-    "problem": "line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z, line R Z V, line T Y V, line X W V, line R W Y, line T X R, line T W Z\nVX = 204, and RW = 104. Find VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5192.jpg"
-  },
-  {
-    "id": 5321,
-    "problem_id": 5193,
-    "problem": "line A D H, line B E G, line F E D C, line A D H, line B E G, line F E D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5193.jpg"
-  },
-  {
-    "id": 5322,
-    "problem_id": 5194,
-    "problem": "line A P D, line B P Q E, line C R Q F, line A P D, line B P Q E, line C R Q F\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5194.jpg"
-  },
-  {
-    "id": 5323,
-    "problem_id": 5195,
-    "problem": "line A P D, line B P Q E, line C R Q F, line A P D, line B P Q E, line C R Q F\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5195.jpg"
-  },
-  {
-    "id": 5324,
-    "problem_id": 5196,
-    "problem": "line A P D, line B P Q E, line C R Q F, line A P D, line B P Q E, line C R Q F\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5196.jpg"
-  },
-  {
-    "id": 5325,
-    "problem_id": 5197,
-    "problem": "line A P D, line B P Q E, line C R Q F, line A P D, line B P Q E, line C R Q F\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5197.jpg"
-  },
-  {
-    "id": 5326,
-    "problem_id": 5198,
-    "problem": "line A P D, line B P Q E, line C R Q F, line A P D, line B P Q E, line C R Q F\nSolve for n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5198.jpg"
-  },
-  {
-    "id": 5327,
-    "problem_id": 5199,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5199.jpg"
-  },
-  {
-    "id": 5329,
-    "problem_id": 5200,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5200.jpg"
-  },
-  {
-    "id": 5330,
-    "problem_id": 5201,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5201.jpg"
-  },
-  {
-    "id": 5331,
-    "problem_id": 5202,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5202.jpg"
-  },
-  {
-    "id": 5332,
-    "problem_id": 5203,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5203.jpg"
-  },
-  {
-    "id": 5333,
-    "problem_id": 5204,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5204.jpg"
-  },
-  {
-    "id": 5334,
-    "problem_id": 5205,
-    "problem": "line A B, line B D F, line E F, line A C E, line C D, line A B, line B D F, line E F, line A C E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5205.jpg"
-  },
-  {
-    "id": 5335,
-    "problem_id": 5206,
-    "problem": "line A B, line B D F, line E F, line A C E, line C D, line A B, line B D F, line E F, line A C E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5206.jpg"
-  },
-  {
-    "id": 5336,
-    "problem_id": 5207,
-    "problem": "line A B, line B D F, line E F, line A C E, line C D, line A B, line B D F, line E F, line A C E, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5207.jpg"
-  },
-  {
-    "id": 5337,
-    "problem_id": 5208,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5208.jpg"
-  },
-  {
-    "id": 5338,
-    "problem_id": 5209,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5209.jpg"
-  },
-  {
-    "id": 5339,
-    "problem_id": 5210,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5210.jpg"
-  },
-  {
-    "id": 5340,
-    "problem_id": 5211,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5211.jpg"
-  },
-  {
-    "id": 5341,
-    "problem_id": 5212,
-    "problem": "line C D E F, line B D H, line A E G, line C D E F, line B D H, line A E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5212.jpg"
-  },
-  {
-    "id": 5342,
-    "problem_id": 5213,
-    "problem": "line C D E F, line B D H, line A E G, line C D E F, line B D H, line A E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5213.jpg"
-  },
-  {
-    "id": 5343,
-    "problem_id": 5214,
-    "problem": "line C D E F, line B D H, line A E G, line C D E F, line B D H, line A E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5214.jpg"
-  },
-  {
-    "id": 5344,
-    "problem_id": 5215,
-    "problem": "line C D E F, line B D H, line A E G, line C D E F, line B D H, line A E G\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5215.jpg"
-  },
-  {
-    "id": 5345,
-    "problem_id": 5216,
-    "problem": "line A B, line B C, line A C, line D F, line D E, line F E, line A B, line B C, line A C, line D F, line D E, line F E\nFor the pair of similar figures, the area of the blue figure is 96 in^{2} and the green figure is 150 in^{2}, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5216.jpg"
-  },
-  {
-    "id": 5346,
-    "problem_id": 5217,
-    "problem": "line D E B, line A E C, line A B, \\odot E lieson A D C B, line D E B, line A E C, line A B, \\odot E lieson A D C B\nSuppose BD = 12 millimeters. Find the radius of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5217.jpg"
-  },
-  {
-    "id": 5347,
-    "problem_id": 5218,
-    "problem": "line D E B, line A E C, line A B, \\odot E lieson A D C B, line D E B, line A E C, line A B, \\odot E lieson A D C B\nSuppose BD = 12 millimeters. Find the radius of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5218.jpg"
-  },
-  {
-    "id": 5348,
-    "problem_id": 5219,
-    "problem": "line T W, line Y Z, line V R, line T Y V, line W Z R, line T W, line Y Z, line V R, line T Y V, line W Z R\nYZ is the midsegment of trapezoid TWRV. Determine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5219.jpg"
-  },
-  {
-    "id": 5349,
-    "problem_id": 5220,
-    "problem": "line T W, line Y Z, line V R, line T Y V, line W Z R, line T W, line Y Z, line V R, line T Y V, line W Z R\nYZ is the midsegment of trapezoid TWRV. Determine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5220.jpg"
-  },
-  {
-    "id": 5350,
-    "problem_id": 5221,
-    "problem": "line T W, line Y Z, line V R, line T Y V, line W Z R, line T W, line Y Z, line V R, line T Y V, line W Z R\nYZ is the midsegment of trapezoid TWRV. Determine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5221.jpg"
-  },
-  {
-    "id": 5351,
-    "problem_id": 5222,
-    "problem": "line T W, line Y Z, line V R, line T Y V, line W Z R, line T W, line Y Z, line V R, line T Y V, line W Z R\nYZ is the midsegment of trapezoid TWRV. Determine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5222.jpg"
-  },
-  {
-    "id": 5352,
-    "problem_id": 5223,
-    "problem": "line A D G, line C F G, line B E G, line E D, line D F, line A D G, line C F G, line B E G, line E D, line D F\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5223.jpg"
-  },
-  {
-    "id": 5353,
-    "problem_id": 5224,
-    "problem": "line A D G, line C F G, line B E G, line E D, line D F, line A D G, line C F G, line B E G, line E D, line D F\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5224.jpg"
-  },
-  {
-    "id": 5354,
-    "problem_id": 5225,
-    "problem": "line A D G, line C F G, line B E G, line E D, line D F, line A D G, line C F G, line B E G, line E D, line D F\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5225.jpg"
-  },
-  {
-    "id": 5355,
-    "problem_id": 5226,
-    "problem": "line A D G, line C F G, line B E G, line E D, line D F, line A D G, line C F G, line B E G, line E D, line D F\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5226.jpg"
-  },
-  {
-    "id": 5356,
-    "problem_id": 5227,
-    "problem": "line A C E, line D C B, line D E, line A B, line A D, line B E, line A C E, line D C B, line D E, line A B, line A D, line B E\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5227.jpg"
-  },
-  {
-    "id": 5357,
-    "problem_id": 5228,
-    "problem": "line A C E, line D C B, line D E, line A B, line A D, line B E, line A C E, line D C B, line D E, line A B, line A D, line B E\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5228.jpg"
-  },
-  {
-    "id": 5358,
-    "problem_id": 5229,
-    "problem": "line A C E, line D C B, line D E, line A B, line A D, line B E, line A C E, line D C B, line D E, line A B, line A D, line B E\nFind the measure of \\angle 1 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5229.jpg"
-  },
-  {
-    "id": 5359,
-    "problem_id": 5230,
-    "problem": "line L K, line M L, line H J, line G M, line J K, line G H, line L K, line M L, line H J, line G M, line J K, line G H\nFind ML. Perimeter = 90 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5230.jpg"
-  },
-  {
-    "id": 5360,
-    "problem_id": 5231,
-    "problem": "line L K, line M L, line H J, line G M, line J K, line G H, line L K, line M L, line H J, line G M, line J K, line G H\nFind ML. Perimeter = 90 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5231.jpg"
-  },
-  {
-    "id": 5361,
-    "problem_id": 5232,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5232.jpg"
-  },
-  {
-    "id": 5362,
-    "problem_id": 5233,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5233.jpg"
-  },
-  {
-    "id": 5363,
-    "problem_id": 5234,
-    "problem": "line A F, line C B A, line D E A, line C D, line B E F, line A F, line C B A, line D E A, line C D, line B E F\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5234.jpg"
-  },
-  {
-    "id": 5364,
-    "problem_id": 5235,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5235.jpg"
-  },
-  {
-    "id": 5365,
-    "problem_id": 5236,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5236.jpg"
-  },
-  {
-    "id": 5366,
-    "problem_id": 5237,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5237.jpg"
-  },
-  {
-    "id": 5367,
-    "problem_id": 5238,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5238.jpg"
-  },
-  {
-    "id": 5368,
-    "problem_id": 5239,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5239.jpg"
-  },
-  {
-    "id": 5369,
-    "problem_id": 5240,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5240.jpg"
-  },
-  {
-    "id": 5370,
-    "problem_id": 5241,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind the perimeter of parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5241.jpg"
-  },
-  {
-    "id": 5371,
-    "problem_id": 5242,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5242.jpg"
-  },
-  {
-    "id": 5372,
-    "problem_id": 5243,
-    "problem": "line B C D, line A C E, line B C D, line A C E\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5243.jpg"
-  },
-  {
-    "id": 5373,
-    "problem_id": 5244,
-    "problem": "line N M A, line N Q B, line N P C, line M Q, line Q P, line N M A, line N Q B, line N P C, line M Q, line Q P\nFind the measure of MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5244.jpg"
-  },
-  {
-    "id": 5374,
-    "problem_id": 5245,
-    "problem": "line N M A, line N Q B, line N P C, line M Q, line Q P, line N M A, line N Q B, line N P C, line M Q, line Q P\nFind the measure of MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5245.jpg"
-  },
-  {
-    "id": 5375,
-    "problem_id": 5246,
-    "problem": "line N M A, line N Q B, line N P C, line M Q, line Q P, line N M A, line N Q B, line N P C, line M Q, line Q P\nFind the measure of MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5246.jpg"
-  },
-  {
-    "id": 5376,
-    "problem_id": 5247,
-    "problem": "line C D E, line A E, line D A, line B D, line B C, line C D E, line A E, line D A, line B D, line B C\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5247.jpg"
-  },
-  {
-    "id": 5377,
-    "problem_id": 5248,
-    "problem": "line C D E, line A E, line D A, line B D, line B C, line C D E, line A E, line D A, line B D, line B C\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5248.jpg"
-  },
-  {
-    "id": 5378,
-    "problem_id": 5249,
-    "problem": "line C D E, line A E, line D A, line B D, line B C, line C D E, line A E, line D A, line B D, line B C\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5249.jpg"
-  },
-  {
-    "id": 5379,
-    "problem_id": 5250,
-    "problem": "line C D E, line A E, line D A, line B D, line B C, line C D E, line A E, line D A, line B D, line B C\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5250.jpg"
-  },
-  {
-    "id": 5380,
-    "problem_id": 5251,
-    "problem": "line C D E, line A E, line D A, line B D, line B C, line C D E, line A E, line D A, line B D, line B C\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5251.jpg"
-  },
-  {
-    "id": 5381,
-    "problem_id": 5252,
-    "problem": "line A X Z, line Y X, \\odot X lieson A Y Z, line A X Z, line Y X, \\odot X lieson A Y Z\nFind the length of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5252.jpg"
-  },
-  {
-    "id": 5382,
-    "problem_id": 5253,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5253.jpg"
-  },
-  {
-    "id": 5383,
-    "problem_id": 5254,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5254.jpg"
-  },
-  {
-    "id": 5384,
-    "problem_id": 5255,
-    "problem": "line B A, line B C, line C D, line A D, line B A, line B C, line C D, line A D\nUse the diagram of \\parallelogram ABCD to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5255.jpg"
-  },
-  {
-    "id": 5385,
-    "problem_id": 5256,
-    "problem": "line R P S, line R T, line S Q T, line P Q, line R P S, line R T, line S Q T, line P Q\nPQ is a midsegment of \\triangle RST. What is the length of RT?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5256.jpg"
-  },
-  {
-    "id": 5386,
-    "problem_id": 5257,
-    "problem": "line S R, line X W, line P Q, line Q R, line T V, line S P, line V W, line X T, line S R, line X W, line P Q, line Q R, line T V, line S P, line V W, line X T\nPQRS \\sim TVWX. Find the value of u.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5257.jpg"
-  },
-  {
-    "id": 5387,
-    "problem_id": 5258,
-    "problem": "line A C D, line B C, line B D, line B A, line A C D, line B C, line B D, line B A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5258.jpg"
-  },
-  {
-    "id": 5388,
-    "problem_id": 5259,
-    "problem": "line A C D, line B C, line B D, line B A, line A C D, line B C, line B D, line B A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5259.jpg"
-  },
-  {
-    "id": 5389,
-    "problem_id": 5260,
-    "problem": "line A C D, line B C, line B D, line B A, line A C D, line B C, line B D, line B A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5260.jpg"
-  },
-  {
-    "id": 5390,
-    "problem_id": 5261,
-    "problem": "line A C D, line B C, line B D, line B A, line A C D, line B C, line B D, line B A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5261.jpg"
-  },
-  {
-    "id": 5391,
-    "problem_id": 5262,
-    "problem": "line A C D, line B C, line B D, line B A, line A C D, line B C, line B D, line B A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5262.jpg"
-  },
-  {
-    "id": 5392,
-    "problem_id": 5263,
-    "problem": "line A D F, line A B, line E D B, \\odot C lieson A E F B, line A D F, line A B, line E D B, \\odot C lieson A E F B\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5263.jpg"
-  },
-  {
-    "id": 5393,
-    "problem_id": 5264,
-    "problem": "line A D F, line A B, line E D B, \\odot C lieson A E F B, line A D F, line A B, line E D B, \\odot C lieson A E F B\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5264.jpg"
-  },
-  {
-    "id": 5394,
-    "problem_id": 5265,
-    "problem": "line D A, line A C, line A B, line D C B, line D A, line A C, line A B, line D C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5265.jpg"
-  },
-  {
-    "id": 5395,
-    "problem_id": 5266,
-    "problem": "line D A, line A C, line A B, line D C B, line D A, line A C, line A B, line D C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5266.jpg"
-  },
-  {
-    "id": 5396,
-    "problem_id": 5267,
-    "problem": "line D A, line A C, line A B, line D C B, line D A, line A C, line A B, line D C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5267.jpg"
-  },
-  {
-    "id": 5397,
-    "problem_id": 5268,
-    "problem": "line D A, line A C, line A B, line D C B, line D A, line A C, line A B, line D C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5268.jpg"
-  },
-  {
-    "id": 5399,
-    "problem_id": 5269,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5269.jpg"
-  },
-  {
-    "id": 5400,
-    "problem_id": 5270,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5270.jpg"
-  },
-  {
-    "id": 5401,
-    "problem_id": 5271,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5271.jpg"
-  },
-  {
-    "id": 5402,
-    "problem_id": 5272,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5272.jpg"
-  },
-  {
-    "id": 5403,
-    "problem_id": 5273,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5273.jpg"
-  },
-  {
-    "id": 5404,
-    "problem_id": 5274,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the value of w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5274.jpg"
-  },
-  {
-    "id": 5405,
-    "problem_id": 5275,
-    "problem": "line A D F, line C E D, line B A, line C F, line B C, line B E, line A D F, line C E D, line B A, line C F, line B C, line B E\nFind the area of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5275.jpg"
-  },
-  {
-    "id": 5406,
-    "problem_id": 5276,
-    "problem": "line A D F, line C E D, line B A, line C F, line B C, line B E, line A D F, line C E D, line B A, line C F, line B C, line B E\nFind the area of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5276.jpg"
-  },
-  {
-    "id": 5407,
-    "problem_id": 5277,
-    "problem": "line A D F, line C E D, line B A, line C F, line B C, line B E, line A D F, line C E D, line B A, line C F, line B C, line B E\nFind the area of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5277.jpg"
-  },
-  {
-    "id": 5408,
-    "problem_id": 5278,
-    "problem": "line Q T S, line S R, line T R, line Q R, line Q T S, line S R, line T R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5278.jpg"
-  },
-  {
-    "id": 5409,
-    "problem_id": 5279,
-    "problem": "line Q T S, line S R, line T R, line Q R, line Q T S, line S R, line T R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5279.jpg"
-  },
-  {
-    "id": 5410,
-    "problem_id": 5280,
-    "problem": "line Q T S, line S R, line T R, line Q R, line Q T S, line S R, line T R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5280.jpg"
-  },
-  {
-    "id": 5411,
-    "problem_id": 5281,
-    "problem": "line Q T S, line S R, line T R, line Q R, line Q T S, line S R, line T R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5281.jpg"
-  },
-  {
-    "id": 5412,
-    "problem_id": 5282,
-    "problem": "line Q T S, line S R, line T R, line Q R, line Q T S, line S R, line T R, line Q R\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5282.jpg"
-  },
-  {
-    "id": 5414,
-    "problem_id": 5283,
-    "problem": "line A P D, line B P Q E, line C R Q F, line A P D, line B P Q E, line C R Q F\nFind m \\angle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5283.jpg"
-  },
-  {
-    "id": 5415,
-    "problem_id": 5284,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of e.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5284.jpg"
-  },
-  {
-    "id": 5416,
-    "problem_id": 5285,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of e.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5285.jpg"
-  },
-  {
-    "id": 5417,
-    "problem_id": 5286,
-    "problem": "line B C, line A D C, line A B, line B D, line B C, line A D C, line A B, line B D\nFind the value of e.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5286.jpg"
-  },
-  {
-    "id": 5418,
-    "problem_id": 5287,
-    "problem": "line B A, \\odot A lieson B, line B A, \\odot A lieson B\nFind the circumference of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5287.jpg"
-  },
-  {
-    "id": 5419,
-    "problem_id": 5288,
-    "problem": "line B A, \\odot A lieson B, line B A, \\odot A lieson B\nFind the circumference of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5288.jpg"
-  },
-  {
-    "id": 5420,
-    "problem_id": 5289,
-    "problem": "line B A, \\odot A lieson B, line B A, \\odot A lieson B\nFind the circumference of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5289.jpg"
-  },
-  {
-    "id": 5421,
-    "problem_id": 5290,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5290.jpg"
-  },
-  {
-    "id": 5422,
-    "problem_id": 5291,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5291.jpg"
-  },
-  {
-    "id": 5423,
-    "problem_id": 5292,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5292.jpg"
-  },
-  {
-    "id": 5424,
-    "problem_id": 5293,
-    "problem": "line B C D, line A C F H, line E F G, line B C D, line A C F H, line E F G\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5293.jpg"
-  },
-  {
-    "id": 5425,
-    "problem_id": 5294,
-    "problem": "line A C, line A E, line C D E, line B D, line A C, line A E, line C D E, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5294.jpg"
-  },
-  {
-    "id": 5426,
-    "problem_id": 5295,
-    "problem": "line A C, line A E, line C D E, line B D, line A C, line A E, line C D E, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5295.jpg"
-  },
-  {
-    "id": 5427,
-    "problem_id": 5296,
-    "problem": "line G F, line E F, line G E, line G F, line E F, line G E\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5296.jpg"
-  },
-  {
-    "id": 5428,
-    "problem_id": 5297,
-    "problem": "line G F, line E F, line G E, line G F, line E F, line G E\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5297.jpg"
-  },
-  {
-    "id": 5429,
-    "problem_id": 5298,
-    "problem": "line G F, line E F, line G E, line G F, line E F, line G E\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5298.jpg"
-  },
-  {
-    "id": 5430,
-    "problem_id": 5299,
-    "problem": "line G F, line E F, line G E, line G F, line E F, line G E\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5299.jpg"
-  },
-  {
-    "id": 5431,
-    "problem_id": 5300,
-    "problem": "line A D, line E D, line C E, line C A, line A B E, line C B D, line A D, line E D, line C E, line C A, line A B E, line C B D\nFind the measure of \\angle 1 in the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5300.jpg"
-  },
-  {
-    "id": 5432,
-    "problem_id": 5301,
-    "problem": "line R S T, line R S T\nS is between R and T. Find RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5301.jpg"
-  },
-  {
-    "id": 5433,
-    "problem_id": 5302,
-    "problem": "line R S T, line R S T\nS is between R and T. Find RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5302.jpg"
-  },
-  {
-    "id": 5434,
-    "problem_id": 5303,
-    "problem": "line R S T, line R S T\nS is between R and T. Find RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5303.jpg"
-  },
-  {
-    "id": 5435,
-    "problem_id": 5304,
-    "problem": "line R S T, line R S T\nS is between R and T. Find RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5304.jpg"
-  },
-  {
-    "id": 5436,
-    "problem_id": 5305,
-    "problem": "line A B D, line C B, \\odot B lieson A C D, line A B D, line C B, \\odot B lieson A C D\nFind the length of \\widehat AC shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5305.jpg"
-  },
-  {
-    "id": 5437,
-    "problem_id": 5306,
-    "problem": "line A B D, line C B, \\odot B lieson A C D, line A B D, line C B, \\odot B lieson A C D\nFind the length of \\widehat AC shown in red.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5306.jpg"
-  },
-  {
-    "id": 5438,
-    "problem_id": 5307,
-    "problem": "line A B, line B D, line D F, line E F, line C E, line A C, line A B, line B D, line D F, line E F, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5307.jpg"
-  },
-  {
-    "id": 5439,
-    "problem_id": 5308,
-    "problem": "line A B, line B D, line D F, line E F, line C E, line A C, line A B, line B D, line D F, line E F, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5308.jpg"
-  },
-  {
-    "id": 5440,
-    "problem_id": 5309,
-    "problem": "line A B, line B D, line D F, line E F, line C E, line A C, line A B, line B D, line D F, line E F, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5309.jpg"
-  },
-  {
-    "id": 5441,
-    "problem_id": 5310,
-    "problem": "line A B, line B D, line D F, line E F, line C E, line A C, line A B, line B D, line D F, line E F, line C E, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5310.jpg"
-  },
-  {
-    "id": 5442,
-    "problem_id": 5311,
-    "problem": "line A C E, line D C B, line B E, line A B, line A D, line D E, line A C E, line D C B, line B E, line A B, line A D, line D E\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5311.jpg"
-  },
-  {
-    "id": 5443,
-    "problem_id": 5312,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5312.jpg"
-  },
-  {
-    "id": 5444,
-    "problem_id": 5313,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5313.jpg"
-  },
-  {
-    "id": 5445,
-    "problem_id": 5314,
-    "problem": "line J M K, line J L, line K L, line M L, line J M K, line J L, line K L, line M L\nFind JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5314.jpg"
-  },
-  {
-    "id": 5446,
-    "problem_id": 5315,
-    "problem": "line K L, line J M L, line K J, line K M, line K L, line J M L, line K J, line K M\nGiven isosceles \\triangle JKL with base JL. If JL = 5, find ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5315.jpg"
-  },
-  {
-    "id": 5447,
-    "problem_id": 5316,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5316.jpg"
-  },
-  {
-    "id": 5448,
-    "problem_id": 5317,
-    "problem": "line B E D, line A E C, line D C, line B C, line A B, line A D, line B E D, line A E C, line D C, line B C, line A B, line A D\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5317.jpg"
-  },
-  {
-    "id": 5449,
-    "problem_id": 5318,
-    "problem": "line S R Q, line P Q, \\odot A lieson S R P, line S R Q, line P Q, \\odot A lieson S R P\nPQ is tangent to the circle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5318.jpg"
-  },
-  {
-    "id": 5450,
-    "problem_id": 5319,
-    "problem": "line A D, line A B E, line D C E, line B C, line A D, line A B E, line D C E, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5319.jpg"
-  },
-  {
-    "id": 5451,
-    "problem_id": 5320,
-    "problem": "line A D, line A B E, line D C E, line B C, line A D, line A B E, line D C E, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5320.jpg"
-  },
-  {
-    "id": 5452,
-    "problem_id": 5321,
-    "problem": "line A D, line A B E, line D C E, line B C, line A D, line A B E, line D C E, line B C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5321.jpg"
-  },
-  {
-    "id": 5453,
-    "problem_id": 5322,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5322.jpg"
-  },
-  {
-    "id": 5454,
-    "problem_id": 5323,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5323.jpg"
-  },
-  {
-    "id": 5455,
-    "problem_id": 5324,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf a = 4, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5324.jpg"
-  },
-  {
-    "id": 5456,
-    "problem_id": 5325,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf a = 4, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5325.jpg"
-  },
-  {
-    "id": 5457,
-    "problem_id": 5326,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf a = 4, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5326.jpg"
-  },
-  {
-    "id": 5458,
-    "problem_id": 5327,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf a = 4, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5327.jpg"
-  },
-  {
-    "id": 5459,
-    "problem_id": 5328,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf a = 4, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5328.jpg"
-  },
-  {
-    "id": 5460,
-    "problem_id": 5329,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf a = 4, find b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5329.jpg"
-  },
-  {
-    "id": 5461,
-    "problem_id": 5330,
-    "problem": "line Z W, line Y Z, line X W, line Y X, line Z W, line Y Z, line X W, line Y X\nWhat is m \\angle 3 in the isosceles trapezoid?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5330.jpg"
-  },
-  {
-    "id": 5462,
-    "problem_id": 5331,
-    "problem": "line Z W, line Y Z, line X W, line Y X, line Z W, line Y Z, line X W, line Y X\nWhat is m \\angle 3 in the isosceles trapezoid?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5331.jpg"
-  },
-  {
-    "id": 5463,
-    "problem_id": 5332,
-    "problem": "line Z W, line Y Z, line X W, line Y X, line Z W, line Y Z, line X W, line Y X\nWhat is m \\angle 3 in the isosceles trapezoid?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5332.jpg"
-  },
-  {
-    "id": 5464,
-    "problem_id": 5333,
-    "problem": "line C D B, line A B, line C A, \\odot E lieson C D A, line C D B, line A B, line C A, \\odot E lieson C D A\nSolve for m \\angle CAB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5333.jpg"
-  },
-  {
-    "id": 5465,
-    "problem_id": 5334,
-    "problem": "line T Q V, line R T, line R S V, line S Q, line T Q V, line R T, line R S V, line S Q\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5334.jpg"
-  },
-  {
-    "id": 5466,
-    "problem_id": 5335,
-    "problem": "line T Q V, line R T, line R S V, line S Q, line T Q V, line R T, line R S V, line S Q\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5335.jpg"
-  },
-  {
-    "id": 5467,
-    "problem_id": 5336,
-    "problem": "line T Q V, line R T, line R S V, line S Q, line T Q V, line R T, line R S V, line S Q\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5336.jpg"
-  },
-  {
-    "id": 5468,
-    "problem_id": 5337,
-    "problem": "line T Q V, line R T, line R S V, line S Q, line T Q V, line R T, line R S V, line S Q\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5337.jpg"
-  },
-  {
-    "id": 5469,
-    "problem_id": 5338,
-    "problem": "line T Q V, line R T, line R S V, line S Q, line T Q V, line R T, line R S V, line S Q\nFind the measure of RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5338.jpg"
-  },
-  {
-    "id": 5470,
-    "problem_id": 5339,
-    "problem": "line A D, line C B, line C D, line B A, line B D, line A D, line C B, line C D, line B A, line B D\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5339.jpg"
-  },
-  {
-    "id": 5471,
-    "problem_id": 5340,
-    "problem": "line A D, line C B, line C D, line B A, line B D, line A D, line C B, line C D, line B A, line B D\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5340.jpg"
-  },
-  {
-    "id": 5472,
-    "problem_id": 5341,
-    "problem": "line A D, line C B, line C D, line B A, line B D, line A D, line C B, line C D, line B A, line B D\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5341.jpg"
-  },
-  {
-    "id": 5473,
-    "problem_id": 5342,
-    "problem": "line A D, line C B, line C D, line B A, line B D, line A D, line C B, line C D, line B A, line B D\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5342.jpg"
-  },
-  {
-    "id": 5474,
-    "problem_id": 5343,
-    "problem": "line A D, line C B, line C D, line B A, line B D, line A D, line C B, line C D, line B A, line B D\nSolve for the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5343.jpg"
-  },
-  {
-    "id": 5475,
-    "problem_id": 5344,
-    "problem": "line A C F H, line k lieson E F G, line j lieson B C D, line A C F H, line k lieson E F G, line j lieson B C D\nline j \\parallel line k. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5344.jpg"
-  },
-  {
-    "id": 5476,
-    "problem_id": 5345,
-    "problem": "line E C B, line A E, line B D, line A C D, line A B, line E D, line E C B, line A E, line B D, line A C D, line A B, line E D\nDetermine the measure of \\angle 3 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5345.jpg"
-  },
-  {
-    "id": 5477,
-    "problem_id": 5346,
-    "problem": "line D C B, line A C E, \\odot F lieson A D E B, line D C B, line A C E, \\odot F lieson A D E B\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5346.jpg"
-  },
-  {
-    "id": 5478,
-    "problem_id": 5347,
-    "problem": "line D C B, line A C E, \\odot F lieson A D E B, line D C B, line A C E, \\odot F lieson A D E B\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5347.jpg"
-  },
-  {
-    "id": 5479,
-    "problem_id": 5348,
-    "problem": "line A D F, line A B, line E D B, \\odot C lieson A E F B, line A D F, line A B, line E D B, \\odot C lieson A E F B\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5348.jpg"
-  },
-  {
-    "id": 5480,
-    "problem_id": 5349,
-    "problem": "line A D F, line A B, line E D B, \\odot C lieson A E F B, line A D F, line A B, line E D B, \\odot C lieson A E F B\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5349.jpg"
-  },
-  {
-    "id": 5481,
-    "problem_id": 5350,
-    "problem": "line X Y Z, line X Y Z\nIf XZ = 50, what is YZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5350.jpg"
-  },
-  {
-    "id": 5482,
-    "problem_id": 5351,
-    "problem": "line X Y Z, line X Y Z\nIf XZ = 50, what is YZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5351.jpg"
-  },
-  {
-    "id": 5483,
-    "problem_id": 5352,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 4?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5352.jpg"
-  },
-  {
-    "id": 5484,
-    "problem_id": 5353,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 4?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5353.jpg"
-  },
-  {
-    "id": 5485,
-    "problem_id": 5354,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 4?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5354.jpg"
-  },
-  {
-    "id": 5486,
-    "problem_id": 5355,
-    "problem": "line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B, line p lieson G H K L, line q lieson F E D C, line l lieson I H E A, line m lieson J K D B\nWhat is the measure of \\angle 4?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5355.jpg"
-  },
-  {
-    "id": 5487,
-    "problem_id": 5356,
-    "problem": "line A B C, line B D, \\odot B lieson A D C, line A B C, line B D, \\odot B lieson A D C\nFind the area of the shaded region of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5356.jpg"
-  },
-  {
-    "id": 5488,
-    "problem_id": 5357,
-    "problem": "line A B C, line B D, \\odot B lieson A D C, line A B C, line B D, \\odot B lieson A D C\nFind the area of the shaded region of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5357.jpg"
-  },
-  {
-    "id": 5489,
-    "problem_id": 5358,
-    "problem": "line A B C, line B D, \\odot B lieson A D C, line A B C, line B D, \\odot B lieson A D C\nFind the area of the shaded region of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5358.jpg"
-  },
-  {
-    "id": 5490,
-    "problem_id": 5359,
-    "problem": "line A B C, line B D, \\odot B lieson A D C, line A B C, line B D, \\odot B lieson A D C\nFind the area of the shaded region of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5359.jpg"
-  },
-  {
-    "id": 5491,
-    "problem_id": 5360,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5360.jpg"
-  },
-  {
-    "id": 5492,
-    "problem_id": 5361,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5361.jpg"
-  },
-  {
-    "id": 5493,
-    "problem_id": 5362,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5362.jpg"
-  },
-  {
-    "id": 5494,
-    "problem_id": 5363,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5363.jpg"
-  },
-  {
-    "id": 5495,
-    "problem_id": 5364,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5364.jpg"
-  },
-  {
-    "id": 5496,
-    "problem_id": 5365,
-    "problem": "line A B C, line E B D, \\odot F lieson A E C D, line A B C, line E B D, \\odot F lieson A E C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5365.jpg"
-  },
-  {
-    "id": 5497,
-    "problem_id": 5366,
-    "problem": "line A B C, line E B D, \\odot F lieson A E C D, line A B C, line E B D, \\odot F lieson A E C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5366.jpg"
-  },
-  {
-    "id": 5498,
-    "problem_id": 5367,
-    "problem": "line A B C, line E B D, \\odot F lieson A E C D, line A B C, line E B D, \\odot F lieson A E C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5367.jpg"
-  },
-  {
-    "id": 5499,
-    "problem_id": 5368,
-    "problem": "line A B C, line E B D, \\odot F lieson A E C D, line A B C, line E B D, \\odot F lieson A E C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5368.jpg"
-  },
-  {
-    "id": 5500,
-    "problem_id": 5369,
-    "problem": "line A B C, line E D C, line B D, line A B C, line E D C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5369.jpg"
-  },
-  {
-    "id": 5501,
-    "problem_id": 5370,
-    "problem": "line A B C, line E D C, line B D, line A B C, line E D C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5370.jpg"
-  },
-  {
-    "id": 5502,
-    "problem_id": 5371,
-    "problem": "line A B C, line E D C, line B D, line A B C, line E D C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5371.jpg"
-  },
-  {
-    "id": 5503,
-    "problem_id": 5372,
-    "problem": "line A B C, line E D C, line B D, line A B C, line E D C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5372.jpg"
-  },
-  {
-    "id": 5504,
-    "problem_id": 5373,
-    "problem": "line A B C, line E D C, line B D, line A B C, line E D C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5373.jpg"
-  },
-  {
-    "id": 5505,
-    "problem_id": 5374,
-    "problem": "line D C, line A D, line A B, line C B, line D C, line A D, line A B, line C B\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5374.jpg"
-  },
-  {
-    "id": 5506,
-    "problem_id": 5375,
-    "problem": "line D C, line A D, line A B, line C B, line D C, line A D, line A B, line C B\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5375.jpg"
-  },
-  {
-    "id": 5507,
-    "problem_id": 5376,
-    "problem": "line D C, line A D, line A B, line C B, line D C, line A D, line A B, line C B\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5376.jpg"
-  },
-  {
-    "id": 5508,
-    "problem_id": 5377,
-    "problem": "line D C, line A D, line A B, line C B, line D C, line A D, line A B, line C B\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5377.jpg"
-  },
-  {
-    "id": 5509,
-    "problem_id": 5378,
-    "problem": "line D C, line A D, line A B, line C B, line D C, line A D, line A B, line C B\nSolve for the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5378.jpg"
-  },
-  {
-    "id": 5511,
-    "problem_id": 5379,
-    "problem": "line D E, line A B D, line A E, line A C, line B C, line D E, line A B D, line A E, line A C, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5379.jpg"
-  },
-  {
-    "id": 5512,
-    "problem_id": 5380,
-    "problem": "line D E, line A B D, line A E, line A C, line B C, line D E, line A B D, line A E, line A C, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5380.jpg"
-  },
-  {
-    "id": 5513,
-    "problem_id": 5381,
-    "problem": "line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B, line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B\nFind the area of the inscribed regular polygon shown.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5381.jpg"
-  },
-  {
-    "id": 5514,
-    "problem_id": 5382,
-    "problem": "line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B, line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B\nFind the area of the inscribed regular polygon shown.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5382.jpg"
-  },
-  {
-    "id": 5515,
-    "problem_id": 5383,
-    "problem": "line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B, line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B\nFind the area of the inscribed regular polygon shown.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5383.jpg"
-  },
-  {
-    "id": 5516,
-    "problem_id": 5384,
-    "problem": "line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B, line F E, line A F, line A B, line B C, line C D, line E H D, line G E, line G H, \\odot G lieson A F E D C B\nFind the area of the inscribed regular polygon shown.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5384.jpg"
-  },
-  {
-    "id": 5517,
-    "problem_id": 5385,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5385.jpg"
-  },
-  {
-    "id": 5518,
-    "problem_id": 5386,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5386.jpg"
-  },
-  {
-    "id": 5519,
-    "problem_id": 5387,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5387.jpg"
-  },
-  {
-    "id": 5520,
-    "problem_id": 5388,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5388.jpg"
-  },
-  {
-    "id": 5521,
-    "problem_id": 5389,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5389.jpg"
-  },
-  {
-    "id": 5522,
-    "problem_id": 5390,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5390.jpg"
-  },
-  {
-    "id": 5523,
-    "problem_id": 5391,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5391.jpg"
-  },
-  {
-    "id": 5524,
-    "problem_id": 5392,
-    "problem": "line A E D, line B C D, line E C, line B E, line A B, line A E D, line B C D, line E C, line B E, line A B\nm \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5392.jpg"
-  },
-  {
-    "id": 5525,
-    "problem_id": 5393,
-    "problem": "line A F C, line B F D, line D C, line A D, line A B, line B C, line A F C, line B F D, line D C, line A D, line A B, line B C\nUse rhombus ABCD with m \\angle 1 = 2x+20, m \\angle 2 = 5x-4, AC = 15, and m \\angle 3 = y^{2}+26. Solve for m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5393.jpg"
-  },
-  {
-    "id": 5526,
-    "problem_id": 5394,
-    "problem": "line A D C, line E D B, line A B, line B C, line A E, line E C, line A D C, line E D B, line A B, line B C, line A E, line E C\nFind x in the kite. Area = 104 ft^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5394.jpg"
-  },
-  {
-    "id": 5527,
-    "problem_id": 5395,
-    "problem": "line B C D, line B A, line A C, \\odot A lieson B D, line B C D, line B A, line A C, \\odot A lieson B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5395.jpg"
-  },
-  {
-    "id": 5528,
-    "problem_id": 5396,
-    "problem": "line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C, line A C, line B C, line B D, line E D C, line C F, \\odot D lieson B E F C\nFind the value of variable c. Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5396.jpg"
-  },
-  {
-    "id": 5529,
-    "problem_id": 5397,
-    "problem": "line D C, line B C, line A B, line A D, line D E B, line A E C, line D C, line B C, line A B, line A D, line D E B, line A E C\nIn rhombus ABCD, AB = 2x+3 and BC = 5x. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5397.jpg"
-  },
-  {
-    "id": 5530,
-    "problem_id": 5398,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the area of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5398.jpg"
-  },
-  {
-    "id": 5531,
-    "problem_id": 5399,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the area of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5399.jpg"
-  },
-  {
-    "id": 5532,
-    "problem_id": 5400,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the area of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5400.jpg"
-  },
-  {
-    "id": 5533,
-    "problem_id": 5401,
-    "problem": "line X Y, line Z Y, line W Z, line W X, line X Y, line Z Y, line W Z, line W X\nWhat is the area of rectangle WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5401.jpg"
-  },
-  {
-    "id": 5534,
-    "problem_id": 5402,
-    "problem": "line E G D, line E J F, line E C H, line D H F, line G C F, line D C J, line E G D, line E J F, line E C H, line D H F, line G C F, line D C J\nFind the length of HF, given that DE = FE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5402.jpg"
-  },
-  {
-    "id": 5535,
-    "problem_id": 5403,
-    "problem": "line E G D, line E J F, line E C H, line D H F, line G C F, line D C J, line E G D, line E J F, line E C H, line D H F, line G C F, line D C J\nFind the length of HF, given that DE = FE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5403.jpg"
-  },
-  {
-    "id": 5536,
-    "problem_id": 5404,
-    "problem": "line E G D, line G A F, line B F C, \\odot A lieson E D C B, line E G D, line G A F, line B F C, \\odot A lieson E D C B\nFind the length of ED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5404.jpg"
-  },
-  {
-    "id": 5537,
-    "problem_id": 5405,
-    "problem": "line J M L, line K L, line K M, line K J, line J M L, line K L, line K M, line K J\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5405.jpg"
-  },
-  {
-    "id": 5538,
-    "problem_id": 5406,
-    "problem": "line J M L, line K L, line K M, line K J, line J M L, line K L, line K M, line K J\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5406.jpg"
-  },
-  {
-    "id": 5539,
-    "problem_id": 5407,
-    "problem": "line J M L, line K L, line K M, line K J, line J M L, line K L, line K M, line K J\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5407.jpg"
-  },
-  {
-    "id": 5540,
-    "problem_id": 5408,
-    "problem": "line J M L, line K L, line K M, line K J, line J M L, line K L, line K M, line K J\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5408.jpg"
-  },
-  {
-    "id": 5541,
-    "problem_id": 5409,
-    "problem": "line M N, line R Q, line R P, line L N, line L M, line Q P, line M N, line R Q, line R P, line L N, line L M, line Q P\n\\triangle LMN \\cong \\triangle PQR. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5409.jpg"
-  },
-  {
-    "id": 5542,
-    "problem_id": 5410,
-    "problem": "line M N, line R Q, line R P, line L N, line L M, line Q P, line M N, line R Q, line R P, line L N, line L M, line Q P\n\\triangle LMN \\cong \\triangle PQR. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5410.jpg"
-  },
-  {
-    "id": 5543,
-    "problem_id": 5411,
-    "problem": "line J M K, line J L, line K L, line M L, line J M K, line J L, line K L, line M L\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5411.jpg"
-  },
-  {
-    "id": 5544,
-    "problem_id": 5412,
-    "problem": "line J M K, line J L, line K L, line M L, line J M K, line J L, line K L, line M L\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5412.jpg"
-  },
-  {
-    "id": 5545,
-    "problem_id": 5413,
-    "problem": "line J M K, line J L, line K L, line M L, line J M K, line J L, line K L, line M L\nFind JM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5413.jpg"
-  },
-  {
-    "id": 5546,
-    "problem_id": 5414,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5414.jpg"
-  },
-  {
-    "id": 5547,
-    "problem_id": 5415,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5415.jpg"
-  },
-  {
-    "id": 5548,
-    "problem_id": 5416,
-    "problem": "line E A B C D F, line E A B C D F\nFind the measurement of BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5416.jpg"
-  },
-  {
-    "id": 5549,
-    "problem_id": 5417,
-    "problem": "line M N, line M P, line N P, line J L, line K L, line J K, line M N, line M P, line N P, line J L, line K L, line J K\n\\triangle JKL \\sim \\triangle MNP. Find PM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5417.jpg"
-  },
-  {
-    "id": 5550,
-    "problem_id": 5418,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5418.jpg"
-  },
-  {
-    "id": 5551,
-    "problem_id": 5419,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5419.jpg"
-  },
-  {
-    "id": 5552,
-    "problem_id": 5420,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5420.jpg"
-  },
-  {
-    "id": 5553,
-    "problem_id": 5421,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5421.jpg"
-  },
-  {
-    "id": 5554,
-    "problem_id": 5422,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5422.jpg"
-  },
-  {
-    "id": 5555,
-    "problem_id": 5423,
-    "problem": "line B A C D, line E H, line A F, line G H, line C E, line F G, line B A C D, line E H, line A F, line G H, line C E, line F G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5423.jpg"
-  },
-  {
-    "id": 5556,
-    "problem_id": 5424,
-    "problem": "line Q R S, line P R T, line P Q, line S T, line Q R S, line P R T, line P Q, line S T\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5424.jpg"
-  },
-  {
-    "id": 5558,
-    "problem_id": 5425,
-    "problem": "line Q R S, line P R T, line P Q, line S T, line Q R S, line P R T, line P Q, line S T\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5425.jpg"
-  },
-  {
-    "id": 5559,
-    "problem_id": 5426,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5426.jpg"
-  },
-  {
-    "id": 5560,
-    "problem_id": 5427,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5427.jpg"
-  },
-  {
-    "id": 5561,
-    "problem_id": 5428,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5428.jpg"
-  },
-  {
-    "id": 5562,
-    "problem_id": 5429,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5429.jpg"
-  },
-  {
-    "id": 5563,
-    "problem_id": 5430,
-    "problem": "line B A, line D C B, line C A, line B A, line D C B, line C A\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5430.jpg"
-  },
-  {
-    "id": 5564,
-    "problem_id": 5431,
-    "problem": "line B A, line D C B, line C A, line B A, line D C B, line C A\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5431.jpg"
-  },
-  {
-    "id": 5565,
-    "problem_id": 5432,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5432.jpg"
-  },
-  {
-    "id": 5566,
-    "problem_id": 5433,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5433.jpg"
-  },
-  {
-    "id": 5567,
-    "problem_id": 5434,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5434.jpg"
-  },
-  {
-    "id": 5568,
-    "problem_id": 5435,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5435.jpg"
-  },
-  {
-    "id": 5569,
-    "problem_id": 5436,
-    "problem": "line C D B, line D A, line A B, line C D B, line D A, line A B\nWhat is the value of b?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5436.jpg"
-  },
-  {
-    "id": 5570,
-    "problem_id": 5437,
-    "problem": "line C D B, line D A, line A B, line C D B, line D A, line A B\nWhat is the value of b?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5437.jpg"
-  },
-  {
-    "id": 5571,
-    "problem_id": 5438,
-    "problem": "line A C, line B C, line C D, line A C, line B C, line C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5438.jpg"
-  },
-  {
-    "id": 5572,
-    "problem_id": 5439,
-    "problem": "line A C, line B C, line C D, line A C, line B C, line C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5439.jpg"
-  },
-  {
-    "id": 5573,
-    "problem_id": 5440,
-    "problem": "line A C, line B C, line C D, line A C, line B C, line C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5440.jpg"
-  },
-  {
-    "id": 5574,
-    "problem_id": 5441,
-    "problem": "line A C, line B C, line C D, line A C, line B C, line C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5441.jpg"
-  },
-  {
-    "id": 5575,
-    "problem_id": 5442,
-    "problem": "line a lieson B C D, line b lieson E F G, line A C F H, line a lieson B C D, line b lieson E F G, line A C F H\nDetermine the value of x for which line a \\parallel line b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5442.jpg"
-  },
-  {
-    "id": 5576,
-    "problem_id": 5443,
-    "problem": "line a lieson B C D, line b lieson E F G, line A C F H, line a lieson B C D, line b lieson E F G, line A C F H\nDetermine the value of x for which line a \\parallel line b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5443.jpg"
-  },
-  {
-    "id": 5577,
-    "problem_id": 5444,
-    "problem": "line a lieson B C D, line b lieson E F G, line A C F H, line a lieson B C D, line b lieson E F G, line A C F H\nDetermine the value of x for which line a \\parallel line b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5444.jpg"
-  },
-  {
-    "id": 5578,
-    "problem_id": 5445,
-    "problem": "line a lieson B C D, line b lieson E F G, line A C F H, line a lieson B C D, line b lieson E F G, line A C F H\nDetermine the value of x for which line a \\parallel line b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5445.jpg"
-  },
-  {
-    "id": 5579,
-    "problem_id": 5446,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5446.jpg"
-  },
-  {
-    "id": 5580,
-    "problem_id": 5447,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5447.jpg"
-  },
-  {
-    "id": 5581,
-    "problem_id": 5448,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5448.jpg"
-  },
-  {
-    "id": 5582,
-    "problem_id": 5449,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFor what value of variable y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5449.jpg"
-  },
-  {
-    "id": 5583,
-    "problem_id": 5450,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5450.jpg"
-  },
-  {
-    "id": 5584,
-    "problem_id": 5451,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5451.jpg"
-  },
-  {
-    "id": 5585,
-    "problem_id": 5452,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5452.jpg"
-  },
-  {
-    "id": 5586,
-    "problem_id": 5453,
-    "problem": "line a lieson E D B, line b lieson H F C, line A D F G, line a lieson E D B, line b lieson H F C, line A D F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5453.jpg"
-  },
-  {
-    "id": 5587,
-    "problem_id": 5454,
-    "problem": "line a lieson E D B, line b lieson H F C, line A D F G, line a lieson E D B, line b lieson H F C, line A D F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5454.jpg"
-  },
-  {
-    "id": 5588,
-    "problem_id": 5455,
-    "problem": "line N P, line M P, line Q P, line N Q, line M N, line N P, line M P, line Q P, line N Q, line M N\n\\triangle MNP \\cong \\triangle QNP, what is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5455.jpg"
-  },
-  {
-    "id": 5589,
-    "problem_id": 5456,
-    "problem": "line N P, line M P, line Q P, line N Q, line M N, line N P, line M P, line Q P, line N Q, line M N\n\\triangle MNP \\cong \\triangle QNP, what is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5456.jpg"
-  },
-  {
-    "id": 5590,
-    "problem_id": 5457,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind DB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5457.jpg"
-  },
-  {
-    "id": 5591,
-    "problem_id": 5458,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5458.jpg"
-  },
-  {
-    "id": 5592,
-    "problem_id": 5459,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5459.jpg"
-  },
-  {
-    "id": 5593,
-    "problem_id": 5460,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5460.jpg"
-  },
-  {
-    "id": 5594,
-    "problem_id": 5461,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5461.jpg"
-  },
-  {
-    "id": 5595,
-    "problem_id": 5462,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5462.jpg"
-  },
-  {
-    "id": 5596,
-    "problem_id": 5463,
-    "problem": "line C B, line A B, line A C, line C B, line A B, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5463.jpg"
-  },
-  {
-    "id": 5597,
-    "problem_id": 5464,
-    "problem": "line J M, line J K, line K L, line M L, line J M, line J K, line K L, line M L\nIf JM = KL = JK, what is the length of KJ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5464.jpg"
-  },
-  {
-    "id": 5598,
-    "problem_id": 5465,
-    "problem": "line A D, line A B, line B C, line D C, line A D, line A B, line B C, line D C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5465.jpg"
-  },
-  {
-    "id": 5599,
-    "problem_id": 5466,
-    "problem": "line A D, line A B, line B C, line D C, line A D, line A B, line B C, line D C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5466.jpg"
-  },
-  {
-    "id": 5600,
-    "problem_id": 5467,
-    "problem": "line A D, line A B, line B C, line D C, line A D, line A B, line B C, line D C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5467.jpg"
-  },
-  {
-    "id": 5601,
-    "problem_id": 5468,
-    "problem": "line A D, line A B, line B C, line D C, line A D, line A B, line B C, line D C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5468.jpg"
-  },
-  {
-    "id": 5602,
-    "problem_id": 5469,
-    "problem": "line A D, line A B, line B C, line D C, line A D, line A B, line B C, line D C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5469.jpg"
-  },
-  {
-    "id": 5603,
-    "problem_id": 5470,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5470.jpg"
-  },
-  {
-    "id": 5604,
-    "problem_id": 5471,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5471.jpg"
-  },
-  {
-    "id": 5605,
-    "problem_id": 5472,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5472.jpg"
-  },
-  {
-    "id": 5606,
-    "problem_id": 5473,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5473.jpg"
-  },
-  {
-    "id": 5607,
-    "problem_id": 5474,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5474.jpg"
-  },
-  {
-    "id": 5608,
-    "problem_id": 5475,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5475.jpg"
-  },
-  {
-    "id": 5609,
-    "problem_id": 5476,
-    "problem": "line L P, line M N, line P N, line L M, line L P, line M N, line P N, line L M\nFor what value of y must PLMN be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5476.jpg"
-  },
-  {
-    "id": 5610,
-    "problem_id": 5477,
-    "problem": "line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S, line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S\nTRSU \\sim NMYZ. Find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5477.jpg"
-  },
-  {
-    "id": 5611,
-    "problem_id": 5478,
-    "problem": "line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S, line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S\nTRSU \\sim NMYZ. Find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5478.jpg"
-  },
-  {
-    "id": 5612,
-    "problem_id": 5479,
-    "problem": "line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S, line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S\nTRSU \\sim NMYZ. Find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5479.jpg"
-  },
-  {
-    "id": 5613,
-    "problem_id": 5480,
-    "problem": "line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S, line Y Z, line S U, line N Z, line T U, line R T, line M Y, line M N, line R S\nTRSU \\sim NMYZ. Find the value of b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5480.jpg"
-  },
-  {
-    "id": 5614,
-    "problem_id": 5481,
-    "problem": "line S V, line T U V, line S U, line T S, line S V, line T U V, line S U, line T S\nFind the length of TU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5481.jpg"
-  },
-  {
-    "id": 5615,
-    "problem_id": 5482,
-    "problem": "line S V, line T U V, line S U, line T S, line S V, line T U V, line S U, line T S\nFind the length of TU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5482.jpg"
-  },
-  {
-    "id": 5616,
-    "problem_id": 5483,
-    "problem": "line C B D, line A D, line A C, line A B, line C B D, line A D, line A C, line A B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5483.jpg"
-  },
-  {
-    "id": 5617,
-    "problem_id": 5484,
-    "problem": "line C B D, line A D, line A C, line A B, line C B D, line A D, line A C, line A B\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5484.jpg"
-  },
-  {
-    "id": 5618,
-    "problem_id": 5485,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind y that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5485.jpg"
-  },
-  {
-    "id": 5619,
-    "problem_id": 5486,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind y that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5486.jpg"
-  },
-  {
-    "id": 5620,
-    "problem_id": 5487,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind y that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5487.jpg"
-  },
-  {
-    "id": 5621,
-    "problem_id": 5488,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind y that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5488.jpg"
-  },
-  {
-    "id": 5623,
-    "problem_id": 5489,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind y that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5489.jpg"
-  },
-  {
-    "id": 5624,
-    "problem_id": 5490,
-    "problem": "line D C A, line D E, line B D, line B A, line A E, line B C E, line D C A, line D E, line B D, line B A, line A E, line B C E\nFind y that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5490.jpg"
-  },
-  {
-    "id": 5625,
-    "problem_id": 5491,
-    "problem": "line A O, line B C O, line B A, \\odot O lieson A C, line A O, line B C O, line B A, \\odot O lieson A C\nIn \\odot O, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5491.jpg"
-  },
-  {
-    "id": 5626,
-    "problem_id": 5492,
-    "problem": "line G E D B, line A D F, line C E H, line G E D B, line A D F, line C E H\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5492.jpg"
-  },
-  {
-    "id": 5627,
-    "problem_id": 5493,
-    "problem": "line G E D B, line A D F, line C E H, line G E D B, line A D F, line C E H\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5493.jpg"
-  },
-  {
-    "id": 5628,
-    "problem_id": 5494,
-    "problem": "line G E D B, line A D F, line C E H, line G E D B, line A D F, line C E H\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5494.jpg"
-  },
-  {
-    "id": 5629,
-    "problem_id": 5495,
-    "problem": "line G E D B, line A D F, line C E H, line G E D B, line A D F, line C E H\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5495.jpg"
-  },
-  {
-    "id": 5630,
-    "problem_id": 5496,
-    "problem": "line G E D B, line A D F, line C E H, line G E D B, line A D F, line C E H\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5496.jpg"
-  },
-  {
-    "id": 5631,
-    "problem_id": 5497,
-    "problem": "line C P B, line A P, line P D, \\odot P lieson A C D B, line C P B, line A P, line P D, \\odot P lieson A C D B\nWhat is m \\widehat BCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5497.jpg"
-  },
-  {
-    "id": 5632,
-    "problem_id": 5498,
-    "problem": "line Q S T, line A S R B, line T R, line Q R, line Q S T, line A S R B, line T R, line Q R\nFind RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5498.jpg"
-  },
-  {
-    "id": 5633,
-    "problem_id": 5499,
-    "problem": "line Q S T, line A S R B, line T R, line Q R, line Q S T, line A S R B, line T R, line Q R\nFind RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5499.jpg"
-  },
-  {
-    "id": 5634,
-    "problem_id": 5500,
-    "problem": "line Q S T, line A S R B, line T R, line Q R, line Q S T, line A S R B, line T R, line Q R\nFind RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5500.jpg"
-  },
-  {
-    "id": 5635,
-    "problem_id": 5501,
-    "problem": "line A C E, line B C D, line A B, line B E, line D E, line A D, line A C E, line B C D, line A B, line B E, line D E, line A D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5501.jpg"
-  },
-  {
-    "id": 5636,
-    "problem_id": 5502,
-    "problem": "line A C E, line B C D, line A B, line B E, line D E, line A D, line A C E, line B C D, line A B, line B E, line D E, line A D\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5502.jpg"
-  },
-  {
-    "id": 5637,
-    "problem_id": 5503,
-    "problem": "line P S, line P X Q, line X Y, line R Y S, line Q R, line P S, line P X Q, line X Y, line R Y S, line Q R\nIn trapezoid PQRS, what is the length sum of QR and PS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5503.jpg"
-  },
-  {
-    "id": 5638,
-    "problem_id": 5504,
-    "problem": "line P S, line P X Q, line X Y, line R Y S, line Q R, line P S, line P X Q, line X Y, line R Y S, line Q R\nIn trapezoid PQRS, what is the length sum of QR and PS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5504.jpg"
-  },
-  {
-    "id": 5639,
-    "problem_id": 5505,
-    "problem": "line P S, line P X Q, line X Y, line R Y S, line Q R, line P S, line P X Q, line X Y, line R Y S, line Q R\nIn trapezoid PQRS, what is the length sum of QR and PS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5505.jpg"
-  },
-  {
-    "id": 5640,
-    "problem_id": 5506,
-    "problem": "line P S, line P X Q, line X Y, line R Y S, line Q R, line P S, line P X Q, line X Y, line R Y S, line Q R\nIn trapezoid PQRS, what is the length sum of QR and PS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5506.jpg"
-  },
-  {
-    "id": 5641,
-    "problem_id": 5507,
-    "problem": "line P S, line P X Q, line X Y, line R Y S, line Q R, line P S, line P X Q, line X Y, line R Y S, line Q R\nIn trapezoid PQRS, what is the length sum of QR and PS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5507.jpg"
-  },
-  {
-    "id": 5642,
-    "problem_id": 5508,
-    "problem": "line P S, line P X Q, line X Y, line R Y S, line Q R, line P S, line P X Q, line X Y, line R Y S, line Q R\nIn trapezoid PQRS, what is the length sum of QR and PS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5508.jpg"
-  },
-  {
-    "id": 5643,
-    "problem_id": 5509,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5509.jpg"
-  },
-  {
-    "id": 5644,
-    "problem_id": 5510,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5510.jpg"
-  },
-  {
-    "id": 5645,
-    "problem_id": 5511,
-    "problem": "line A B D, line C D E, line B E F, line A B D, line C D E, line B E F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5511.jpg"
-  },
-  {
-    "id": 5646,
-    "problem_id": 5512,
-    "problem": "line K J, line Q P, line P S, line L M, line J M, line K L, line R S, line Q R, line K J, line Q P, line P S, line L M, line J M, line K L, line R S, line Q R\nPQRS \\sim JKLM. Find the perimeter of PQRS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5512.jpg"
-  },
-  {
-    "id": 5647,
-    "problem_id": 5513,
-    "problem": "line A C, line D A, line A B, line D B C, line A C, line D A, line A B, line D B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5513.jpg"
-  },
-  {
-    "id": 5648,
-    "problem_id": 5514,
-    "problem": "line A C, line D A, line A B, line D B C, line A C, line D A, line A B, line D B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5514.jpg"
-  },
-  {
-    "id": 5649,
-    "problem_id": 5515,
-    "problem": "line A C, line D A, line A B, line D B C, line A C, line D A, line A B, line D B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5515.jpg"
-  },
-  {
-    "id": 5650,
-    "problem_id": 5516,
-    "problem": "line A C, line B D, line A D, line C D, line A B, line A C, line B D, line A D, line C D, line A B\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5516.jpg"
-  },
-  {
-    "id": 5651,
-    "problem_id": 5517,
-    "problem": "line A C, line B D, line A D, line C D, line A B, line A C, line B D, line A D, line C D, line A B\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5517.jpg"
-  },
-  {
-    "id": 5652,
-    "problem_id": 5518,
-    "problem": "line A C, line B D, line A D, line C D, line A B, line A C, line B D, line A D, line C D, line A B\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5518.jpg"
-  },
-  {
-    "id": 5653,
-    "problem_id": 5519,
-    "problem": "line A D B, line A C, line C D, line C B, line A D B, line A C, line C D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5519.jpg"
-  },
-  {
-    "id": 5654,
-    "problem_id": 5520,
-    "problem": "line A B, line C B, line A C, \\odot C lieson B A, line A B, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5520.jpg"
-  },
-  {
-    "id": 5655,
-    "problem_id": 5521,
-    "problem": "line A B, line C B, line A C, \\odot C lieson B A, line A B, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5521.jpg"
-  },
-  {
-    "id": 5656,
-    "problem_id": 5522,
-    "problem": "line A B, line C B, line A C, \\odot C lieson B A, line A B, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5522.jpg"
-  },
-  {
-    "id": 5657,
-    "problem_id": 5523,
-    "problem": "line A B, line C B, line A C, \\odot C lieson B A, line A B, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5523.jpg"
-  },
-  {
-    "id": 5658,
-    "problem_id": 5524,
-    "problem": "line A B, line C B, line A C, \\odot C lieson B A, line A B, line C B, line A C, \\odot C lieson B A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5524.jpg"
-  },
-  {
-    "id": 5659,
-    "problem_id": 5525,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFor what value of y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5525.jpg"
-  },
-  {
-    "id": 5660,
-    "problem_id": 5526,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFor what value of y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5526.jpg"
-  },
-  {
-    "id": 5661,
-    "problem_id": 5527,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFor what value of y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5527.jpg"
-  },
-  {
-    "id": 5662,
-    "problem_id": 5528,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFor what value of y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5528.jpg"
-  },
-  {
-    "id": 5663,
-    "problem_id": 5529,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFor what value of y must ABCD be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5529.jpg"
-  },
-  {
-    "id": 5664,
-    "problem_id": 5530,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5530.jpg"
-  },
-  {
-    "id": 5665,
-    "problem_id": 5531,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5531.jpg"
-  },
-  {
-    "id": 5666,
-    "problem_id": 5532,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5532.jpg"
-  },
-  {
-    "id": 5667,
-    "problem_id": 5533,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5533.jpg"
-  },
-  {
-    "id": 5668,
-    "problem_id": 5534,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5534.jpg"
-  },
-  {
-    "id": 5669,
-    "problem_id": 5535,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5535.jpg"
-  },
-  {
-    "id": 5670,
-    "problem_id": 5536,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5536.jpg"
-  },
-  {
-    "id": 5671,
-    "problem_id": 5537,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5537.jpg"
-  },
-  {
-    "id": 5672,
-    "problem_id": 5538,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5538.jpg"
-  },
-  {
-    "id": 5673,
-    "problem_id": 5539,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5539.jpg"
-  },
-  {
-    "id": 5674,
-    "problem_id": 5540,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5540.jpg"
-  },
-  {
-    "id": 5675,
-    "problem_id": 5541,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5541.jpg"
-  },
-  {
-    "id": 5676,
-    "problem_id": 5542,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5542.jpg"
-  },
-  {
-    "id": 5677,
-    "problem_id": 5543,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 3?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5543.jpg"
-  },
-  {
-    "id": 5678,
-    "problem_id": 5544,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5544.jpg"
-  },
-  {
-    "id": 5679,
-    "problem_id": 5545,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5545.jpg"
-  },
-  {
-    "id": 5680,
-    "problem_id": 5546,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5546.jpg"
-  },
-  {
-    "id": 5681,
-    "problem_id": 5547,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5547.jpg"
-  },
-  {
-    "id": 5682,
-    "problem_id": 5548,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5548.jpg"
-  },
-  {
-    "id": 5683,
-    "problem_id": 5549,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5549.jpg"
-  },
-  {
-    "id": 5684,
-    "problem_id": 5550,
-    "problem": "line A B C, line E B, line F E D, line D C, line F A, line A B C, line E B, line F E D, line D C, line F A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5550.jpg"
-  },
-  {
-    "id": 5685,
-    "problem_id": 5551,
-    "problem": "line A B C, line E B, line F E D, line D C, line F A, line A B C, line E B, line F E D, line D C, line F A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5551.jpg"
-  },
-  {
-    "id": 5686,
-    "problem_id": 5552,
-    "problem": "line A B C, line E B, line F E D, line D C, line F A, line A B C, line E B, line F E D, line D C, line F A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5552.jpg"
-  },
-  {
-    "id": 5687,
-    "problem_id": 5553,
-    "problem": "line A D, line A B, line A C, line B C D, line A D, line A B, line A C, line B C D\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5553.jpg"
-  },
-  {
-    "id": 5688,
-    "problem_id": 5554,
-    "problem": "line A D, line A B, line A C, line B C D, line A D, line A B, line A C, line B C D\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5554.jpg"
-  },
-  {
-    "id": 5689,
-    "problem_id": 5555,
-    "problem": "line A D, line A B, line A C, line B C D, line A D, line A B, line A C, line B C D\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5555.jpg"
-  },
-  {
-    "id": 5690,
-    "problem_id": 5556,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5556.jpg"
-  },
-  {
-    "id": 5691,
-    "problem_id": 5557,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5557.jpg"
-  },
-  {
-    "id": 5692,
-    "problem_id": 5558,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5558.jpg"
-  },
-  {
-    "id": 5693,
-    "problem_id": 5559,
-    "problem": "line A B, line C B, line D C, line D E B, line A E C, line A B, line C B, line D C, line D E B, line A E C\nFind m \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5559.jpg"
-  },
-  {
-    "id": 5694,
-    "problem_id": 5560,
-    "problem": "line B C, line B A, line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5560.jpg"
-  },
-  {
-    "id": 5695,
-    "problem_id": 5561,
-    "problem": "line B C, line B A, line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5561.jpg"
-  },
-  {
-    "id": 5696,
-    "problem_id": 5562,
-    "problem": "line B C, line B A, line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5562.jpg"
-  },
-  {
-    "id": 5697,
-    "problem_id": 5563,
-    "problem": "line B C, line B A, line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5563.jpg"
-  },
-  {
-    "id": 5698,
-    "problem_id": 5564,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5564.jpg"
-  },
-  {
-    "id": 5699,
-    "problem_id": 5565,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5565.jpg"
-  },
-  {
-    "id": 5701,
-    "problem_id": 5566,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5566.jpg"
-  },
-  {
-    "id": 5702,
-    "problem_id": 5567,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5567.jpg"
-  },
-  {
-    "id": 5703,
-    "problem_id": 5568,
-    "problem": "line D B, line B C, line B A, \\odot B lieson D A C, line D B, line B C, line B A, \\odot B lieson D A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5568.jpg"
-  },
-  {
-    "id": 5704,
-    "problem_id": 5569,
-    "problem": "line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C, line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5569.jpg"
-  },
-  {
-    "id": 5705,
-    "problem_id": 5570,
-    "problem": "line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C, line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5570.jpg"
-  },
-  {
-    "id": 5706,
-    "problem_id": 5571,
-    "problem": "line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C, line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5571.jpg"
-  },
-  {
-    "id": 5707,
-    "problem_id": 5572,
-    "problem": "line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C, line A B, line A C, line B C, \\odot B lieson A C, \\odot D lieson A B C\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5572.jpg"
-  },
-  {
-    "id": 5708,
-    "problem_id": 5573,
-    "problem": "line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F, line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F\nm \\angle 4 = 104, m \\angle 14 = 118. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5573.jpg"
-  },
-  {
-    "id": 5709,
-    "problem_id": 5574,
-    "problem": "line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F, line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F\nm \\angle 4 = 104, m \\angle 14 = 118. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5574.jpg"
-  },
-  {
-    "id": 5710,
-    "problem_id": 5575,
-    "problem": "line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F, line d lieson B E I K, line c lieson A D H L, line b lieson G H I J, line a lieson C D E F\nm \\angle 4 = 104, m \\angle 14 = 118. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5575.jpg"
-  },
-  {
-    "id": 5711,
-    "problem_id": 5576,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5576.jpg"
-  },
-  {
-    "id": 5712,
-    "problem_id": 5577,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5577.jpg"
-  },
-  {
-    "id": 5713,
-    "problem_id": 5578,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5578.jpg"
-  },
-  {
-    "id": 5714,
-    "problem_id": 5579,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the perimeter of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5579.jpg"
-  },
-  {
-    "id": 5715,
-    "problem_id": 5580,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5580.jpg"
-  },
-  {
-    "id": 5716,
-    "problem_id": 5581,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5581.jpg"
-  },
-  {
-    "id": 5717,
-    "problem_id": 5582,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the perimeter of \\triangle EFG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5582.jpg"
-  },
-  {
-    "id": 5718,
-    "problem_id": 5583,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5583.jpg"
-  },
-  {
-    "id": 5719,
-    "problem_id": 5584,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5584.jpg"
-  },
-  {
-    "id": 5720,
-    "problem_id": 5585,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5585.jpg"
-  },
-  {
-    "id": 5721,
-    "problem_id": 5586,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5586.jpg"
-  },
-  {
-    "id": 5722,
-    "problem_id": 5587,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5587.jpg"
-  },
-  {
-    "id": 5723,
-    "problem_id": 5588,
-    "problem": "line U T, line T V, line U V, line U T, line T V, line U V\nFind m \\angle TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5588.jpg"
-  },
-  {
-    "id": 5724,
-    "problem_id": 5589,
-    "problem": "line S V T, line W X T, line W V, line S U W, line V X, line U V, line S V T, line W X T, line W V, line S U W, line V X, line U V\nWhat is the length of VU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5589.jpg"
-  },
-  {
-    "id": 5725,
-    "problem_id": 5590,
-    "problem": "line L M, line M N Q, line L N P, line Q P, line L M, line M N Q, line L N P, line Q P\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5590.jpg"
-  },
-  {
-    "id": 5726,
-    "problem_id": 5591,
-    "problem": "line L M, line M N Q, line L N P, line Q P, line L M, line M N Q, line L N P, line Q P\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5591.jpg"
-  },
-  {
-    "id": 5727,
-    "problem_id": 5592,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind RS in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5592.jpg"
-  },
-  {
-    "id": 5728,
-    "problem_id": 5593,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind RS in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5593.jpg"
-  },
-  {
-    "id": 5729,
-    "problem_id": 5594,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind RS in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5594.jpg"
-  },
-  {
-    "id": 5730,
-    "problem_id": 5595,
-    "problem": "line R S, line T S, line Q T, line Q R, line R S, line T S, line Q T, line Q R\nFind RS in the given parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5595.jpg"
-  },
-  {
-    "id": 5731,
-    "problem_id": 5596,
-    "problem": "line B C D, line A C E H, line G E F, line B C D, line A C E H, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5596.jpg"
-  },
-  {
-    "id": 5732,
-    "problem_id": 5597,
-    "problem": "line B C D, line A C E H, line G E F, line B C D, line A C E H, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5597.jpg"
-  },
-  {
-    "id": 5733,
-    "problem_id": 5598,
-    "problem": "line B C D, line A C E H, line G E F, line B C D, line A C E H, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5598.jpg"
-  },
-  {
-    "id": 5734,
-    "problem_id": 5599,
-    "problem": "line B C, line D C, line E D, line A E, line A B, line B C, line D C, line E D, line A E, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5599.jpg"
-  },
-  {
-    "id": 5735,
-    "problem_id": 5600,
-    "problem": "line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C, line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5600.jpg"
-  },
-  {
-    "id": 5736,
-    "problem_id": 5601,
-    "problem": "line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C, line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5601.jpg"
-  },
-  {
-    "id": 5737,
-    "problem_id": 5602,
-    "problem": "line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C, line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5602.jpg"
-  },
-  {
-    "id": 5738,
-    "problem_id": 5603,
-    "problem": "line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C, line A D B E C, \\odot B0 lieson D E, \\odot B1 lieson A C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5603.jpg"
-  },
-  {
-    "id": 5740,
-    "problem_id": 5604,
-    "problem": "line F E, line C D, line D E, line C F, line F E, line C D, line D E, line C F\nEDCF is a rectangle. Find the measure of \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5604.jpg"
-  },
-  {
-    "id": 5741,
-    "problem_id": 5605,
-    "problem": "line F E, line C D, line D E, line C F, line F E, line C D, line D E, line C F\nEDCF is a rectangle. Find the measure of \\angle CFE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5605.jpg"
-  },
-  {
-    "id": 5742,
-    "problem_id": 5606,
-    "problem": "line A B D, line C D, \\odot E lieson A B C, line A B D, line C D, \\odot E lieson A B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5606.jpg"
-  },
-  {
-    "id": 5743,
-    "problem_id": 5607,
-    "problem": "line A B D, line C D, \\odot E lieson A B C, line A B D, line C D, \\odot E lieson A B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5607.jpg"
-  },
-  {
-    "id": 5744,
-    "problem_id": 5608,
-    "problem": "line W X Y Z, line W X Y Z\nWX = YZ. What is the length of WY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5608.jpg"
-  },
-  {
-    "id": 5745,
-    "problem_id": 5609,
-    "problem": "line A B C, line D C, line E D, line E A, line E B, line A B C, line D C, line E D, line E A, line E B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5609.jpg"
-  },
-  {
-    "id": 5746,
-    "problem_id": 5610,
-    "problem": "line A B C, line D C, line E D, line E A, line E B, line A B C, line D C, line E D, line E A, line E B\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5610.jpg"
-  },
-  {
-    "id": 5747,
-    "problem_id": 5611,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5611.jpg"
-  },
-  {
-    "id": 5748,
-    "problem_id": 5612,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5612.jpg"
-  },
-  {
-    "id": 5749,
-    "problem_id": 5613,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5613.jpg"
-  },
-  {
-    "id": 5750,
-    "problem_id": 5614,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5614.jpg"
-  },
-  {
-    "id": 5751,
-    "problem_id": 5615,
-    "problem": "line A D, line A B, line B C D, \\odot C lieson A D B, line A D, line A B, line B C D, \\odot C lieson A D B\nFind the exact circumference of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5615.jpg"
-  },
-  {
-    "id": 5752,
-    "problem_id": 5616,
-    "problem": "line E B D, line A D C, line B A, line B C, line E B D, line A D C, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5616.jpg"
-  },
-  {
-    "id": 5753,
-    "problem_id": 5617,
-    "problem": "line G J, line H G, line H I, line I J, line M L, line M N, line N O, line L O, line G J, line H G, line H I, line I J, line M L, line M N, line N O, line L O\nEach pair of polygons is similar. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5617.jpg"
-  },
-  {
-    "id": 5754,
-    "problem_id": 5618,
-    "problem": "line E G H B, line m lieson F G D, line n lieson A H C, line E G H B, line m lieson F G D, line n lieson A H C\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5618.jpg"
-  },
-  {
-    "id": 5755,
-    "problem_id": 5619,
-    "problem": "line C D E, line A B C, line B F, line F D, line A F E, line C D E, line A B C, line B F, line F D, line A F E\nFind CD if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\\frac{10}{3}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5619.jpg"
-  },
-  {
-    "id": 5756,
-    "problem_id": 5620,
-    "problem": "line E C A, line B C D, line A D, line B E, line E C A, line B C D, line A D, line B E\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5620.jpg"
-  },
-  {
-    "id": 5757,
-    "problem_id": 5621,
-    "problem": "line E C A, line B C D, line A D, line B E, line E C A, line B C D, line A D, line B E\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5621.jpg"
-  },
-  {
-    "id": 5758,
-    "problem_id": 5622,
-    "problem": "line E D C, line A B E, \\odot F lieson B D, line E D C, line A B E, \\odot F lieson B D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5622.jpg"
-  },
-  {
-    "id": 5759,
-    "problem_id": 5623,
-    "problem": "line E D C, line A B E, \\odot F lieson B D, line E D C, line A B E, \\odot F lieson B D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5623.jpg"
-  },
-  {
-    "id": 5760,
-    "problem_id": 5624,
-    "problem": "line E D C, line A B E, \\odot F lieson B D, line E D C, line A B E, \\odot F lieson B D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5624.jpg"
-  },
-  {
-    "id": 5761,
-    "problem_id": 5625,
-    "problem": "line E D C, line A B E, \\odot F lieson B D, line E D C, line A B E, \\odot F lieson B D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5625.jpg"
-  },
-  {
-    "id": 5762,
-    "problem_id": 5626,
-    "problem": "line E D C, line A B E, \\odot F lieson B D, line E D C, line A B E, \\odot F lieson B D\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5626.jpg"
-  },
-  {
-    "id": 5763,
-    "problem_id": 5627,
-    "problem": "line P Q, line Q R, line P R, line P Q, line Q R, line P R\nFind the measure of \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5627.jpg"
-  },
-  {
-    "id": 5764,
-    "problem_id": 5628,
-    "problem": "line P Q, line Q R, line P R, line P Q, line Q R, line P R\nFind the measure of \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5628.jpg"
-  },
-  {
-    "id": 5766,
-    "problem_id": 5629,
-    "problem": "line P Q, line Q R, line P R, line P Q, line Q R, line P R\nFind the measure of \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5629.jpg"
-  },
-  {
-    "id": 5767,
-    "problem_id": 5630,
-    "problem": "line A B C, line A B C\nWhat is the measure of AB if B is the midpoint of AC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5630.jpg"
-  },
-  {
-    "id": 5768,
-    "problem_id": 5631,
-    "problem": "line A B C, line A B C\nWhat is the measure of AB if B is the midpoint of AC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5631.jpg"
-  },
-  {
-    "id": 5769,
-    "problem_id": 5632,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5632.jpg"
-  },
-  {
-    "id": 5770,
-    "problem_id": 5633,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5633.jpg"
-  },
-  {
-    "id": 5771,
-    "problem_id": 5634,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5634.jpg"
-  },
-  {
-    "id": 5772,
-    "problem_id": 5635,
-    "problem": "line M N, line M L, line L N, line M N, line M L, line L N\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5635.jpg"
-  },
-  {
-    "id": 5773,
-    "problem_id": 5636,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind \\sin A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5636.jpg"
-  },
-  {
-    "id": 5774,
-    "problem_id": 5637,
-    "problem": "line E D C A, line G F A, line B D G, \\odot P lieson E G F C B, line E D C A, line G F A, line B D G, \\odot P lieson E G F C B\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5637.jpg"
-  },
-  {
-    "id": 5775,
-    "problem_id": 5638,
-    "problem": "line Q B B' E, line D C A Q, line A B, line C B', line Q B B' E, line D C A Q, line A B, line C B'\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5638.jpg"
-  },
-  {
-    "id": 5776,
-    "problem_id": 5639,
-    "problem": "line Q B B' E, line D C A Q, line A B, line C B', line Q B B' E, line D C A Q, line A B, line C B'\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5639.jpg"
-  },
-  {
-    "id": 5777,
-    "problem_id": 5640,
-    "problem": "line Q B B' E, line D C A Q, line A B, line C B', line Q B B' E, line D C A Q, line A B, line C B'\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5640.jpg"
-  },
-  {
-    "id": 5778,
-    "problem_id": 5641,
-    "problem": "line Q T, line Q S, \\odot Q lieson T S, line Q T, line Q S, \\odot Q lieson T S\nFind the radius of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5641.jpg"
-  },
-  {
-    "id": 5779,
-    "problem_id": 5642,
-    "problem": "line A C B, line D C, line A C B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5642.jpg"
-  },
-  {
-    "id": 5780,
-    "problem_id": 5643,
-    "problem": "line A C B, line D C, line A C B, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5643.jpg"
-  },
-  {
-    "id": 5781,
-    "problem_id": 5644,
-    "problem": "line A C F H, line n lieson G F E, line m lieson B C D, line A C F H, line n lieson G F E, line m lieson B C D\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5644.jpg"
-  },
-  {
-    "id": 5782,
-    "problem_id": 5645,
-    "problem": "line A C F H, line n lieson G F E, line m lieson B C D, line A C F H, line n lieson G F E, line m lieson B C D\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5645.jpg"
-  },
-  {
-    "id": 5783,
-    "problem_id": 5646,
-    "problem": "line A C F H, line n lieson G F E, line m lieson B C D, line A C F H, line n lieson G F E, line m lieson B C D\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5646.jpg"
-  },
-  {
-    "id": 5784,
-    "problem_id": 5647,
-    "problem": "line A B, line D B, line D E, line B E, \\odot C lieson A D E B, line A B, line D B, line D E, line B E, \\odot C lieson A D E B\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5647.jpg"
-  },
-  {
-    "id": 5785,
-    "problem_id": 5648,
-    "problem": "line A E C, line D E B, line D C, line C B, line A B, line D A, line A E C, line D E B, line D C, line C B, line A B, line D A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5648.jpg"
-  },
-  {
-    "id": 5786,
-    "problem_id": 5649,
-    "problem": "line A E C, line D E B, line D C, line C B, line A B, line D A, line A E C, line D E B, line D C, line C B, line A B, line D A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5649.jpg"
-  },
-  {
-    "id": 5787,
-    "problem_id": 5650,
-    "problem": "line A E C, line D E B, line D C, line C B, line A B, line D A, line A E C, line D E B, line D C, line C B, line A B, line D A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5650.jpg"
-  },
-  {
-    "id": 5788,
-    "problem_id": 5651,
-    "problem": "line A E C, line D E B, line D C, line C B, line A B, line D A, line A E C, line D E B, line D C, line C B, line A B, line D A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5651.jpg"
-  },
-  {
-    "id": 5789,
-    "problem_id": 5652,
-    "problem": "line A E C, line D E B, line D C, line C B, line A B, line D A, line A E C, line D E B, line D C, line C B, line A B, line D A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5652.jpg"
-  },
-  {
-    "id": 5790,
-    "problem_id": 5653,
-    "problem": "line A E C, line D E B, line D C, line C B, line A B, line D A, line A E C, line D E B, line D C, line C B, line A B, line D A\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5653.jpg"
-  },
-  {
-    "id": 5791,
-    "problem_id": 5654,
-    "problem": "line W X Y, line W X Y\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5654.jpg"
-  },
-  {
-    "id": 5792,
-    "problem_id": 5655,
-    "problem": "line W X Y, line W X Y\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5655.jpg"
-  },
-  {
-    "id": 5793,
-    "problem_id": 5656,
-    "problem": "line W X Y, line W X Y\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5656.jpg"
-  },
-  {
-    "id": 5794,
-    "problem_id": 5657,
-    "problem": "line W X Y, line W X Y\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5657.jpg"
-  },
-  {
-    "id": 5795,
-    "problem_id": 5658,
-    "problem": "line W X Y, line W X Y\nFind the measurement of XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5658.jpg"
-  },
-  {
-    "id": 5796,
-    "problem_id": 5659,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5659.jpg"
-  },
-  {
-    "id": 5797,
-    "problem_id": 5660,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5660.jpg"
-  },
-  {
-    "id": 5798,
-    "problem_id": 5661,
-    "problem": "line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L, line d lieson B D I K, line b lieson G H I J, line a lieson F E D C, line c lieson A E H L\nm \\angle 3 = 43. Find the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5661.jpg"
-  },
-  {
-    "id": 5799,
-    "problem_id": 5662,
-    "problem": "line A D E, line E F G, line B H G, line A C B, \\odot I lieson D F H C, line A D E, line E F G, line B H G, line A C B, \\odot I lieson D F H C\nFind the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5662.jpg"
-  },
-  {
-    "id": 5800,
-    "problem_id": 5663,
-    "problem": "line A D E, line E F G, line B H G, line A C B, \\odot I lieson D F H C, line A D E, line E F G, line B H G, line A C B, \\odot I lieson D F H C\nFind the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5663.jpg"
-  },
-  {
-    "id": 5801,
-    "problem_id": 5664,
-    "problem": "line C D, line A B, line C A, line D B, line C D, line A B, line C A, line D B\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5664.jpg"
-  },
-  {
-    "id": 5802,
-    "problem_id": 5665,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the measure of \\angle 1 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5665.jpg"
-  },
-  {
-    "id": 5803,
-    "problem_id": 5666,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the measure of \\angle 1 in the isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5666.jpg"
-  },
-  {
-    "id": 5804,
-    "problem_id": 5667,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the length of the midsegment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5667.jpg"
-  },
-  {
-    "id": 5805,
-    "problem_id": 5668,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the length of the midsegment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5668.jpg"
-  },
-  {
-    "id": 5806,
-    "problem_id": 5669,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the length of the midsegment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5669.jpg"
-  },
-  {
-    "id": 5807,
-    "problem_id": 5670,
-    "problem": "line A B, line F C B, line E F, line E D A, line D C, line A B, line F C B, line E F, line E D A, line D C\nFind the length of the midsegment.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5670.jpg"
-  },
-  {
-    "id": 5808,
-    "problem_id": 5671,
-    "problem": "line A C, line B C, \\odot C lieson A B, line A C, line B C, \\odot C lieson A B\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5671.jpg"
-  },
-  {
-    "id": 5809,
-    "problem_id": 5672,
-    "problem": "line A C, line B C, \\odot C lieson A B, line A C, line B C, \\odot C lieson A B\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5672.jpg"
-  },
-  {
-    "id": 5810,
-    "problem_id": 5673,
-    "problem": "line A C, line B C, \\odot C lieson A B, line A C, line B C, \\odot C lieson A B\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5673.jpg"
-  },
-  {
-    "id": 5811,
-    "problem_id": 5674,
-    "problem": "line A C, line B C, \\odot C lieson A B, line A C, line B C, \\odot C lieson A B\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5674.jpg"
-  },
-  {
-    "id": 5812,
-    "problem_id": 5675,
-    "problem": "line A E F B, line A D, line D E, line C F, line D C, line C B, line A E F B, line A D, line D E, line C F, line D C, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5675.jpg"
-  },
-  {
-    "id": 5813,
-    "problem_id": 5676,
-    "problem": "line P G, line P H, \\odot P lieson G H, line P G, line P H, \\odot P lieson G H\nWhat is the area of sector GPH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5676.jpg"
-  },
-  {
-    "id": 5814,
-    "problem_id": 5677,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5677.jpg"
-  },
-  {
-    "id": 5815,
-    "problem_id": 5678,
-    "problem": "line E F C D G, line D A, line C H, line B F, line E F C D G, line D A, line C H, line B F\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5678.jpg"
-  },
-  {
-    "id": 5817,
-    "problem_id": 5679,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the value of variable y in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5679.jpg"
-  },
-  {
-    "id": 5819,
-    "problem_id": 5680,
-    "problem": "line J I H G, line A D E F, line K I D B, line L H E C, line J I H G, line A D E F, line K I D B, line L H E C\nm \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5680.jpg"
-  },
-  {
-    "id": 5820,
-    "problem_id": 5681,
-    "problem": "line J I H G, line A D E F, line K I D B, line L H E C, line J I H G, line A D E F, line K I D B, line L H E C\nm \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5681.jpg"
-  },
-  {
-    "id": 5821,
-    "problem_id": 5682,
-    "problem": "line W X Y Z, line W X Y Z\nFind the measurement of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5682.jpg"
-  },
-  {
-    "id": 5822,
-    "problem_id": 5683,
-    "problem": "line W X Y Z, line W X Y Z\nFind the measurement of WY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5683.jpg"
-  },
-  {
-    "id": 5823,
-    "problem_id": 5684,
-    "problem": "line A E C, line D C, line C B, line D E B, line D A, line A B, line A E C, line D C, line C B, line D E B, line D A, line A B\nFind x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5684.jpg"
-  },
-  {
-    "id": 5824,
-    "problem_id": 5685,
-    "problem": "line A E C, line D C, line C B, line D E B, line D A, line A B, line A E C, line D C, line C B, line D E B, line D A, line A B\nFind x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5685.jpg"
-  },
-  {
-    "id": 5825,
-    "problem_id": 5686,
-    "problem": "line A E C, line D C, line C B, line D E B, line D A, line A B, line A E C, line D C, line C B, line D E B, line D A, line A B\nFind x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5686.jpg"
-  },
-  {
-    "id": 5826,
-    "problem_id": 5687,
-    "problem": "line A E C, line D C, line C B, line D E B, line D A, line A B, line A E C, line D C, line C B, line D E B, line D A, line A B\nFind x in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5687.jpg"
-  },
-  {
-    "id": 5827,
-    "problem_id": 5688,
-    "problem": "line A B, line C B, line A D, line D C, line D B, line A B, line C B, line A D, line D C, line D B\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5688.jpg"
-  },
-  {
-    "id": 5828,
-    "problem_id": 5689,
-    "problem": "line A B, line C B, line A D, line D C, line D B, line A B, line C B, line A D, line D C, line D B\nFind the area of the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5689.jpg"
-  },
-  {
-    "id": 5829,
-    "problem_id": 5690,
-    "problem": "line A C, line B D C, line A B, line A D, line A C, line B D C, line A B, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5690.jpg"
-  },
-  {
-    "id": 5830,
-    "problem_id": 5691,
-    "problem": "line A C, line B D C, line A B, line A D, line A C, line B D C, line A B, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5691.jpg"
-  },
-  {
-    "id": 5831,
-    "problem_id": 5692,
-    "problem": "line A C, line B D C, line A B, line A D, line A C, line B D C, line A B, line A D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5692.jpg"
-  },
-  {
-    "id": 5832,
-    "problem_id": 5693,
-    "problem": "line S T, line R T, line S R, line S T, line R T, line S R\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5693.jpg"
-  },
-  {
-    "id": 5833,
-    "problem_id": 5694,
-    "problem": "line S T, line R T, line S R, line S T, line R T, line S R\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5694.jpg"
-  },
-  {
-    "id": 5834,
-    "problem_id": 5695,
-    "problem": "line S T, line R T, line S R, line S T, line R T, line S R\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5695.jpg"
-  },
-  {
-    "id": 5835,
-    "problem_id": 5696,
-    "problem": "line S T, line R T, line S R, line S T, line R T, line S R\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5696.jpg"
-  },
-  {
-    "id": 5836,
-    "problem_id": 5697,
-    "problem": "line S T, line R T, line S R, line S T, line R T, line S R\nFind m \\angle SRT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5697.jpg"
-  },
-  {
-    "id": 5837,
-    "problem_id": 5698,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5698.jpg"
-  },
-  {
-    "id": 5838,
-    "problem_id": 5699,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5699.jpg"
-  },
-  {
-    "id": 5839,
-    "problem_id": 5700,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5700.jpg"
-  },
-  {
-    "id": 5840,
-    "problem_id": 5701,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5701.jpg"
-  },
-  {
-    "id": 5841,
-    "problem_id": 5702,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5702.jpg"
-  },
-  {
-    "id": 5842,
-    "problem_id": 5703,
-    "problem": "line B C, line B A, line A C, line B C, line B A, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5703.jpg"
-  },
-  {
-    "id": 5843,
-    "problem_id": 5704,
-    "problem": "line W X Y Z, line W X Y Z\nWX = YZ. What is the length of YX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5704.jpg"
-  },
-  {
-    "id": 5844,
-    "problem_id": 5705,
-    "problem": "line W X Y Z, line W X Y Z\nWX = YZ. What is the length of YX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5705.jpg"
-  },
-  {
-    "id": 5845,
-    "problem_id": 5706,
-    "problem": "line W X Y Z, line W X Y Z\nWX = YZ. What is the length of YX?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5706.jpg"
-  },
-  {
-    "id": 5846,
-    "problem_id": 5707,
-    "problem": "line A P, line B P, line P C, \\odot P lieson A D C B, line A P, line B P, line P C, \\odot P lieson A D C B\nFind the measure of \\angle BPC for \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5707.jpg"
-  },
-  {
-    "id": 5847,
-    "problem_id": 5708,
-    "problem": "line A P, line B P, line P C, \\odot P lieson A D C B, line A P, line B P, line P C, \\odot P lieson A D C B\nFind the measure of \\angle BPC for \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5708.jpg"
-  },
-  {
-    "id": 5848,
-    "problem_id": 5709,
-    "problem": "line R S T, line R S T\nFind the measurement of ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5709.jpg"
-  },
-  {
-    "id": 5849,
-    "problem_id": 5710,
-    "problem": "line R S T, line R S T\nFind the measurement of ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5710.jpg"
-  },
-  {
-    "id": 5850,
-    "problem_id": 5711,
-    "problem": "line R S T, line R S T\nFind the measurement of ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5711.jpg"
-  },
-  {
-    "id": 5851,
-    "problem_id": 5712,
-    "problem": "line R S T, line R S T\nFind the measurement of ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5712.jpg"
-  },
-  {
-    "id": 5852,
-    "problem_id": 5713,
-    "problem": "line R S T, line R S T\nFind the measurement of ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5713.jpg"
-  },
-  {
-    "id": 5853,
-    "problem_id": 5714,
-    "problem": "line F A D B I, line J C D, line K G D, line H E D, line F A D B I, line J C D, line K G D, line H E D\nGiven that DE \\perp DG and AB \\perp DC. If m \\angle 3 = 15, what is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5714.jpg"
-  },
-  {
-    "id": 5854,
-    "problem_id": 5715,
-    "problem": "line F A D B I, line J C D, line K G D, line H E D, line F A D B I, line J C D, line K G D, line H E D\nGiven that DE \\perp DG and AB \\perp DC. If m \\angle 3 = 15, what is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5715.jpg"
-  },
-  {
-    "id": 5855,
-    "problem_id": 5716,
-    "problem": "line A B C, line D B, line A B C, line D B\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5716.jpg"
-  },
-  {
-    "id": 5856,
-    "problem_id": 5717,
-    "problem": "line A B C, line D B, line A B C, line D B\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5717.jpg"
-  },
-  {
-    "id": 5857,
-    "problem_id": 5718,
-    "problem": "line A B C, line D B, line A B C, line D B\nFind the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5718.jpg"
-  },
-  {
-    "id": 5858,
-    "problem_id": 5719,
-    "problem": "line A B C, line D A, line D C, \\odot B lieson D A C, line A B C, line D A, line D C, \\odot B lieson D A C\nThe triangle is inscribed into the circle. Find the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5719.jpg"
-  },
-  {
-    "id": 5859,
-    "problem_id": 5720,
-    "problem": "line A B C, line D A, line D C, \\odot B lieson D A C, line A B C, line D A, line D C, \\odot B lieson D A C\nThe triangle is inscribed into the circle. Find the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5720.jpg"
-  },
-  {
-    "id": 5860,
-    "problem_id": 5721,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5721.jpg"
-  },
-  {
-    "id": 5861,
-    "problem_id": 5722,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5722.jpg"
-  },
-  {
-    "id": 5862,
-    "problem_id": 5723,
-    "problem": "line A C, line A D, line D B C, line A B, line A C, line A D, line D B C, line A B\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5723.jpg"
-  },
-  {
-    "id": 5863,
-    "problem_id": 5724,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle D of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5724.jpg"
-  },
-  {
-    "id": 5864,
-    "problem_id": 5725,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle D of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5725.jpg"
-  },
-  {
-    "id": 5865,
-    "problem_id": 5726,
-    "problem": "line A B, line B C, line D C, line A D, line A B, line B C, line D C, line A D\nSolve for the measure of \\angle D of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5726.jpg"
-  },
-  {
-    "id": 5866,
-    "problem_id": 5727,
-    "problem": "line A D, line C D, line A B C, line B D, line A D, line C D, line A B C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5727.jpg"
-  },
-  {
-    "id": 5867,
-    "problem_id": 5728,
-    "problem": "line A D, line C D, line A B C, line B D, line A D, line C D, line A B C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5728.jpg"
-  },
-  {
-    "id": 5868,
-    "problem_id": 5729,
-    "problem": "line A D, line C D, line A B C, line B D, line A D, line C D, line A B C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5729.jpg"
-  },
-  {
-    "id": 5869,
-    "problem_id": 5730,
-    "problem": "line A D, line C D, line A B C, line B D, line A D, line C D, line A B C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5730.jpg"
-  },
-  {
-    "id": 5870,
-    "problem_id": 5731,
-    "problem": "line Q S, line R Q, line R S, line Q S, line R Q, line R S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5731.jpg"
-  },
-  {
-    "id": 5871,
-    "problem_id": 5732,
-    "problem": "line Q S, line R Q, line R S, line Q S, line R Q, line R S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5732.jpg"
-  },
-  {
-    "id": 5872,
-    "problem_id": 5733,
-    "problem": "line Q S, line R Q, line R S, line Q S, line R Q, line R S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5733.jpg"
-  },
-  {
-    "id": 5873,
-    "problem_id": 5734,
-    "problem": "line Q S, line R Q, line R S, line Q S, line R Q, line R S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5734.jpg"
-  },
-  {
-    "id": 5874,
-    "problem_id": 5735,
-    "problem": "line Q S, line R Q, line R S, line Q S, line R Q, line R S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5735.jpg"
-  },
-  {
-    "id": 5875,
-    "problem_id": 5736,
-    "problem": "line B C D E, line A E, line A C F, \\odot D lieson A B F E, line B C D E, line A E, line A C F, \\odot D lieson A B F E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5736.jpg"
-  },
-  {
-    "id": 5876,
-    "problem_id": 5737,
-    "problem": "line B C D E, line A E, line A C F, \\odot D lieson A B F E, line B C D E, line A E, line A C F, \\odot D lieson A B F E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5737.jpg"
-  },
-  {
-    "id": 5877,
-    "problem_id": 5738,
-    "problem": "line B C D E, line A E, line A C F, \\odot D lieson A B F E, line B C D E, line A E, line A C F, \\odot D lieson A B F E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5738.jpg"
-  },
-  {
-    "id": 5878,
-    "problem_id": 5739,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5739.jpg"
-  },
-  {
-    "id": 5879,
-    "problem_id": 5740,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5740.jpg"
-  },
-  {
-    "id": 5880,
-    "problem_id": 5741,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5741.jpg"
-  },
-  {
-    "id": 5881,
-    "problem_id": 5742,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5742.jpg"
-  },
-  {
-    "id": 5882,
-    "problem_id": 5743,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5743.jpg"
-  },
-  {
-    "id": 5883,
-    "problem_id": 5744,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5744.jpg"
-  },
-  {
-    "id": 5884,
-    "problem_id": 5745,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5745.jpg"
-  },
-  {
-    "id": 5885,
-    "problem_id": 5746,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5746.jpg"
-  },
-  {
-    "id": 5886,
-    "problem_id": 5747,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5747.jpg"
-  },
-  {
-    "id": 5887,
-    "problem_id": 5748,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5748.jpg"
-  },
-  {
-    "id": 5888,
-    "problem_id": 5749,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5749.jpg"
-  },
-  {
-    "id": 5889,
-    "problem_id": 5750,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5750.jpg"
-  },
-  {
-    "id": 5890,
-    "problem_id": 5751,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5751.jpg"
-  },
-  {
-    "id": 5891,
-    "problem_id": 5752,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5752.jpg"
-  },
-  {
-    "id": 5892,
-    "problem_id": 5753,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5753.jpg"
-  },
-  {
-    "id": 5893,
-    "problem_id": 5754,
-    "problem": "line S T, line S R, line T R, line S T, line S R, line T R\nFind RT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5754.jpg"
-  },
-  {
-    "id": 5894,
-    "problem_id": 5755,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nSolve for the length of SV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5755.jpg"
-  },
-  {
-    "id": 5895,
-    "problem_id": 5756,
-    "problem": "line S V, line S T U, line U V, line T V, line S V, line S T U, line U V, line T V\nSolve for the length of SV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5756.jpg"
-  },
-  {
-    "id": 5896,
-    "problem_id": 5757,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 4?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5757.jpg"
-  },
-  {
-    "id": 5897,
-    "problem_id": 5758,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5758.jpg"
-  },
-  {
-    "id": 5898,
-    "problem_id": 5759,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5759.jpg"
-  },
-  {
-    "id": 5899,
-    "problem_id": 5760,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5760.jpg"
-  },
-  {
-    "id": 5900,
-    "problem_id": 5761,
-    "problem": "line B F, line C D E F, line A C, line A B, line B E, line A D, line B F, line C D E F, line A C, line A B, line B E, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5761.jpg"
-  },
-  {
-    "id": 5901,
-    "problem_id": 5762,
-    "problem": "line B F, line C D E F, line A C, line A B, line B E, line A D, line B F, line C D E F, line A C, line A B, line B E, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5762.jpg"
-  },
-  {
-    "id": 5902,
-    "problem_id": 5763,
-    "problem": "line B F, line C D E F, line A C, line A B, line B E, line A D, line B F, line C D E F, line A C, line A B, line B E, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5763.jpg"
-  },
-  {
-    "id": 5903,
-    "problem_id": 5764,
-    "problem": "line B F, line C D E F, line A C, line A B, line B E, line A D, line B F, line C D E F, line A C, line A B, line B E, line A D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5764.jpg"
-  },
-  {
-    "id": 5904,
-    "problem_id": 5765,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5765.jpg"
-  },
-  {
-    "id": 5905,
-    "problem_id": 5766,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5766.jpg"
-  },
-  {
-    "id": 5906,
-    "problem_id": 5767,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5767.jpg"
-  },
-  {
-    "id": 5907,
-    "problem_id": 5768,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5768.jpg"
-  },
-  {
-    "id": 5908,
-    "problem_id": 5769,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5769.jpg"
-  },
-  {
-    "id": 5909,
-    "problem_id": 5770,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5770.jpg"
-  },
-  {
-    "id": 5910,
-    "problem_id": 5771,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5771.jpg"
-  },
-  {
-    "id": 5911,
-    "problem_id": 5772,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5772.jpg"
-  },
-  {
-    "id": 5912,
-    "problem_id": 5773,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5773.jpg"
-  },
-  {
-    "id": 5913,
-    "problem_id": 5774,
-    "problem": "line X Z B, line X W A, line X Y C, line Z Y, line W Z, line X Z B, line X W A, line X Y C, line Z Y, line W Z\nWhat is the measure of \\angle WXY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5774.jpg"
-  },
-  {
-    "id": 5914,
-    "problem_id": 5775,
-    "problem": "line X Z B, line X W A, line X Y C, line Z Y, line W Z, line X Z B, line X W A, line X Y C, line Z Y, line W Z\nWhat is the measure of \\angle WXY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5775.jpg"
-  },
-  {
-    "id": 5915,
-    "problem_id": 5776,
-    "problem": "line L N O, line M N P, line M L, line O P, line L N O, line M N P, line M L, line O P\nWhat is the measure of MN?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5776.jpg"
-  },
-  {
-    "id": 5916,
-    "problem_id": 5777,
-    "problem": "line L N O, line M N P, line M L, line O P, line L N O, line M N P, line M L, line O P\nWhat is the measure of MN?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5777.jpg"
-  },
-  {
-    "id": 5917,
-    "problem_id": 5778,
-    "problem": "line L N O, line M N P, line M L, line O P, line L N O, line M N P, line M L, line O P\nWhat is the measure of MN?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5778.jpg"
-  },
-  {
-    "id": 5918,
-    "problem_id": 5779,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5779.jpg"
-  },
-  {
-    "id": 5919,
-    "problem_id": 5780,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5780.jpg"
-  },
-  {
-    "id": 5920,
-    "problem_id": 5781,
-    "problem": "line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V, line q lieson N O P Q R S, line p lieson H I J K L M, line k lieson D F G J P U, line j lieson C E I O T, line n lieson B F L R W, line m lieson A E G K Q V\nm \\angle 1 = 50 and m \\angle 3 = 60. Find the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5781.jpg"
-  },
-  {
-    "id": 5921,
-    "problem_id": 5782,
-    "problem": "line A B, line B H, line G H, line A G, line C D, line D F, line E F, line C E, line A B, line B H, line G H, line A G, line C D, line D F, line E F, line C E\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5782.jpg"
-  },
-  {
-    "id": 5922,
-    "problem_id": 5783,
-    "problem": "line A B, line B H, line G H, line A G, line C D, line D F, line E F, line C E, line A B, line B H, line G H, line A G, line C D, line D F, line E F, line C E\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5783.jpg"
-  },
-  {
-    "id": 5923,
-    "problem_id": 5784,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5784.jpg"
-  },
-  {
-    "id": 5924,
-    "problem_id": 5785,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5785.jpg"
-  },
-  {
-    "id": 5925,
-    "problem_id": 5786,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5786.jpg"
-  },
-  {
-    "id": 5926,
-    "problem_id": 5787,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5787.jpg"
-  },
-  {
-    "id": 5927,
-    "problem_id": 5788,
-    "problem": "line D A, line A B, line B C, line D C, \\odot E lieson D C B A, line D A, line A B, line B C, line D C, \\odot E lieson D C B A\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5788.jpg"
-  },
-  {
-    "id": 5928,
-    "problem_id": 5789,
-    "problem": "line A D G, line F G, line E F, line E B A, line B C, line C D, line A D G, line F G, line E F, line E B A, line B C, line C D\nABCD \\sim AEFG. Find AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5789.jpg"
-  },
-  {
-    "id": 5929,
-    "problem_id": 5790,
-    "problem": "line A D G, line F G, line E F, line E B A, line B C, line C D, line A D G, line F G, line E F, line E B A, line B C, line C D\nABCD \\sim AEFG. Find AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5790.jpg"
-  },
-  {
-    "id": 5930,
-    "problem_id": 5791,
-    "problem": "line A F G, line E H G, line E F, line H F, line A F G, line E H G, line E F, line H F\nDetermine the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5791.jpg"
-  },
-  {
-    "id": 5931,
-    "problem_id": 5792,
-    "problem": "line A F G, line E H G, line E F, line H F, line A F G, line E H G, line E F, line H F\nDetermine the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5792.jpg"
-  },
-  {
-    "id": 5932,
-    "problem_id": 5793,
-    "problem": "line A F G, line E H G, line E F, line H F, line A F G, line E H G, line E F, line H F\nDetermine the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5793.jpg"
-  },
-  {
-    "id": 5933,
-    "problem_id": 5794,
-    "problem": "line A F G, line E H G, line E F, line H F, line A F G, line E H G, line E F, line H F\nDetermine the value of c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5794.jpg"
-  },
-  {
-    "id": 5934,
-    "problem_id": 5795,
-    "problem": "line C B, line C A, \\odot C lieson B A, line C B, line C A, \\odot C lieson B A\nDetermine the circumference of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5795.jpg"
-  },
-  {
-    "id": 5935,
-    "problem_id": 5796,
-    "problem": "line C B, line C A, \\odot C lieson B A, line C B, line C A, \\odot C lieson B A\nDetermine the circumference of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5796.jpg"
-  },
-  {
-    "id": 5936,
-    "problem_id": 5797,
-    "problem": "line C B, line C A, \\odot C lieson B A, line C B, line C A, \\odot C lieson B A\nDetermine the circumference of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5797.jpg"
-  },
-  {
-    "id": 5937,
-    "problem_id": 5798,
-    "problem": "line C B, line C A, \\odot C lieson B A, line C B, line C A, \\odot C lieson B A\nDetermine the circumference of \\odot C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5798.jpg"
-  },
-  {
-    "id": 5938,
-    "problem_id": 5799,
-    "problem": "line A B F, line A C E, line F D E, line B C, line C D, line B D, line A B F, line A C E, line F D E, line B C, line C D, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5799.jpg"
-  },
-  {
-    "id": 5939,
-    "problem_id": 5800,
-    "problem": "line A B F, line A C E, line F D E, line B C, line C D, line B D, line A B F, line A C E, line F D E, line B C, line C D, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5800.jpg"
-  },
-  {
-    "id": 5940,
-    "problem_id": 5801,
-    "problem": "line A B F, line A C E, line F D E, line B C, line C D, line B D, line A B F, line A C E, line F D E, line B C, line C D, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5801.jpg"
-  },
-  {
-    "id": 5941,
-    "problem_id": 5802,
-    "problem": "line H G, line E F, line F G, line E H, line H G, line E F, line F G, line E H\nFor what value of y must EFGH be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5802.jpg"
-  },
-  {
-    "id": 5942,
-    "problem_id": 5803,
-    "problem": "line H G, line E F, line F G, line E H, line H G, line E F, line F G, line E H\nFor what value of y must EFGH be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5803.jpg"
-  },
-  {
-    "id": 5943,
-    "problem_id": 5804,
-    "problem": "line H G, line E F, line F G, line E H, line H G, line E F, line F G, line E H\nFor what value of y must EFGH be a parallelogram?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5804.jpg"
-  },
-  {
-    "id": 5944,
-    "problem_id": 5805,
-    "problem": "line A D I K P, line B E J N O, line C D E F, line H I J G, line M K N L, line A D I K P, line B E J N O, line C D E F, line H I J G, line M K N L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5805.jpg"
-  },
-  {
-    "id": 5945,
-    "problem_id": 5806,
-    "problem": "line A D I K P, line B E J N O, line C D E F, line H I J G, line M K N L, line A D I K P, line B E J N O, line C D E F, line H I J G, line M K N L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5806.jpg"
-  },
-  {
-    "id": 5946,
-    "problem_id": 5807,
-    "problem": "line A D I K P, line B E J N O, line C D E F, line H I J G, line M K N L, line A D I K P, line B E J N O, line C D E F, line H I J G, line M K N L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5807.jpg"
-  },
-  {
-    "id": 5947,
-    "problem_id": 5808,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5808.jpg"
-  },
-  {
-    "id": 5948,
-    "problem_id": 5809,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5809.jpg"
-  },
-  {
-    "id": 5949,
-    "problem_id": 5810,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5810.jpg"
-  },
-  {
-    "id": 5950,
-    "problem_id": 5811,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5811.jpg"
-  },
-  {
-    "id": 5951,
-    "problem_id": 5812,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5812.jpg"
-  },
-  {
-    "id": 5952,
-    "problem_id": 5813,
-    "problem": "line A D, line B E D, line B C, line A E C, line A D, line B E D, line B C, line A E C\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5813.jpg"
-  },
-  {
-    "id": 5953,
-    "problem_id": 5814,
-    "problem": "line C B A, \\odot B lieson C A, line C B A, \\odot B lieson C A\nFind the radius of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5814.jpg"
-  },
-  {
-    "id": 5954,
-    "problem_id": 5815,
-    "problem": "line C B A, \\odot B lieson C A, line C B A, \\odot B lieson C A\nFind the radius of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5815.jpg"
-  },
-  {
-    "id": 5955,
-    "problem_id": 5816,
-    "problem": "line C B A, \\odot B lieson C A, line C B A, \\odot B lieson C A\nFind the radius of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5816.jpg"
-  },
-  {
-    "id": 5956,
-    "problem_id": 5817,
-    "problem": "line C B A, \\odot B lieson C A, line C B A, \\odot B lieson C A\nFind the radius of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5817.jpg"
-  },
-  {
-    "id": 5957,
-    "problem_id": 5818,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind JM if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5818.jpg"
-  },
-  {
-    "id": 5958,
-    "problem_id": 5819,
-    "problem": "line M J, line J N, line M N, line M J, line J N, line M N\nFind JM if \\triangle JMN is an isosceles triangle with JM = MN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5819.jpg"
-  },
-  {
-    "id": 5959,
-    "problem_id": 5820,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. Determine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5820.jpg"
-  },
-  {
-    "id": 5960,
-    "problem_id": 5821,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. Determine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5821.jpg"
-  },
-  {
-    "id": 5961,
-    "problem_id": 5822,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. Determine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5822.jpg"
-  },
-  {
-    "id": 5962,
-    "problem_id": 5823,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. Determine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5823.jpg"
-  },
-  {
-    "id": 5963,
-    "problem_id": 5824,
-    "problem": "line B A, line B C D, line A D, line A C, line B A, line B C D, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5824.jpg"
-  },
-  {
-    "id": 5964,
-    "problem_id": 5825,
-    "problem": "line B A, line B C D, line A D, line A C, line B A, line B C D, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5825.jpg"
-  },
-  {
-    "id": 5965,
-    "problem_id": 5826,
-    "problem": "line B A, line B C D, line A D, line A C, line B A, line B C D, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5826.jpg"
-  },
-  {
-    "id": 5966,
-    "problem_id": 5827,
-    "problem": "line B A, line B C D, line A D, line A C, line B A, line B C D, line A D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5827.jpg"
-  },
-  {
-    "id": 5967,
-    "problem_id": 5828,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5828.jpg"
-  },
-  {
-    "id": 5968,
-    "problem_id": 5829,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5829.jpg"
-  },
-  {
-    "id": 5969,
-    "problem_id": 5830,
-    "problem": "line B C D, line B A, line A D, line A C, line B C D, line B A, line A D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5830.jpg"
-  },
-  {
-    "id": 5970,
-    "problem_id": 5831,
-    "problem": "line C B, line A B, line C A, line C B, line A B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5831.jpg"
-  },
-  {
-    "id": 5971,
-    "problem_id": 5832,
-    "problem": "line C B, line A B, line C A, line C B, line A B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5832.jpg"
-  },
-  {
-    "id": 5972,
-    "problem_id": 5833,
-    "problem": "line C B, line A B, line C A, line C B, line A B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5833.jpg"
-  },
-  {
-    "id": 5973,
-    "problem_id": 5834,
-    "problem": "line C B, line A B, line C A, line C B, line A B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5834.jpg"
-  },
-  {
-    "id": 5974,
-    "problem_id": 5835,
-    "problem": "line C B, line A B, line C A, line C B, line A B, line C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5835.jpg"
-  },
-  {
-    "id": 5975,
-    "problem_id": 5836,
-    "problem": "line D E, line B C E, line D C A, line D E, line B C E, line D C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5836.jpg"
-  },
-  {
-    "id": 5976,
-    "problem_id": 5837,
-    "problem": "line D E, line B C E, line D C A, line D E, line B C E, line D C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5837.jpg"
-  },
-  {
-    "id": 5977,
-    "problem_id": 5838,
-    "problem": "line D E, line B C E, line D C A, line D E, line B C E, line D C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5838.jpg"
-  },
-  {
-    "id": 5978,
-    "problem_id": 5839,
-    "problem": "line D E, line B C E, line D C A, line D E, line B C E, line D C A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5839.jpg"
-  },
-  {
-    "id": 5979,
-    "problem_id": 5840,
-    "problem": "line B C D, line B E, line B A, line E D, line A D, line A C E, line B C D, line B E, line B A, line E D, line A D, line A C E\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5840.jpg"
-  },
-  {
-    "id": 5980,
-    "problem_id": 5841,
-    "problem": "line D C A, line B C E, line A E, line B D, line D C A, line B C E, line A E, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5841.jpg"
-  },
-  {
-    "id": 5981,
-    "problem_id": 5842,
-    "problem": "line D C A, line B C E, line A E, line B D, line D C A, line B C E, line A E, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5842.jpg"
-  },
-  {
-    "id": 5982,
-    "problem_id": 5843,
-    "problem": "line D C A, line B C E, line A E, line B D, line D C A, line B C E, line A E, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5843.jpg"
-  },
-  {
-    "id": 5983,
-    "problem_id": 5844,
-    "problem": "line D C A, line B C E, line A E, line B D, line D C A, line B C E, line A E, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5844.jpg"
-  },
-  {
-    "id": 5984,
-    "problem_id": 5845,
-    "problem": "line D C A, line B C E, line A E, line B D, line D C A, line B C E, line A E, line B D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5845.jpg"
-  },
-  {
-    "id": 5985,
-    "problem_id": 5846,
-    "problem": "line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H, line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5846.jpg"
-  },
-  {
-    "id": 5986,
-    "problem_id": 5847,
-    "problem": "line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H, line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5847.jpg"
-  },
-  {
-    "id": 5987,
-    "problem_id": 5848,
-    "problem": "line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H, line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5848.jpg"
-  },
-  {
-    "id": 5988,
-    "problem_id": 5849,
-    "problem": "line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H, line A B D, line C D, line C A, line C B, line E F G, line G H, line E H, line F H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5849.jpg"
-  },
-  {
-    "id": 5989,
-    "problem_id": 5850,
-    "problem": "line O E F G H P, line J B F R, line I A E Q, line N A B C D M, line K C G S, line L D H T, line O E F G H P, line J B F R, line I A E Q, line N A B C D M, line K C G S, line L D H T\nIf EF = FG = GH = 6 and AD = 15, what is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5850.jpg"
-  },
-  {
-    "id": 5990,
-    "problem_id": 5851,
-    "problem": "line O E F G H P, line J B F R, line I A E Q, line N A B C D M, line K C G S, line L D H T, line O E F G H P, line J B F R, line I A E Q, line N A B C D M, line K C G S, line L D H T\nIf EF = FG = GH = 6 and AD = 15, what is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5851.jpg"
-  },
-  {
-    "id": 5991,
-    "problem_id": 5852,
-    "problem": "line P Q R, line P Q R\nQ is the midpoint of RP. What is PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5852.jpg"
-  },
-  {
-    "id": 5993,
-    "problem_id": 5853,
-    "problem": "line P Q R, line P Q R\nQ is the midpoint of RP. What is PQ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5853.jpg"
-  },
-  {
-    "id": 5994,
-    "problem_id": 5854,
-    "problem": "line A E F H, line B G H, \\odot C lieson D G F E, line A E F H, line B G H, \\odot C lieson D G F E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5854.jpg"
-  },
-  {
-    "id": 5995,
-    "problem_id": 5855,
-    "problem": "line H E C, line G D A, line B D E F, line H E C, line G D A, line B D E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5855.jpg"
-  },
-  {
-    "id": 5996,
-    "problem_id": 5856,
-    "problem": "line H E C, line G D A, line B D E F, line H E C, line G D A, line B D E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5856.jpg"
-  },
-  {
-    "id": 5997,
-    "problem_id": 5857,
-    "problem": "line H E C, line G D A, line B D E F, line H E C, line G D A, line B D E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5857.jpg"
-  },
-  {
-    "id": 5998,
-    "problem_id": 5858,
-    "problem": "line H E C, line G D A, line B D E F, line H E C, line G D A, line B D E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5858.jpg"
-  },
-  {
-    "id": 5999,
-    "problem_id": 5859,
-    "problem": "line H E C, line G D A, line B D E F, line H E C, line G D A, line B D E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5859.jpg"
-  },
-  {
-    "id": 6000,
-    "problem_id": 5860,
-    "problem": "line H E C, line G D A, line B D E F, line H E C, line G D A, line B D E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5860.jpg"
-  },
-  {
-    "id": 6001,
-    "problem_id": 5861,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5861.jpg"
-  },
-  {
-    "id": 6002,
-    "problem_id": 5862,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5862.jpg"
-  },
-  {
-    "id": 6003,
-    "problem_id": 5863,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5863.jpg"
-  },
-  {
-    "id": 6004,
-    "problem_id": 5864,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5864.jpg"
-  },
-  {
-    "id": 6005,
-    "problem_id": 5865,
-    "problem": "line K L M, line K L M\nIf KM = 35, find the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5865.jpg"
-  },
-  {
-    "id": 6006,
-    "problem_id": 5866,
-    "problem": "line K L M, line K L M\nIf KM = 35, find the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5866.jpg"
-  },
-  {
-    "id": 6007,
-    "problem_id": 5867,
-    "problem": "line K L M, line K L M\nIf KM = 35, find the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5867.jpg"
-  },
-  {
-    "id": 6008,
-    "problem_id": 5868,
-    "problem": "line K L M, line K L M\nIf KM = 35, find the length of LK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5868.jpg"
-  },
-  {
-    "id": 6009,
-    "problem_id": 5869,
-    "problem": "line A P D, line B D C, line B E A, line A F C, line E P C, line B P F, line A P D, line B D C, line B E A, line A F C, line E P C, line B P F\nIf PC = 6.6, find the length of PE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5869.jpg"
-  },
-  {
-    "id": 6010,
-    "problem_id": 5870,
-    "problem": "line E A G, line D A F, line G F, line E F, line E D, line D G, line E A G, line D A F, line G F, line E F, line E D, line D G\nQuadrilateral DEFG is a kite. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5870.jpg"
-  },
-  {
-    "id": 6011,
-    "problem_id": 5871,
-    "problem": "line E A G, line D A F, line G F, line E F, line E D, line D G, line E A G, line D A F, line G F, line E F, line E D, line D G\nQuadrilateral DEFG is a kite. Find m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5871.jpg"
-  },
-  {
-    "id": 6012,
-    "problem_id": 5872,
-    "problem": "line A B, line E B, line A C F, line C B, \\odot B lieson A F E, line A B, line E B, line A C F, line C B, \\odot B lieson A F E\nWhat is the value of variable y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5872.jpg"
-  },
-  {
-    "id": 6013,
-    "problem_id": 5873,
-    "problem": "line A B C, line E D B, \\odot F lieson B D, line A B C, line E D B, \\odot F lieson B D\nFind the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5873.jpg"
-  },
-  {
-    "id": 6014,
-    "problem_id": 5874,
-    "problem": "line A B C, line E D B, \\odot F lieson B D, line A B C, line E D B, \\odot F lieson B D\nFind the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5874.jpg"
-  },
-  {
-    "id": 6015,
-    "problem_id": 5875,
-    "problem": "line A B C, line E D B, \\odot F lieson B D, line A B C, line E D B, \\odot F lieson B D\nFind the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5875.jpg"
-  },
-  {
-    "id": 6016,
-    "problem_id": 5876,
-    "problem": "line A B C, line E D B, \\odot F lieson B D, line A B C, line E D B, \\odot F lieson B D\nFind the measure of \\angle 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5876.jpg"
-  },
-  {
-    "id": 6017,
-    "problem_id": 5877,
-    "problem": "line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G, line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5877.jpg"
-  },
-  {
-    "id": 6018,
-    "problem_id": 5878,
-    "problem": "line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G, line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5878.jpg"
-  },
-  {
-    "id": 6019,
-    "problem_id": 5879,
-    "problem": "line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G, line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5879.jpg"
-  },
-  {
-    "id": 6020,
-    "problem_id": 5880,
-    "problem": "line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G, line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5880.jpg"
-  },
-  {
-    "id": 6021,
-    "problem_id": 5881,
-    "problem": "line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G, line C D E, line A E, line F G H, line B H, line A C, line A D, line B F, line B G\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5881.jpg"
-  },
-  {
-    "id": 6022,
-    "problem_id": 5882,
-    "problem": "line W Z, line X Y, line W X, line Z Y, line W Z, line X Y, line W X, line Z Y\nFor isosceles trapezoid XYZW, find the length of the median.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5882.jpg"
-  },
-  {
-    "id": 6023,
-    "problem_id": 5883,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5883.jpg"
-  },
-  {
-    "id": 6025,
-    "problem_id": 5884,
-    "problem": "line C B, line C D, \\odot C lieson D B, line C B, line C D, \\odot C lieson D B\nWhat is the area of the shaded region?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5884.jpg"
-  },
-  {
-    "id": 6026,
-    "problem_id": 5885,
-    "problem": "line A B C, line D B, line D A, line D C, line A B C, line D B, line D A, line D C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5885.jpg"
-  },
-  {
-    "id": 6027,
-    "problem_id": 5886,
-    "problem": "line A B C, line D B, line D A, line D C, line A B C, line D B, line D A, line D C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5886.jpg"
-  },
-  {
-    "id": 6028,
-    "problem_id": 5887,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5887.jpg"
-  },
-  {
-    "id": 6029,
-    "problem_id": 5888,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5888.jpg"
-  },
-  {
-    "id": 6030,
-    "problem_id": 5889,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5889.jpg"
-  },
-  {
-    "id": 6031,
-    "problem_id": 5890,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5890.jpg"
-  },
-  {
-    "id": 6032,
-    "problem_id": 5891,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5891.jpg"
-  },
-  {
-    "id": 6033,
-    "problem_id": 5892,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5892.jpg"
-  },
-  {
-    "id": 6034,
-    "problem_id": 5893,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5893.jpg"
-  },
-  {
-    "id": 6035,
-    "problem_id": 5894,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5894.jpg"
-  },
-  {
-    "id": 6036,
-    "problem_id": 5895,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5895.jpg"
-  },
-  {
-    "id": 6037,
-    "problem_id": 5896,
-    "problem": "line B C D, line A C E, line B E, line B A, line A D, line E D, line B C D, line A C E, line B E, line B A, line A D, line E D\nWhat is the measure of \\angle 3 in the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5896.jpg"
-  },
-  {
-    "id": 6038,
-    "problem_id": 5897,
-    "problem": "line A B C, line C E H, line A D F, line F G H, \\odot P lieson D G E B, line A B C, line C E H, line A D F, line F G H, \\odot P lieson D G E B\nFind the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5897.jpg"
-  },
-  {
-    "id": 6039,
-    "problem_id": 5898,
-    "problem": "line A B C, line C E H, line A D F, line F G H, \\odot P lieson D G E B, line A B C, line C E H, line A D F, line F G H, \\odot P lieson D G E B\nFind the exact circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5898.jpg"
-  },
-  {
-    "id": 6040,
-    "problem_id": 5899,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5899.jpg"
-  },
-  {
-    "id": 6041,
-    "problem_id": 5900,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5900.jpg"
-  },
-  {
-    "id": 6042,
-    "problem_id": 5901,
-    "problem": "line B C D, line E D, line A E, line A B, line A C, line B C D, line E D, line A E, line A B, line A C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5901.jpg"
-  },
-  {
-    "id": 6043,
-    "problem_id": 5902,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5902.jpg"
-  },
-  {
-    "id": 6044,
-    "problem_id": 5903,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5903.jpg"
-  },
-  {
-    "id": 6045,
-    "problem_id": 5904,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5904.jpg"
-  },
-  {
-    "id": 6046,
-    "problem_id": 5905,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5905.jpg"
-  },
-  {
-    "id": 6047,
-    "problem_id": 5906,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5906.jpg"
-  },
-  {
-    "id": 6048,
-    "problem_id": 5907,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5907.jpg"
-  },
-  {
-    "id": 6049,
-    "problem_id": 5908,
-    "problem": "line Q T S, line R S, line Q R, line R T, line Q T S, line R S, line Q R, line R T\nFind RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5908.jpg"
-  },
-  {
-    "id": 6050,
-    "problem_id": 5909,
-    "problem": "line Q T S, line R S, line Q R, line R T, line Q T S, line R S, line Q R, line R T\nFind RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5909.jpg"
-  },
-  {
-    "id": 6051,
-    "problem_id": 5910,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5910.jpg"
-  },
-  {
-    "id": 6052,
-    "problem_id": 5911,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5911.jpg"
-  },
-  {
-    "id": 6053,
-    "problem_id": 5912,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5912.jpg"
-  },
-  {
-    "id": 6054,
-    "problem_id": 5913,
-    "problem": "line A C, line C E, line D E, line A B D, line B C, line A C, line C E, line D E, line A B D, line B C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5913.jpg"
-  },
-  {
-    "id": 6055,
-    "problem_id": 5914,
-    "problem": "line F G H C, line B G E, line A H D, line F G H C, line B G E, line A H D\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5914.jpg"
-  },
-  {
-    "id": 6056,
-    "problem_id": 5915,
-    "problem": "line F G H C, line B G E, line A H D, line F G H C, line B G E, line A H D\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5915.jpg"
-  },
-  {
-    "id": 6057,
-    "problem_id": 5916,
-    "problem": "line F G H C, line B G E, line A H D, line F G H C, line B G E, line A H D\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5916.jpg"
-  },
-  {
-    "id": 6058,
-    "problem_id": 5917,
-    "problem": "line F G H C, line B G E, line A H D, line F G H C, line B G E, line A H D\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5917.jpg"
-  },
-  {
-    "id": 6059,
-    "problem_id": 5918,
-    "problem": "line F G H C, line B G E, line A H D, line F G H C, line B G E, line A H D\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5918.jpg"
-  },
-  {
-    "id": 6060,
-    "problem_id": 5919,
-    "problem": "line Q A P, line O P, line N B O, line B A, line N Q, line Q A P, line O P, line N B O, line B A, line N Q\nTrapezoid NOPQ has an area of 250 square inches. Find the height of NOPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5919.jpg"
-  },
-  {
-    "id": 6061,
-    "problem_id": 5920,
-    "problem": "line Q A P, line O P, line N B O, line B A, line N Q, line Q A P, line O P, line N B O, line B A, line N Q\nTrapezoid NOPQ has an area of 250 square inches. Find the height of NOPQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5920.jpg"
-  },
-  {
-    "id": 6062,
-    "problem_id": 5921,
-    "problem": "line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D, line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5921.jpg"
-  },
-  {
-    "id": 6063,
-    "problem_id": 5922,
-    "problem": "line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D, line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5922.jpg"
-  },
-  {
-    "id": 6064,
-    "problem_id": 5923,
-    "problem": "line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D, line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5923.jpg"
-  },
-  {
-    "id": 6065,
-    "problem_id": 5924,
-    "problem": "line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D, line C D E, line A B C, \\odot C0 lieson A E, \\odot C1 lieson B D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5924.jpg"
-  },
-  {
-    "id": 6067,
-    "problem_id": 5925,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5925.jpg"
-  },
-  {
-    "id": 6068,
-    "problem_id": 5926,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5926.jpg"
-  },
-  {
-    "id": 6069,
-    "problem_id": 5927,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5927.jpg"
-  },
-  {
-    "id": 6070,
-    "problem_id": 5928,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5928.jpg"
-  },
-  {
-    "id": 6071,
-    "problem_id": 5929,
-    "problem": "line A B, line B E, line D C E, line A D, line A C, line A B, line B E, line D C E, line A D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5929.jpg"
-  },
-  {
-    "id": 6072,
-    "problem_id": 5930,
-    "problem": "line M P, line R Q, line Q O, line R O, \\odot O lieson R M P Q, line M P, line R Q, line Q O, line R O, \\odot O lieson R M P Q\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5930.jpg"
-  },
-  {
-    "id": 6073,
-    "problem_id": 5931,
-    "problem": "line K L, line J N L, line K N M, line J M, line K J, line L M, line K L, line J N L, line K N M, line J M, line K J, line L M\nJN = 10.6, and NL = 14.8. Find KM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5931.jpg"
-  },
-  {
-    "id": 6074,
-    "problem_id": 5932,
-    "problem": "line K L, line J N L, line K N M, line J M, line K J, line L M, line K L, line J N L, line K N M, line J M, line K J, line L M\nJN = 10.6, and NL = 14.8. Find KM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5932.jpg"
-  },
-  {
-    "id": 6075,
-    "problem_id": 5933,
-    "problem": "line K L, line J N L, line K N M, line J M, line K J, line L M, line K L, line J N L, line K N M, line J M, line K J, line L M\nJN = 10.6, and NL = 14.8. Find KM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5933.jpg"
-  },
-  {
-    "id": 6076,
-    "problem_id": 5934,
-    "problem": "line C B D, line A B E, line E D, line C A, line C B D, line A B E, line E D, line C A\n\\triangle ABC \\cong \\triangle DBE. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5934.jpg"
-  },
-  {
-    "id": 6077,
-    "problem_id": 5935,
-    "problem": "line A B, line B D, line C D, line A C, \\odot E lieson A C D B, line A B, line B D, line C D, line A C, \\odot E lieson A C D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5935.jpg"
-  },
-  {
-    "id": 6078,
-    "problem_id": 5936,
-    "problem": "line A B, line B D, line C D, line A C, \\odot E lieson A C D B, line A B, line B D, line C D, line A C, \\odot E lieson A C D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5936.jpg"
-  },
-  {
-    "id": 6079,
-    "problem_id": 5937,
-    "problem": "line A B, line B D, line C D, line A C, \\odot E lieson A C D B, line A B, line B D, line C D, line A C, \\odot E lieson A C D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5937.jpg"
-  },
-  {
-    "id": 6080,
-    "problem_id": 5938,
-    "problem": "line A B, line B D, line C D, line A C, \\odot E lieson A C D B, line A B, line B D, line C D, line A C, \\odot E lieson A C D B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5938.jpg"
-  },
-  {
-    "id": 6081,
-    "problem_id": 5939,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5939.jpg"
-  },
-  {
-    "id": 6082,
-    "problem_id": 5940,
-    "problem": "line A C D, line C B, \\odot E lieson C B, line A C D, line C B, \\odot E lieson C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5940.jpg"
-  },
-  {
-    "id": 6083,
-    "problem_id": 5941,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5941.jpg"
-  },
-  {
-    "id": 6084,
-    "problem_id": 5942,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5942.jpg"
-  },
-  {
-    "id": 6085,
-    "problem_id": 5943,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5943.jpg"
-  },
-  {
-    "id": 6086,
-    "problem_id": 5944,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5944.jpg"
-  },
-  {
-    "id": 6087,
-    "problem_id": 5945,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5945.jpg"
-  },
-  {
-    "id": 6088,
-    "problem_id": 5946,
-    "problem": "line P T, line P S, line L N, line T S, line M N, line M L, line P T, line P S, line L N, line T S, line M N, line M L\n\\triangle MNL \\sim \\triangle SPT. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5946.jpg"
-  },
-  {
-    "id": 6089,
-    "problem_id": 5947,
-    "problem": "line P T, line P S, line L N, line T S, line M N, line M L, line P T, line P S, line L N, line T S, line M N, line M L\n\\triangle MNL \\sim \\triangle SPT. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5947.jpg"
-  },
-  {
-    "id": 6090,
-    "problem_id": 5948,
-    "problem": "line P T, line P S, line L N, line T S, line M N, line M L, line P T, line P S, line L N, line T S, line M N, line M L\n\\triangle MNL \\sim \\triangle SPT. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5948.jpg"
-  },
-  {
-    "id": 6091,
-    "problem_id": 5949,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5949.jpg"
-  },
-  {
-    "id": 6092,
-    "problem_id": 5950,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5950.jpg"
-  },
-  {
-    "id": 6093,
-    "problem_id": 5951,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5951.jpg"
-  },
-  {
-    "id": 6094,
-    "problem_id": 5952,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5952.jpg"
-  },
-  {
-    "id": 6095,
-    "problem_id": 5953,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5953.jpg"
-  },
-  {
-    "id": 6096,
-    "problem_id": 5954,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5954.jpg"
-  },
-  {
-    "id": 6097,
-    "problem_id": 5955,
-    "problem": "line A D H, line F E D B, line C E G, line A D H, line F E D B, line C E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5955.jpg"
-  },
-  {
-    "id": 6098,
-    "problem_id": 5956,
-    "problem": "line A D H, line F E D B, line C E G, line A D H, line F E D B, line C E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5956.jpg"
-  },
-  {
-    "id": 6099,
-    "problem_id": 5957,
-    "problem": "line A D H, line F E D B, line C E G, line A D H, line F E D B, line C E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5957.jpg"
-  },
-  {
-    "id": 6100,
-    "problem_id": 5958,
-    "problem": "line A D H, line F E D B, line C E G, line A D H, line F E D B, line C E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5958.jpg"
-  },
-  {
-    "id": 6101,
-    "problem_id": 5959,
-    "problem": "line A D H, line F E D B, line C E G, line A D H, line F E D B, line C E G\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5959.jpg"
-  },
-  {
-    "id": 6102,
-    "problem_id": 5960,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5960.jpg"
-  },
-  {
-    "id": 6103,
-    "problem_id": 5961,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5961.jpg"
-  },
-  {
-    "id": 6104,
-    "problem_id": 5962,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5962.jpg"
-  },
-  {
-    "id": 6105,
-    "problem_id": 5963,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5963.jpg"
-  },
-  {
-    "id": 6106,
-    "problem_id": 5964,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5964.jpg"
-  },
-  {
-    "id": 6107,
-    "problem_id": 5965,
-    "problem": "line R S, line T S, line R T, line R S, line T S, line R T\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5965.jpg"
-  },
-  {
-    "id": 6108,
-    "problem_id": 5966,
-    "problem": "line R S, line T S, line R T, line R S, line T S, line R T\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5966.jpg"
-  },
-  {
-    "id": 6109,
-    "problem_id": 5967,
-    "problem": "line R S, line T S, line R T, line R S, line T S, line R T\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5967.jpg"
-  },
-  {
-    "id": 6110,
-    "problem_id": 5968,
-    "problem": "line R S, line T S, line R T, line R S, line T S, line R T\nFind m \\angle S.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5968.jpg"
-  },
-  {
-    "id": 6111,
-    "problem_id": 5969,
-    "problem": "line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C, line D C F, line E A D, line B Z D, line E B F, line A Z F, line E Z C\nIn \\triangle DEF, DB = 24.6, and EZ = 11.6. What is DZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5969.jpg"
-  },
-  {
-    "id": 6112,
-    "problem_id": 5970,
-    "problem": "line A B C, line A B C\nFind x if B is the midpoint of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5970.jpg"
-  },
-  {
-    "id": 6113,
-    "problem_id": 5971,
-    "problem": "line A B C, line A B C\nFind x if B is the midpoint of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5971.jpg"
-  },
-  {
-    "id": 6114,
-    "problem_id": 5972,
-    "problem": "line A B C, line A B C\nFind x if B is the midpoint of AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5972.jpg"
-  },
-  {
-    "id": 6115,
-    "problem_id": 5973,
-    "problem": "line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W, line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W\nIf quadrilateral ABCD \\sim quadrilateral WXYZ. What is the length of YZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5973.jpg"
-  },
-  {
-    "id": 6116,
-    "problem_id": 5974,
-    "problem": "line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W, line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W\nIf quadrilateral ABCD \\sim quadrilateral WXYZ. What is the length of YZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5974.jpg"
-  },
-  {
-    "id": 6117,
-    "problem_id": 5975,
-    "problem": "line M P O, line N O, line N P, line N M, line M P O, line N O, line N P, line N M\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5975.jpg"
-  },
-  {
-    "id": 6118,
-    "problem_id": 5976,
-    "problem": "line M P O, line N O, line N P, line N M, line M P O, line N O, line N P, line N M\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5976.jpg"
-  },
-  {
-    "id": 6119,
-    "problem_id": 5977,
-    "problem": "line M P O, line N O, line N P, line N M, line M P O, line N O, line N P, line N M\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5977.jpg"
-  },
-  {
-    "id": 6120,
-    "problem_id": 5978,
-    "problem": "line M P O, line N O, line N P, line N M, line M P O, line N O, line N P, line N M\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5978.jpg"
-  },
-  {
-    "id": 6121,
-    "problem_id": 5979,
-    "problem": "line B D, line A D, line D C, line A B, line B C, line B D, line A D, line D C, line A B, line B C\nFor what value of x is \\parallelogram ABCD a rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5979.jpg"
-  },
-  {
-    "id": 6122,
-    "problem_id": 5980,
-    "problem": "line B D, line A D, line D C, line A B, line B C, line B D, line A D, line D C, line A B, line B C\nFor what value of x is \\parallelogram ABCD a rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5980.jpg"
-  },
-  {
-    "id": 6123,
-    "problem_id": 5981,
-    "problem": "line B D, line A D, line D C, line A B, line B C, line B D, line A D, line D C, line A B, line B C\nFor what value of x is \\parallelogram ABCD a rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5981.jpg"
-  },
-  {
-    "id": 6124,
-    "problem_id": 5982,
-    "problem": "line B D, line A D, line D C, line A B, line B C, line B D, line A D, line D C, line A B, line B C\nFor what value of x is \\parallelogram ABCD a rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5982.jpg"
-  },
-  {
-    "id": 6125,
-    "problem_id": 5983,
-    "problem": "line B D, line A D, line D C, line A B, line B C, line B D, line A D, line D C, line A B, line B C\nFor what value of x is \\parallelogram ABCD a rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5983.jpg"
-  },
-  {
-    "id": 6126,
-    "problem_id": 5984,
-    "problem": "line A C, line C B, line A B, \\odot O lieson A B C, line A C, line C B, line A B, \\odot O lieson A B C\nFind m \\widehat BC for \\odot O.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5984.jpg"
-  },
-  {
-    "id": 6127,
-    "problem_id": 5985,
-    "problem": "line A C, line C B, line A B, \\odot O lieson A B C, line A C, line C B, line A B, \\odot O lieson A B C\nFind m \\widehat BC for \\odot O.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5985.jpg"
-  },
-  {
-    "id": 6128,
-    "problem_id": 5986,
-    "problem": "line A C, line C B, line A B, \\odot O lieson A B C, line A C, line C B, line A B, \\odot O lieson A B C\nFind m \\widehat BC for \\odot O.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5986.jpg"
-  },
-  {
-    "id": 6129,
-    "problem_id": 5987,
-    "problem": "line M P, line P N, line N O, \\odot A lieson M N O P, line M P, line P N, line N O, \\odot A lieson M N O P\nFind m \\widehat PO.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5987.jpg"
-  },
-  {
-    "id": 6130,
-    "problem_id": 5988,
-    "problem": "line M P, line P N, line N O, \\odot A lieson M N O P, line M P, line P N, line N O, \\odot A lieson M N O P\nFind m \\widehat PO.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5988.jpg"
-  },
-  {
-    "id": 6131,
-    "problem_id": 5989,
-    "problem": "line M P, line P N, line N O, \\odot A lieson M N O P, line M P, line P N, line N O, \\odot A lieson M N O P\nFind m \\widehat PO.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5989.jpg"
-  },
-  {
-    "id": 6132,
-    "problem_id": 5990,
-    "problem": "line M P, line P N, line N O, \\odot A lieson M N O P, line M P, line P N, line N O, \\odot A lieson M N O P\nFind m \\widehat PO.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5990.jpg"
-  },
-  {
-    "id": 6133,
-    "problem_id": 5991,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5991.jpg"
-  },
-  {
-    "id": 6134,
-    "problem_id": 5992,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5992.jpg"
-  },
-  {
-    "id": 6135,
-    "problem_id": 5993,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5993.jpg"
-  },
-  {
-    "id": 6136,
-    "problem_id": 5994,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5994.jpg"
-  },
-  {
-    "id": 6137,
-    "problem_id": 5995,
-    "problem": "line L N, line L M, line N M, \\odot N lieson M L, line L N, line L M, line N M, \\odot N lieson M L\nSolve for the measure of \\angle NML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5995.jpg"
-  },
-  {
-    "id": 6138,
-    "problem_id": 5996,
-    "problem": "line L N, line L M, line N M, \\odot N lieson M L, line L N, line L M, line N M, \\odot N lieson M L\nSolve for the measure of \\angle NML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5996.jpg"
-  },
-  {
-    "id": 6139,
-    "problem_id": 5997,
-    "problem": "line A B E, line C D E, line A C, line B D, line A B E, line C D E, line A C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5997.jpg"
-  },
-  {
-    "id": 6140,
-    "problem_id": 5998,
-    "problem": "line A B E, line C D E, line A C, line B D, line A B E, line C D E, line A C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5998.jpg"
-  },
-  {
-    "id": 6141,
-    "problem_id": 5999,
-    "problem": "line A B E, line C D E, line A C, line B D, line A B E, line C D E, line A C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/5999.jpg"
-  },
-  {
-    "id": 6142,
-    "problem_id": 6000,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the figure. Perimeter = 84 meters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6000.jpg"
-  },
-  {
-    "id": 6143,
-    "problem_id": 6001,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the figure. Perimeter = 84 meters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6001.jpg"
-  },
-  {
-    "id": 6144,
-    "problem_id": 6002,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the figure. Perimeter = 84 meters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6002.jpg"
-  },
-  {
-    "id": 6145,
-    "problem_id": 6003,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the figure. Perimeter = 84 meters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6003.jpg"
-  },
-  {
-    "id": 6146,
-    "problem_id": 6004,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6004.jpg"
-  },
-  {
-    "id": 6147,
-    "problem_id": 6005,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6005.jpg"
-  },
-  {
-    "id": 6148,
-    "problem_id": 6006,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6006.jpg"
-  },
-  {
-    "id": 6149,
-    "problem_id": 6007,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6007.jpg"
-  },
-  {
-    "id": 6150,
-    "problem_id": 6008,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6008.jpg"
-  },
-  {
-    "id": 6151,
-    "problem_id": 6009,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nFind BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6009.jpg"
-  },
-  {
-    "id": 6152,
-    "problem_id": 6010,
-    "problem": "line S R, line T N R, line T M S, line M N, line S R, line T N R, line T M S, line M N\nIn \\triangle TRS, find TS if MN \\parallel SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6010.jpg"
-  },
-  {
-    "id": 6153,
-    "problem_id": 6011,
-    "problem": "line S R, line T N R, line T M S, line M N, line S R, line T N R, line T M S, line M N\nIn \\triangle TRS, find TS if MN \\parallel SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6011.jpg"
-  },
-  {
-    "id": 6154,
-    "problem_id": 6012,
-    "problem": "line S R, line T N R, line T M S, line M N, line S R, line T N R, line T M S, line M N\nIn \\triangle TRS, find TS if MN \\parallel SR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6012.jpg"
-  },
-  {
-    "id": 6155,
-    "problem_id": 6013,
-    "problem": "line C B E, line A B D, line E D, line A C, line C B E, line A B D, line E D, line A C\nFind BE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6013.jpg"
-  },
-  {
-    "id": 6156,
-    "problem_id": 6014,
-    "problem": "line C B E, line A B D, line E D, line A C, line C B E, line A B D, line E D, line A C\nFind BE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6014.jpg"
-  },
-  {
-    "id": 6157,
-    "problem_id": 6015,
-    "problem": "line C B E, line A B D, line E D, line A C, line C B E, line A B D, line E D, line A C\nFind BE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6015.jpg"
-  },
-  {
-    "id": 6158,
-    "problem_id": 6016,
-    "problem": "line B C D, line A C, \\odot E lieson A C, line B C D, line A C, \\odot E lieson A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6016.jpg"
-  },
-  {
-    "id": 6159,
-    "problem_id": 6017,
-    "problem": "line B C D, line A C, \\odot E lieson A C, line B C D, line A C, \\odot E lieson A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6017.jpg"
-  },
-  {
-    "id": 6160,
-    "problem_id": 6018,
-    "problem": "line B C D, line A C, \\odot E lieson A C, line B C D, line A C, \\odot E lieson A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6018.jpg"
-  },
-  {
-    "id": 6161,
-    "problem_id": 6019,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6019.jpg"
-  },
-  {
-    "id": 6162,
-    "problem_id": 6020,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6020.jpg"
-  },
-  {
-    "id": 6163,
-    "problem_id": 6021,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6021.jpg"
-  },
-  {
-    "id": 6164,
-    "problem_id": 6022,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6022.jpg"
-  },
-  {
-    "id": 6165,
-    "problem_id": 6023,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nFind h.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6023.jpg"
-  },
-  {
-    "id": 6166,
-    "problem_id": 6024,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle BCD of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6024.jpg"
-  },
-  {
-    "id": 6167,
-    "problem_id": 6025,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle BCD of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6025.jpg"
-  },
-  {
-    "id": 6168,
-    "problem_id": 6026,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6026.jpg"
-  },
-  {
-    "id": 6169,
-    "problem_id": 6027,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6027.jpg"
-  },
-  {
-    "id": 6170,
-    "problem_id": 6028,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6028.jpg"
-  },
-  {
-    "id": 6172,
-    "problem_id": 6029,
-    "problem": "line C A, line A B E, line D E, line C D, line C B, line C A, line A B E, line D E, line C D, line C B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6029.jpg"
-  },
-  {
-    "id": 6174,
-    "problem_id": 6030,
-    "problem": "line A B, line D A, line D C, line C B, line A B, line D A, line D C, line C B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6030.jpg"
-  },
-  {
-    "id": 6175,
-    "problem_id": 6031,
-    "problem": "line A B, line D A, line D C, line C B, line A B, line D A, line D C, line C B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6031.jpg"
-  },
-  {
-    "id": 6176,
-    "problem_id": 6032,
-    "problem": "line A B, line D A, line D C, line C B, line A B, line D A, line D C, line C B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6032.jpg"
-  },
-  {
-    "id": 6177,
-    "problem_id": 6033,
-    "problem": "line A B, line D A, line D C, line C B, line A B, line D A, line D C, line C B\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6033.jpg"
-  },
-  {
-    "id": 6178,
-    "problem_id": 6034,
-    "problem": "line A C, line A D B, line C B, line C D, line A C, line A D B, line C B, line C D\nIf D is the midpoint of AB, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6034.jpg"
-  },
-  {
-    "id": 6179,
-    "problem_id": 6035,
-    "problem": "line A C, line A D B, line C B, line C D, line A C, line A D B, line C B, line C D\nIf D is the midpoint of AB, find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6035.jpg"
-  },
-  {
-    "id": 6180,
-    "problem_id": 6036,
-    "problem": "line C E A, line A G B, line C F B, line C D G, line E D B, line A D F, line C E A, line A G B, line C F B, line C D G, line E D B, line A D F\nThe area of \\angle ADB is 4.5 cm^{2}. In centimeters, what is DF?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6036.jpg"
-  },
-  {
-    "id": 6181,
-    "problem_id": 6037,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6037.jpg"
-  },
-  {
-    "id": 6182,
-    "problem_id": 6038,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6038.jpg"
-  },
-  {
-    "id": 6183,
-    "problem_id": 6039,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6039.jpg"
-  },
-  {
-    "id": 6184,
-    "problem_id": 6040,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6040.jpg"
-  },
-  {
-    "id": 6185,
-    "problem_id": 6041,
-    "problem": "line C A, line B A, line B C, line C A, line B A, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6041.jpg"
-  },
-  {
-    "id": 6186,
-    "problem_id": 6042,
-    "problem": "line C B, line C D, line A B, line B D, line A C, line C B, line C D, line A B, line B D, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6042.jpg"
-  },
-  {
-    "id": 6188,
-    "problem_id": 6043,
-    "problem": "line C B, line C D, line A B, line B D, line A C, line C B, line C D, line A B, line B D, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6043.jpg"
-  },
-  {
-    "id": 6189,
-    "problem_id": 6044,
-    "problem": "line C B, line C D, line A B, line B D, line A C, line C B, line C D, line A B, line B D, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6044.jpg"
-  },
-  {
-    "id": 6190,
-    "problem_id": 6045,
-    "problem": "line C B, line C D, line A B, line B D, line A C, line C B, line C D, line A B, line B D, line A C\nFind the area of the quadrilateral.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6045.jpg"
-  },
-  {
-    "id": 6191,
-    "problem_id": 6046,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6046.jpg"
-  },
-  {
-    "id": 6192,
-    "problem_id": 6047,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6047.jpg"
-  },
-  {
-    "id": 6193,
-    "problem_id": 6048,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6048.jpg"
-  },
-  {
-    "id": 6194,
-    "problem_id": 6049,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6049.jpg"
-  },
-  {
-    "id": 6195,
-    "problem_id": 6050,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6050.jpg"
-  },
-  {
-    "id": 6196,
-    "problem_id": 6051,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6051.jpg"
-  },
-  {
-    "id": 6197,
-    "problem_id": 6052,
-    "problem": "line A B C, line D A, line D B, line D C, line A B C, line D A, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6052.jpg"
-  },
-  {
-    "id": 6198,
-    "problem_id": 6053,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6053.jpg"
-  },
-  {
-    "id": 6199,
-    "problem_id": 6054,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6054.jpg"
-  },
-  {
-    "id": 6200,
-    "problem_id": 6055,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6055.jpg"
-  },
-  {
-    "id": 6201,
-    "problem_id": 6056,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6056.jpg"
-  },
-  {
-    "id": 6202,
-    "problem_id": 6057,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the value of variable a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6057.jpg"
-  },
-  {
-    "id": 6203,
-    "problem_id": 6058,
-    "problem": "line A C E, line D C B, line A B, line D E, line B E, line A D, line A C E, line D C B, line A B, line D E, line B E, line A D\nFind the value of variable k in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6058.jpg"
-  },
-  {
-    "id": 6204,
-    "problem_id": 6059,
-    "problem": "line A C E, line D C B, line A B, line D E, line B E, line A D, line A C E, line D C B, line A B, line D E, line B E, line A D\nFind the value of variable k in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6059.jpg"
-  },
-  {
-    "id": 6205,
-    "problem_id": 6060,
-    "problem": "line A C, line C D, line A D, line B A, line B C, line A C, line C D, line A D, line B A, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6060.jpg"
-  },
-  {
-    "id": 6206,
-    "problem_id": 6061,
-    "problem": "line A C, line C D, line A D, line B A, line B C, line A C, line C D, line A D, line B A, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6061.jpg"
-  },
-  {
-    "id": 6207,
-    "problem_id": 6062,
-    "problem": "line A C, line C D, line A D, line B A, line B C, line A C, line C D, line A D, line B A, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6062.jpg"
-  },
-  {
-    "id": 6208,
-    "problem_id": 6063,
-    "problem": "line T U, line T Y, line U W, line Y W, line T U, line T Y, line U W, line Y W\nTUWY is a rhombus. What is the length of TY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6063.jpg"
-  },
-  {
-    "id": 6209,
-    "problem_id": 6064,
-    "problem": "line T U, line T Y, line U W, line Y W, line T U, line T Y, line U W, line Y W\nTUWY is a rhombus. What is the length of TY?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6064.jpg"
-  },
-  {
-    "id": 6210,
-    "problem_id": 6065,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6065.jpg"
-  },
-  {
-    "id": 6211,
-    "problem_id": 6066,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6066.jpg"
-  },
-  {
-    "id": 6212,
-    "problem_id": 6067,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6067.jpg"
-  },
-  {
-    "id": 6213,
-    "problem_id": 6068,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6068.jpg"
-  },
-  {
-    "id": 6214,
-    "problem_id": 6069,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6069.jpg"
-  },
-  {
-    "id": 6215,
-    "problem_id": 6070,
-    "problem": "line C B, line A C D, line B D, line A B, line C B, line A C D, line B D, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6070.jpg"
-  },
-  {
-    "id": 6216,
-    "problem_id": 6071,
-    "problem": "line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T, line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T\nGKNM \\sim VRPT. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6071.jpg"
-  },
-  {
-    "id": 6217,
-    "problem_id": 6072,
-    "problem": "line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T, line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T\nGKNM \\sim VRPT. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6072.jpg"
-  },
-  {
-    "id": 6218,
-    "problem_id": 6073,
-    "problem": "line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T, line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T\nGKNM \\sim VRPT. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6073.jpg"
-  },
-  {
-    "id": 6219,
-    "problem_id": 6074,
-    "problem": "line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T, line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T\nGKNM \\sim VRPT. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6074.jpg"
-  },
-  {
-    "id": 6220,
-    "problem_id": 6075,
-    "problem": "line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T, line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T\nGKNM \\sim VRPT. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6075.jpg"
-  },
-  {
-    "id": 6221,
-    "problem_id": 6076,
-    "problem": "line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T, line N K, line G K, line R P, line R V, line M G, line M N, line P T, line V T\nGKNM \\sim VRPT. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6076.jpg"
-  },
-  {
-    "id": 6222,
-    "problem_id": 6077,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6077.jpg"
-  },
-  {
-    "id": 6223,
-    "problem_id": 6078,
-    "problem": "line B A, line A D, line C D, line B C, line B A, line A D, line C D, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6078.jpg"
-  },
-  {
-    "id": 6224,
-    "problem_id": 6079,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6079.jpg"
-  },
-  {
-    "id": 6225,
-    "problem_id": 6080,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6080.jpg"
-  },
-  {
-    "id": 6226,
-    "problem_id": 6081,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6081.jpg"
-  },
-  {
-    "id": 6227,
-    "problem_id": 6082,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6082.jpg"
-  },
-  {
-    "id": 6228,
-    "problem_id": 6083,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6083.jpg"
-  },
-  {
-    "id": 6230,
-    "problem_id": 6084,
-    "problem": "line B A, line A D, line C D E, line B C, line B A, line A D, line C D E, line B C\nSolve for m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6084.jpg"
-  },
-  {
-    "id": 6231,
-    "problem_id": 6085,
-    "problem": "line B D E F C, line E G A, line B D E F C, line E G A\nIf m \\angle DEG is 6\\frac{1}{2} times m \\angle FEG, what is m \\angle DEG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6085.jpg"
-  },
-  {
-    "id": 6233,
-    "problem_id": 6086,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6086.jpg"
-  },
-  {
-    "id": 6234,
-    "problem_id": 6087,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6087.jpg"
-  },
-  {
-    "id": 6235,
-    "problem_id": 6088,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6088.jpg"
-  },
-  {
-    "id": 6236,
-    "problem_id": 6089,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6089.jpg"
-  },
-  {
-    "id": 6237,
-    "problem_id": 6090,
-    "problem": "line A C, line A B, line B C, line A C, line A B, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6090.jpg"
-  },
-  {
-    "id": 6238,
-    "problem_id": 6091,
-    "problem": "line B C, line A D C, line B A, line B D, line B C, line A D C, line B A, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6091.jpg"
-  },
-  {
-    "id": 6239,
-    "problem_id": 6092,
-    "problem": "line B C, line A D C, line B A, line B D, line B C, line A D C, line B A, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6092.jpg"
-  },
-  {
-    "id": 6240,
-    "problem_id": 6093,
-    "problem": "line B C, line A D C, line B A, line B D, line B C, line A D C, line B A, line B D\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6093.jpg"
-  },
-  {
-    "id": 6241,
-    "problem_id": 6094,
-    "problem": "line F D A, line G E C, line B D E H, line F D A, line G E C, line B D E H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6094.jpg"
-  },
-  {
-    "id": 6242,
-    "problem_id": 6095,
-    "problem": "line F D A, line G E C, line B D E H, line F D A, line G E C, line B D E H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6095.jpg"
-  },
-  {
-    "id": 6243,
-    "problem_id": 6096,
-    "problem": "line F D A, line G E C, line B D E H, line F D A, line G E C, line B D E H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6096.jpg"
-  },
-  {
-    "id": 6244,
-    "problem_id": 6097,
-    "problem": "line F D A, line G E C, line B D E H, line F D A, line G E C, line B D E H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6097.jpg"
-  },
-  {
-    "id": 6245,
-    "problem_id": 6098,
-    "problem": "line F D A, line G E C, line B D E H, line F D A, line G E C, line B D E H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6098.jpg"
-  },
-  {
-    "id": 6246,
-    "problem_id": 6099,
-    "problem": "line F D A, line G E C, line B D E H, line F D A, line G E C, line B D E H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6099.jpg"
-  },
-  {
-    "id": 6247,
-    "problem_id": 6100,
-    "problem": "line B C D, line B E, line B A, line A C E, line A D, line E D, line B C D, line B E, line B A, line A C E, line A D, line E D\nWhat is the value of x in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6100.jpg"
-  },
-  {
-    "id": 6248,
-    "problem_id": 6101,
-    "problem": "line B C D, line B E, line B A, line A C E, line A D, line E D, line B C D, line B E, line B A, line A C E, line A D, line E D\nWhat is the value of x in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6101.jpg"
-  },
-  {
-    "id": 6249,
-    "problem_id": 6102,
-    "problem": "line P Q, line R S, \\odot A lieson P R S Q, line P Q, line R S, \\odot A lieson P R S Q\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6102.jpg"
-  },
-  {
-    "id": 6250,
-    "problem_id": 6103,
-    "problem": "line P Q, line R S, \\odot A lieson P R S Q, line P Q, line R S, \\odot A lieson P R S Q\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6103.jpg"
-  },
-  {
-    "id": 6251,
-    "problem_id": 6104,
-    "problem": "line P Q, line R S, \\odot A lieson P R S Q, line P Q, line R S, \\odot A lieson P R S Q\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6104.jpg"
-  },
-  {
-    "id": 6252,
-    "problem_id": 6105,
-    "problem": "line P Q, line R S, \\odot A lieson P R S Q, line P Q, line R S, \\odot A lieson P R S Q\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6105.jpg"
-  },
-  {
-    "id": 6254,
-    "problem_id": 6106,
-    "problem": "line D E, line E B A, line D C A, line C B, line D E, line E B A, line D C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6106.jpg"
-  },
-  {
-    "id": 6255,
-    "problem_id": 6107,
-    "problem": "line D E, line E B A, line D C A, line C B, line D E, line E B A, line D C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6107.jpg"
-  },
-  {
-    "id": 6256,
-    "problem_id": 6108,
-    "problem": "line D E, line E B A, line D C A, line C B, line D E, line E B A, line D C A, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6108.jpg"
-  },
-  {
-    "id": 6257,
-    "problem_id": 6109,
-    "problem": "line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z, line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6109.jpg"
-  },
-  {
-    "id": 6258,
-    "problem_id": 6110,
-    "problem": "line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z, line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6110.jpg"
-  },
-  {
-    "id": 6259,
-    "problem_id": 6111,
-    "problem": "line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z, line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6111.jpg"
-  },
-  {
-    "id": 6260,
-    "problem_id": 6112,
-    "problem": "line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z, line A V Y, line C W Z Y, line W B V, \\odot B lieson W R V Z\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6112.jpg"
-  },
-  {
-    "id": 6261,
-    "problem_id": 6113,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6113.jpg"
-  },
-  {
-    "id": 6262,
-    "problem_id": 6114,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6114.jpg"
-  },
-  {
-    "id": 6263,
-    "problem_id": 6115,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6115.jpg"
-  },
-  {
-    "id": 6264,
-    "problem_id": 6116,
-    "problem": "line A B D F, line E F G, line E D C, line B C, line A B D F, line E F G, line E D C, line B C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6116.jpg"
-  },
-  {
-    "id": 6265,
-    "problem_id": 6117,
-    "problem": "line A P D, line B P C, \\odot P lieson B D C A, line A P D, line B P C, \\odot P lieson B D C A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6117.jpg"
-  },
-  {
-    "id": 6266,
-    "problem_id": 6118,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6118.jpg"
-  },
-  {
-    "id": 6267,
-    "problem_id": 6119,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6119.jpg"
-  },
-  {
-    "id": 6268,
-    "problem_id": 6120,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6120.jpg"
-  },
-  {
-    "id": 6269,
-    "problem_id": 6121,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6121.jpg"
-  },
-  {
-    "id": 6270,
-    "problem_id": 6122,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6122.jpg"
-  },
-  {
-    "id": 6271,
-    "problem_id": 6123,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6123.jpg"
-  },
-  {
-    "id": 6272,
-    "problem_id": 6124,
-    "problem": "line A B C, line D C, line A D, line B D, line A B C, line D C, line A D, line B D\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6124.jpg"
-  },
-  {
-    "id": 6274,
-    "problem_id": 6125,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6125.jpg"
-  },
-  {
-    "id": 6275,
-    "problem_id": 6126,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6126.jpg"
-  },
-  {
-    "id": 6276,
-    "problem_id": 6127,
-    "problem": "line B D, line C E, line B A, line A C, line D F, line F E, line B D, line C E, line B A, line A C, line D F, line F E\nWhat is the perimeter of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6127.jpg"
-  },
-  {
-    "id": 6277,
-    "problem_id": 6128,
-    "problem": "line B D, line C E, line B A, line A C, line D F, line F E, line B D, line C E, line B A, line A C, line D F, line F E\nWhat is the perimeter of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6128.jpg"
-  },
-  {
-    "id": 6278,
-    "problem_id": 6129,
-    "problem": "line B D, line C E, line B A, line A C, line D F, line F E, line B D, line C E, line B A, line A C, line D F, line F E\nWhat is the perimeter of the regular polygon?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6129.jpg"
-  },
-  {
-    "id": 6279,
-    "problem_id": 6130,
-    "problem": "line F A B E, line G C D H, line B D, line A C, line F A B E, line G C D H, line B D, line A C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6130.jpg"
-  },
-  {
-    "id": 6280,
-    "problem_id": 6131,
-    "problem": "line F A B E, line G C D H, line B D, line A C, line F A B E, line G C D H, line B D, line A C\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6131.jpg"
-  },
-  {
-    "id": 6281,
-    "problem_id": 6132,
-    "problem": "line G A E B, line D E F, line B C H, \\odot I lieson A F B D, line G A E B, line D E F, line B C H, \\odot I lieson A F B D\nFind m \\widehat AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6132.jpg"
-  },
-  {
-    "id": 6282,
-    "problem_id": 6133,
-    "problem": "line G A E B, line D E F, line B C H, \\odot I lieson A F B D, line G A E B, line D E F, line B C H, \\odot I lieson A F B D\nFind m \\widehat AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6133.jpg"
-  },
-  {
-    "id": 6283,
-    "problem_id": 6134,
-    "problem": "line A B, line A C D, line B D, line C B, line A B, line A C D, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6134.jpg"
-  },
-  {
-    "id": 6284,
-    "problem_id": 6135,
-    "problem": "line A B, line A C D, line B D, line C B, line A B, line A C D, line B D, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6135.jpg"
-  },
-  {
-    "id": 6285,
-    "problem_id": 6136,
-    "problem": "line I B G E L, line J F G C K, line H A G D M, line I B G E L, line J F G C K, line H A G D M\nIf m \\angle AGB = 4x+7 and m \\angle EGD = 71, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6136.jpg"
-  },
-  {
-    "id": 6286,
-    "problem_id": 6137,
-    "problem": "line I B G E L, line J F G C K, line H A G D M, line I B G E L, line J F G C K, line H A G D M\nIf m \\angle AGB = 4x+7 and m \\angle EGD = 71, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6137.jpg"
-  },
-  {
-    "id": 6287,
-    "problem_id": 6138,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6138.jpg"
-  },
-  {
-    "id": 6288,
-    "problem_id": 6139,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6139.jpg"
-  },
-  {
-    "id": 6289,
-    "problem_id": 6140,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6140.jpg"
-  },
-  {
-    "id": 6290,
-    "problem_id": 6141,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6141.jpg"
-  },
-  {
-    "id": 6291,
-    "problem_id": 6142,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6142.jpg"
-  },
-  {
-    "id": 6292,
-    "problem_id": 6143,
-    "problem": "line A C E, line D C B, line A C E, line D C B\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6143.jpg"
-  },
-  {
-    "id": 6293,
-    "problem_id": 6144,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6144.jpg"
-  },
-  {
-    "id": 6294,
-    "problem_id": 6145,
-    "problem": "line A C, line A B, line B D, line C D, line A C, line A B, line B D, line C D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6145.jpg"
-  },
-  {
-    "id": 6295,
-    "problem_id": 6146,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6146.jpg"
-  },
-  {
-    "id": 6296,
-    "problem_id": 6147,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6147.jpg"
-  },
-  {
-    "id": 6297,
-    "problem_id": 6148,
-    "problem": "line E F H, line C G H, line C D E, line D F, line G F, line E F H, line C G H, line C D E, line D F, line G F\nFind the length of DE if \\triangle DEF \\sim \\triangle GFH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6148.jpg"
-  },
-  {
-    "id": 6298,
-    "problem_id": 6149,
-    "problem": "line E F H, line C G H, line C D E, line D F, line G F, line E F H, line C G H, line C D E, line D F, line G F\nFind the length of DE if \\triangle DEF \\sim \\triangle GFH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6149.jpg"
-  },
-  {
-    "id": 6300,
-    "problem_id": 6150,
-    "problem": "line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X, line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X\nQuadrilateral WXZY is a rectangle. Find the measure of \\angle 10 if m \\angle 1 = 30.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6150.jpg"
-  },
-  {
-    "id": 6302,
-    "problem_id": 6151,
-    "problem": "line A C, line D B C, line A D, line A B, line A C, line D B C, line A D, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6151.jpg"
-  },
-  {
-    "id": 6303,
-    "problem_id": 6152,
-    "problem": "line A C, line D B C, line A D, line A B, line A C, line D B C, line A D, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6152.jpg"
-  },
-  {
-    "id": 6304,
-    "problem_id": 6153,
-    "problem": "line A C, line D B C, line A D, line A B, line A C, line D B C, line A D, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6153.jpg"
-  },
-  {
-    "id": 6305,
-    "problem_id": 6154,
-    "problem": "line A C, line D B C, line A D, line A B, line A C, line D B C, line A D, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6154.jpg"
-  },
-  {
-    "id": 6306,
-    "problem_id": 6155,
-    "problem": "line A C, line D B C, line A D, line A B, line A C, line D B C, line A D, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6155.jpg"
-  },
-  {
-    "id": 6307,
-    "problem_id": 6156,
-    "problem": "line V T, line U T, \\odot T lieson V U, line V T, line U T, \\odot T lieson V U\nFind the circumference of \\odot T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6156.jpg"
-  },
-  {
-    "id": 6308,
-    "problem_id": 6157,
-    "problem": "line D C E, line A C F, line B C, line D C E, line A C F, line B C\nm \\angle 11 = x+40, m \\angle 12 = x+10, m \\angle 13 = 3x+30, what is the measure of \\angle 13?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6157.jpg"
-  },
-  {
-    "id": 6309,
-    "problem_id": 6158,
-    "problem": "line D C E, line A C F, line B C, line D C E, line A C F, line B C\nm \\angle 11 = x+40, m \\angle 12 = x+10, m \\angle 13 = 3x+30, what is the measure of \\angle 13?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6158.jpg"
-  },
-  {
-    "id": 6310,
-    "problem_id": 6159,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf b = 3, find c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6159.jpg"
-  },
-  {
-    "id": 6311,
-    "problem_id": 6160,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf b = 3, find c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6160.jpg"
-  },
-  {
-    "id": 6312,
-    "problem_id": 6161,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nIf b = 3, find c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6161.jpg"
-  },
-  {
-    "id": 6313,
-    "problem_id": 6162,
-    "problem": "line A C, line C B, line C D, line A D B, line A C, line C B, line C D, line A D B\nFind \\sin A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6162.jpg"
-  },
-  {
-    "id": 6314,
-    "problem_id": 6163,
-    "problem": "line A C, line C B, line C D, line A D B, line A C, line C B, line C D, line A D B\nFind \\sin A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6163.jpg"
-  },
-  {
-    "id": 6315,
-    "problem_id": 6164,
-    "problem": "line P O R, line P S, line Q R, line Q P, line R S, line Q O S, line P O R, line P S, line Q R, line Q P, line R S, line Q O S\nIn \\parallelogram PQRS, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6164.jpg"
-  },
-  {
-    "id": 6316,
-    "problem_id": 6165,
-    "problem": "line P O R, line P S, line Q R, line Q P, line R S, line Q O S, line P O R, line P S, line Q R, line Q P, line R S, line Q O S\nIn \\parallelogram PQRS, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6165.jpg"
-  },
-  {
-    "id": 6317,
-    "problem_id": 6166,
-    "problem": "line P O R, line P S, line Q R, line Q P, line R S, line Q O S, line P O R, line P S, line Q R, line Q P, line R S, line Q O S\nIn \\parallelogram PQRS, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6166.jpg"
-  },
-  {
-    "id": 6318,
-    "problem_id": 6167,
-    "problem": "line P O R, line P S, line Q R, line Q P, line R S, line Q O S, line P O R, line P S, line Q R, line Q P, line R S, line Q O S\nIn \\parallelogram PQRS, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6167.jpg"
-  },
-  {
-    "id": 6319,
-    "problem_id": 6168,
-    "problem": "line P O R, line P S, line Q R, line Q P, line R S, line Q O S, line P O R, line P S, line Q R, line Q P, line R S, line Q O S\nIn \\parallelogram PQRS, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6168.jpg"
-  },
-  {
-    "id": 6320,
-    "problem_id": 6169,
-    "problem": "line Y Z, line T U, line S T, line S U, line X Y, line X Z, line Y Z, line T U, line S T, line S U, line X Y, line X Z\n\\triangle XYZ \\cong \\triangle STU, determine the value of t.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6169.jpg"
-  },
-  {
-    "id": 6321,
-    "problem_id": 6170,
-    "problem": "line Y Z, line T U, line S T, line S U, line X Y, line X Z, line Y Z, line T U, line S T, line S U, line X Y, line X Z\n\\triangle XYZ \\cong \\triangle STU, determine the value of t.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6170.jpg"
-  },
-  {
-    "id": 6322,
-    "problem_id": 6171,
-    "problem": "line Y Z, line T U, line S T, line S U, line X Y, line X Z, line Y Z, line T U, line S T, line S U, line X Y, line X Z\n\\triangle XYZ \\cong \\triangle STU, determine the value of t.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6171.jpg"
-  },
-  {
-    "id": 6323,
-    "problem_id": 6172,
-    "problem": "line D E, line B C E, line D C A, line D E, line B C E, line D C A\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6172.jpg"
-  },
-  {
-    "id": 6324,
-    "problem_id": 6173,
-    "problem": "line D E, line B C E, line D C A, line D E, line B C E, line D C A\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6173.jpg"
-  },
-  {
-    "id": 6325,
-    "problem_id": 6174,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6174.jpg"
-  },
-  {
-    "id": 6326,
-    "problem_id": 6175,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6175.jpg"
-  },
-  {
-    "id": 6327,
-    "problem_id": 6176,
-    "problem": "line J I C D, line K I E F, line A C E G, line B I H, line J I C D, line K I E F, line A C E G, line B I H\nm \\angle 11 = 62 and m \\angle 14 = 38. Find the measure of \\angle 6.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6176.jpg"
-  },
-  {
-    "id": 6328,
-    "problem_id": 6177,
-    "problem": "line B A, line A C, line D C, line B D, line B A, line A C, line D C, line B D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6177.jpg"
-  },
-  {
-    "id": 6330,
-    "problem_id": 6178,
-    "problem": "line F Z B, line F P C, line F M A, line M Z, line Z P, line F Z B, line F P C, line F M A, line M Z, line Z P\nSolve for the value of MZP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6178.jpg"
-  },
-  {
-    "id": 6331,
-    "problem_id": 6179,
-    "problem": "line A Q, line B Q, \\odot Q lieson A B, line A Q, line B Q, \\odot Q lieson A B\nWhat is the length of \\widehat AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6179.jpg"
-  },
-  {
-    "id": 6332,
-    "problem_id": 6180,
-    "problem": "line A Q, line B Q, \\odot Q lieson A B, line A Q, line B Q, \\odot Q lieson A B\nWhat is the length of \\widehat AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6180.jpg"
-  },
-  {
-    "id": 6333,
-    "problem_id": 6181,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the length of DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6181.jpg"
-  },
-  {
-    "id": 6334,
-    "problem_id": 6182,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the length of DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6182.jpg"
-  },
-  {
-    "id": 6335,
-    "problem_id": 6183,
-    "problem": "line B C E, line D E, line A C D, line B A, line B C E, line D E, line A C D, line B A\nFind the length of DC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6183.jpg"
-  },
-  {
-    "id": 6336,
-    "problem_id": 6184,
-    "problem": "line D M, line N D L, line J D, line D K, \\odot D lieson N J K L M, line D M, line N D L, line J D, line D K, \\odot D lieson N J K L M\nUse \\odot D to find the length of \\widehat KL if JD = 7 centimeters.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6184.jpg"
-  },
-  {
-    "id": 6337,
-    "problem_id": 6185,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nSolve for b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6185.jpg"
-  },
-  {
-    "id": 6338,
-    "problem_id": 6186,
-    "problem": "line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B, line A B, line D C B, line D E, line A C E, \\odot F lieson A D E B\nSolve for b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6186.jpg"
-  },
-  {
-    "id": 6339,
-    "problem_id": 6187,
-    "problem": "line A B C D, line E D, line F E, line F A, line F B, line E C, line A B C D, line E D, line F E, line F A, line F B, line E C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6187.jpg"
-  },
-  {
-    "id": 6340,
-    "problem_id": 6188,
-    "problem": "line A B C D, line E D, line F E, line F A, line F B, line E C, line A B C D, line E D, line F E, line F A, line F B, line E C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6188.jpg"
-  },
-  {
-    "id": 6341,
-    "problem_id": 6189,
-    "problem": "line A B C D, line E D, line F E, line F A, line F B, line E C, line A B C D, line E D, line F E, line F A, line F B, line E C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6189.jpg"
-  },
-  {
-    "id": 6342,
-    "problem_id": 6190,
-    "problem": "line A B C D, line E D, line F E, line F A, line F B, line E C, line A B C D, line E D, line F E, line F A, line F B, line E C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6190.jpg"
-  },
-  {
-    "id": 6343,
-    "problem_id": 6191,
-    "problem": "line A B D, line B C, line D E F, line A C, line C F, line B E, line A B D, line B C, line D E F, line A C, line C F, line B E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6191.jpg"
-  },
-  {
-    "id": 6344,
-    "problem_id": 6192,
-    "problem": "line A B D, line B C, line D E F, line A C, line C F, line B E, line A B D, line B C, line D E F, line A C, line C F, line B E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6192.jpg"
-  },
-  {
-    "id": 6345,
-    "problem_id": 6193,
-    "problem": "line A B D, line B C, line D E F, line A C, line C F, line B E, line A B D, line B C, line D E F, line A C, line C F, line B E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6193.jpg"
-  },
-  {
-    "id": 6346,
-    "problem_id": 6194,
-    "problem": "line A B D, line B C, line D E F, line A C, line C F, line B E, line A B D, line B C, line D E F, line A C, line C F, line B E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6194.jpg"
-  },
-  {
-    "id": 6347,
-    "problem_id": 6195,
-    "problem": "line A B D, line B C, line D E F, line A C, line C F, line B E, line A B D, line B C, line D E F, line A C, line C F, line B E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6195.jpg"
-  },
-  {
-    "id": 6348,
-    "problem_id": 6196,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6196.jpg"
-  },
-  {
-    "id": 6349,
-    "problem_id": 6197,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6197.jpg"
-  },
-  {
-    "id": 6350,
-    "problem_id": 6198,
-    "problem": "line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C, line K T V P L, line J X Q I, line H Y Z R G, line D W S U E, line A W Y X V N, line B S F R Q P M, line O T X Z F U C\nPQ = QR = RS. Solve for the length of VW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6198.jpg"
-  },
-  {
-    "id": 6351,
-    "problem_id": 6199,
-    "problem": "line F J, line F H, line G F, \\odot F lieson G J H, line F J, line F H, line G F, \\odot F lieson G J H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6199.jpg"
-  },
-  {
-    "id": 6352,
-    "problem_id": 6200,
-    "problem": "line F J, line F H, line G F, \\odot F lieson G J H, line F J, line F H, line G F, \\odot F lieson G J H\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6200.jpg"
-  },
-  {
-    "id": 6353,
-    "problem_id": 6201,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6201.jpg"
-  },
-  {
-    "id": 6354,
-    "problem_id": 6202,
-    "problem": "line A C, line B A, line B C, line A C, line B A, line B C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6202.jpg"
-  },
-  {
-    "id": 6355,
-    "problem_id": 6203,
-    "problem": "line A Z Y, line C X Y, line B W Y, line W Z, line X W, line A Z Y, line C X Y, line B W Y, line W Z, line X W\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6203.jpg"
-  },
-  {
-    "id": 6356,
-    "problem_id": 6204,
-    "problem": "line A Z Y, line C X Y, line B W Y, line W Z, line X W, line A Z Y, line C X Y, line B W Y, line W Z, line X W\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6204.jpg"
-  },
-  {
-    "id": 6357,
-    "problem_id": 6205,
-    "problem": "line A Z Y, line C X Y, line B W Y, line W Z, line X W, line A Z Y, line C X Y, line B W Y, line W Z, line X W\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6205.jpg"
-  },
-  {
-    "id": 6358,
-    "problem_id": 6206,
-    "problem": "line A Z Y, line C X Y, line B W Y, line W Z, line X W, line A Z Y, line C X Y, line B W Y, line W Z, line X W\nFind YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6206.jpg"
-  },
-  {
-    "id": 6359,
-    "problem_id": 6207,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find YA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6207.jpg"
-  },
-  {
-    "id": 6360,
-    "problem_id": 6208,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find YA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6208.jpg"
-  },
-  {
-    "id": 6361,
-    "problem_id": 6209,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find YA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6209.jpg"
-  },
-  {
-    "id": 6362,
-    "problem_id": 6210,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6210.jpg"
-  },
-  {
-    "id": 6363,
-    "problem_id": 6211,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6211.jpg"
-  },
-  {
-    "id": 6364,
-    "problem_id": 6212,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the area of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6212.jpg"
-  },
-  {
-    "id": 6365,
-    "problem_id": 6213,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the area of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6213.jpg"
-  },
-  {
-    "id": 6366,
-    "problem_id": 6214,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the area of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6214.jpg"
-  },
-  {
-    "id": 6367,
-    "problem_id": 6215,
-    "problem": "line W A V, line R V, line T R, line T A, line T W, line W A V, line R V, line T R, line T A, line T W\nFind the area of \\parallelogram TRVW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6215.jpg"
-  },
-  {
-    "id": 6368,
-    "problem_id": 6216,
-    "problem": "line B D E, line C A E, \\odot F lieson P A D, line B D E, line C A E, \\odot F lieson P A D\nFind m \\widehat DA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6216.jpg"
-  },
-  {
-    "id": 6369,
-    "problem_id": 6217,
-    "problem": "line K J, line K L, line J L A, line K J, line K L, line J L A\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6217.jpg"
-  },
-  {
-    "id": 6370,
-    "problem_id": 6218,
-    "problem": "line K J, line K L, line J L A, line K J, line K L, line J L A\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6218.jpg"
-  },
-  {
-    "id": 6371,
-    "problem_id": 6219,
-    "problem": "line K J, line K L, line J L A, line K J, line K L, line J L A\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6219.jpg"
-  },
-  {
-    "id": 6372,
-    "problem_id": 6220,
-    "problem": "line K J, line K L, line J L A, line K J, line K L, line J L A\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6220.jpg"
-  },
-  {
-    "id": 6373,
-    "problem_id": 6221,
-    "problem": "line K J, line K L, line J L A, line K J, line K L, line J L A\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6221.jpg"
-  },
-  {
-    "id": 6374,
-    "problem_id": 6222,
-    "problem": "line K J, line K L, line J L A, line K J, line K L, line J L A\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6222.jpg"
-  },
-  {
-    "id": 6375,
-    "problem_id": 6223,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nFind the measure of \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6223.jpg"
-  },
-  {
-    "id": 6376,
-    "problem_id": 6224,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nFind the measure of \\angle Z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6224.jpg"
-  },
-  {
-    "id": 6377,
-    "problem_id": 6225,
-    "problem": "line B A, line A D, line C D, line B C, line E F, line E H, line H G, line F G, line B A, line A D, line C D, line B C, line E F, line E H, line H G, line F G\nEach pair of polygons is similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6225.jpg"
-  },
-  {
-    "id": 6378,
-    "problem_id": 6226,
-    "problem": "line B A, line A D, line C D, line B C, line E F, line E H, line H G, line F G, line B A, line A D, line C D, line B C, line E F, line E H, line H G, line F G\nEach pair of polygons is similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6226.jpg"
-  },
-  {
-    "id": 6379,
-    "problem_id": 6227,
-    "problem": "line B A, line A D, line C D, line B C, line E F, line E H, line H G, line F G, line B A, line A D, line C D, line B C, line E F, line E H, line H G, line F G\nEach pair of polygons is similar. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6227.jpg"
-  },
-  {
-    "id": 6380,
-    "problem_id": 6228,
-    "problem": "line A B C, line D C, line E B D, line A E, line A B C, line D C, line E B D, line A E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6228.jpg"
-  },
-  {
-    "id": 6381,
-    "problem_id": 6229,
-    "problem": "line A B C, line D C, line E B D, line A E, line A B C, line D C, line E B D, line A E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6229.jpg"
-  },
-  {
-    "id": 6382,
-    "problem_id": 6230,
-    "problem": "line A B C, line D C, line E B D, line A E, line A B C, line D C, line E B D, line A E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6230.jpg"
-  },
-  {
-    "id": 6383,
-    "problem_id": 6231,
-    "problem": "line A B C, line D C, line E B D, line A E, line A B C, line D C, line E B D, line A E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6231.jpg"
-  },
-  {
-    "id": 6384,
-    "problem_id": 6232,
-    "problem": "line A B C, line D C, line E B D, line A E, line A B C, line D C, line E B D, line A E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6232.jpg"
-  },
-  {
-    "id": 6385,
-    "problem_id": 6233,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6233.jpg"
-  },
-  {
-    "id": 6386,
-    "problem_id": 6234,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6234.jpg"
-  },
-  {
-    "id": 6387,
-    "problem_id": 6235,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6235.jpg"
-  },
-  {
-    "id": 6388,
-    "problem_id": 6236,
-    "problem": "line R U Q, line R V S, line Q T S, \\odot W lieson U T V, line R U Q, line R V S, line Q T S, \\odot W lieson U T V\nFind the length of UR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6236.jpg"
-  },
-  {
-    "id": 6389,
-    "problem_id": 6237,
-    "problem": "line K J, line J G, line K H, line H G, line K J, line J G, line K H, line H G\nFind m \\angle J in rhombus JKHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6237.jpg"
-  },
-  {
-    "id": 6390,
-    "problem_id": 6238,
-    "problem": "line K J, line J G, line K H, line H G, line K J, line J G, line K H, line H G\nFind m \\angle J in rhombus JKHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6238.jpg"
-  },
-  {
-    "id": 6391,
-    "problem_id": 6239,
-    "problem": "line A M L B, line C J B, \\odot D lieson N M L J, line A M L B, line C J B, \\odot D lieson N M L J\nFind m \\widehat ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6239.jpg"
-  },
-  {
-    "id": 6392,
-    "problem_id": 6240,
-    "problem": "line A M L B, line C J B, \\odot D lieson N M L J, line A M L B, line C J B, \\odot D lieson N M L J\nFind m \\widehat ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6240.jpg"
-  },
-  {
-    "id": 6393,
-    "problem_id": 6241,
-    "problem": "line A M L B, line C J B, \\odot D lieson N M L J, line A M L B, line C J B, \\odot D lieson N M L J\nFind m \\widehat ML.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6241.jpg"
-  },
-  {
-    "id": 6394,
-    "problem_id": 6242,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6242.jpg"
-  },
-  {
-    "id": 6395,
-    "problem_id": 6243,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6243.jpg"
-  },
-  {
-    "id": 6396,
-    "problem_id": 6244,
-    "problem": "line C D, line B D, line A B, line A C, line C D, line B D, line A B, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6244.jpg"
-  },
-  {
-    "id": 6397,
-    "problem_id": 6245,
-    "problem": "line B C, line B A, \\odot B lieson C A, line B C, line B A, \\odot B lieson C A\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6245.jpg"
-  },
-  {
-    "id": 6398,
-    "problem_id": 6246,
-    "problem": "line B C, line B A, \\odot B lieson C A, line B C, line B A, \\odot B lieson C A\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6246.jpg"
-  },
-  {
-    "id": 6399,
-    "problem_id": 6247,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable g in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6247.jpg"
-  },
-  {
-    "id": 6400,
-    "problem_id": 6248,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable g in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6248.jpg"
-  },
-  {
-    "id": 6401,
-    "problem_id": 6249,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable g in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6249.jpg"
-  },
-  {
-    "id": 6402,
-    "problem_id": 6250,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable g in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6250.jpg"
-  },
-  {
-    "id": 6403,
-    "problem_id": 6251,
-    "problem": "line D C A, line D E, line A E, line B A, line B C E, line B D, line D C A, line D E, line A E, line B A, line B C E, line B D\nFind the value of variable g in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6251.jpg"
-  },
-  {
-    "id": 6404,
-    "problem_id": 6252,
-    "problem": "line A C E, line D C B, line A B, line D E, line A D, line B E, line A C E, line D C B, line A B, line D E, line A D, line B E\nFind the measure of \\angle 2 for the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6252.jpg"
-  },
-  {
-    "id": 6405,
-    "problem_id": 6253,
-    "problem": "line A C E, line D C B, line A B, line D E, line A D, line B E, line A C E, line D C B, line A B, line D E, line A D, line B E\nFind the measure of \\angle 2 for the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6253.jpg"
-  },
-  {
-    "id": 6406,
-    "problem_id": 6254,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the measure of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6254.jpg"
-  },
-  {
-    "id": 6407,
-    "problem_id": 6255,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the measure of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6255.jpg"
-  },
-  {
-    "id": 6408,
-    "problem_id": 6256,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the measure of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6256.jpg"
-  },
-  {
-    "id": 6409,
-    "problem_id": 6257,
-    "problem": "line C H F, line C G, line C D, line D F, line G F, line D H G, line C H F, line C G, line C D, line D F, line G F, line D H G\nCDFG is a rhombus. Find the measure of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6257.jpg"
-  },
-  {
-    "id": 6410,
-    "problem_id": 6258,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6258.jpg"
-  },
-  {
-    "id": 6411,
-    "problem_id": 6259,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6259.jpg"
-  },
-  {
-    "id": 6412,
-    "problem_id": 6260,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6260.jpg"
-  },
-  {
-    "id": 6413,
-    "problem_id": 6261,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6261.jpg"
-  },
-  {
-    "id": 6414,
-    "problem_id": 6262,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6262.jpg"
-  },
-  {
-    "id": 6415,
-    "problem_id": 6263,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6263.jpg"
-  },
-  {
-    "id": 6416,
-    "problem_id": 6264,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6264.jpg"
-  },
-  {
-    "id": 6418,
-    "problem_id": 6265,
-    "problem": "line A B D, line E C D, line A E, line B C, line A B D, line E C D, line A E, line B C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6265.jpg"
-  },
-  {
-    "id": 6419,
-    "problem_id": 6266,
-    "problem": "line A B D, line E C D, line A E, line B C, line A B D, line E C D, line A E, line B C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6266.jpg"
-  },
-  {
-    "id": 6420,
-    "problem_id": 6267,
-    "problem": "line A B D, line E C D, line A E, line B C, line A B D, line E C D, line A E, line B C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6267.jpg"
-  },
-  {
-    "id": 6421,
-    "problem_id": 6268,
-    "problem": "line A B D, line E C D, line A E, line B C, line A B D, line E C D, line A E, line B C\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6268.jpg"
-  },
-  {
-    "id": 6422,
-    "problem_id": 6269,
-    "problem": "line S V T, line W X T, line W V, line S U W, line V X, line U V, line S V T, line W X T, line W V, line S U W, line V X, line U V\nFind SW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6269.jpg"
-  },
-  {
-    "id": 6423,
-    "problem_id": 6270,
-    "problem": "line S V T, line W X T, line W V, line S U W, line V X, line U V, line S V T, line W X T, line W V, line S U W, line V X, line U V\nFind SW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6270.jpg"
-  },
-  {
-    "id": 6424,
-    "problem_id": 6271,
-    "problem": "line B C D, line A C, line B C D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6271.jpg"
-  },
-  {
-    "id": 6425,
-    "problem_id": 6272,
-    "problem": "line B C D, line A C, line B C D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6272.jpg"
-  },
-  {
-    "id": 6426,
-    "problem_id": 6273,
-    "problem": "line B C D, line A C, line B C D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6273.jpg"
-  },
-  {
-    "id": 6427,
-    "problem_id": 6274,
-    "problem": "line B C D, line A C, line B C D, line A C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6274.jpg"
-  },
-  {
-    "id": 6428,
-    "problem_id": 6275,
-    "problem": "line A D, line A B, line C D, line B D, line A C, line A D, line A B, line C D, line B D, line A C\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6275.jpg"
-  },
-  {
-    "id": 6429,
-    "problem_id": 6276,
-    "problem": "line A D, line A B, line C D, line B D, line A C, line A D, line A B, line C D, line B D, line A C\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6276.jpg"
-  },
-  {
-    "id": 6430,
-    "problem_id": 6277,
-    "problem": "line A D, line A B, line C D, line B D, line A C, line A D, line A B, line C D, line B D, line A C\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6277.jpg"
-  },
-  {
-    "id": 6431,
-    "problem_id": 6278,
-    "problem": "line A D, line A B, line C D, line B D, line A C, line A D, line A B, line C D, line B D, line A C\nFind the area of the rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6278.jpg"
-  },
-  {
-    "id": 6432,
-    "problem_id": 6279,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\tan V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6279.jpg"
-  },
-  {
-    "id": 6433,
-    "problem_id": 6280,
-    "problem": "line S T, line R T, line R S, line C B, line B A, line C A, line S T, line R T, line R S, line C B, line B A, line C A\n\\triangle RST \\cong \\triangle ABC. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6280.jpg"
-  },
-  {
-    "id": 6434,
-    "problem_id": 6281,
-    "problem": "line S T, line R S, line Q R, line S T, line R S, line Q R\nIf ST = RS, QR = SR, find TS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6281.jpg"
-  },
-  {
-    "id": 6435,
-    "problem_id": 6282,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6282.jpg"
-  },
-  {
-    "id": 6436,
-    "problem_id": 6283,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6283.jpg"
-  },
-  {
-    "id": 6437,
-    "problem_id": 6284,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6284.jpg"
-  },
-  {
-    "id": 6438,
-    "problem_id": 6285,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6285.jpg"
-  },
-  {
-    "id": 6439,
-    "problem_id": 6286,
-    "problem": "line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F, line A B C, line E D C, line G F E, line G H A, \\odot I lieson H B D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6286.jpg"
-  },
-  {
-    "id": 6440,
-    "problem_id": 6287,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6287.jpg"
-  },
-  {
-    "id": 6441,
-    "problem_id": 6288,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6288.jpg"
-  },
-  {
-    "id": 6442,
-    "problem_id": 6289,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6289.jpg"
-  },
-  {
-    "id": 6443,
-    "problem_id": 6290,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6290.jpg"
-  },
-  {
-    "id": 6444,
-    "problem_id": 6291,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6291.jpg"
-  },
-  {
-    "id": 6445,
-    "problem_id": 6292,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6292.jpg"
-  },
-  {
-    "id": 6446,
-    "problem_id": 6293,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6293.jpg"
-  },
-  {
-    "id": 6447,
-    "problem_id": 6294,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6294.jpg"
-  },
-  {
-    "id": 6448,
-    "problem_id": 6295,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6295.jpg"
-  },
-  {
-    "id": 6449,
-    "problem_id": 6296,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6296.jpg"
-  },
-  {
-    "id": 6450,
-    "problem_id": 6297,
-    "problem": "line A C E, line D E, line A B D, line B C, line A C E, line D E, line A B D, line B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6297.jpg"
-  },
-  {
-    "id": 6451,
-    "problem_id": 6298,
-    "problem": "line D B C, line B A, line D B C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6298.jpg"
-  },
-  {
-    "id": 6452,
-    "problem_id": 6299,
-    "problem": "line D B C, line B A, line D B C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6299.jpg"
-  },
-  {
-    "id": 6453,
-    "problem_id": 6300,
-    "problem": "line D B C, line B A, line D B C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6300.jpg"
-  },
-  {
-    "id": 6454,
-    "problem_id": 6301,
-    "problem": "line D B C, line B A, line D B C, line B A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6301.jpg"
-  },
-  {
-    "id": 6455,
-    "problem_id": 6302,
-    "problem": "line C D A, line C B, line D B, line A B, line C D A, line C B, line D B, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6302.jpg"
-  },
-  {
-    "id": 6456,
-    "problem_id": 6303,
-    "problem": "line C D A, line C B, line D B, line A B, line C D A, line C B, line D B, line A B\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6303.jpg"
-  },
-  {
-    "id": 6457,
-    "problem_id": 6304,
-    "problem": "line C P B, line A P, \\odot P lieson A C B, line C P B, line A P, \\odot P lieson A C B\nFind the circumference of \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6304.jpg"
-  },
-  {
-    "id": 6458,
-    "problem_id": 6305,
-    "problem": "line A C, line A B, line B E, line C D E, line A D, line A C, line A B, line B E, line C D E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6305.jpg"
-  },
-  {
-    "id": 6459,
-    "problem_id": 6306,
-    "problem": "line A C, line A B, line B E, line C D E, line A D, line A C, line A B, line B E, line C D E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6306.jpg"
-  },
-  {
-    "id": 6460,
-    "problem_id": 6307,
-    "problem": "line A C, line A B, line B E, line C D E, line A D, line A C, line A B, line B E, line C D E, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6307.jpg"
-  },
-  {
-    "id": 6461,
-    "problem_id": 6308,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6308.jpg"
-  },
-  {
-    "id": 6462,
-    "problem_id": 6309,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6309.jpg"
-  },
-  {
-    "id": 6463,
-    "problem_id": 6310,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6310.jpg"
-  },
-  {
-    "id": 6464,
-    "problem_id": 6311,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6311.jpg"
-  },
-  {
-    "id": 6465,
-    "problem_id": 6312,
-    "problem": "line X Z, line Z Y, line X Y, line X Z, line Z Y, line X Y\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6312.jpg"
-  },
-  {
-    "id": 6466,
-    "problem_id": 6313,
-    "problem": "line O A M, line L A N, line O N, line L M, line M N, line L O, line O A M, line L A N, line O N, line L M, line M N, line L O\nFind the measure of \\angle 3 in rectangle LMNO if m \\angle 5 = 38.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6313.jpg"
-  },
-  {
-    "id": 6467,
-    "problem_id": 6314,
-    "problem": "line A C E, line B C D, line D E, line A B, line A C E, line B C D, line D E, line A B\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6314.jpg"
-  },
-  {
-    "id": 6468,
-    "problem_id": 6315,
-    "problem": "line A C E, line B C D, line D E, line A B, line A C E, line B C D, line D E, line A B\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6315.jpg"
-  },
-  {
-    "id": 6469,
-    "problem_id": 6316,
-    "problem": "line A C E, line B C D, line D E, line A B, line A C E, line B C D, line D E, line A B\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6316.jpg"
-  },
-  {
-    "id": 6470,
-    "problem_id": 6317,
-    "problem": "line A C E, line B C D, line D E, line A B, line A C E, line B C D, line D E, line A B\nWhat is the measure of \\angle B?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6317.jpg"
-  },
-  {
-    "id": 6471,
-    "problem_id": 6318,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6318.jpg"
-  },
-  {
-    "id": 6472,
-    "problem_id": 6319,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6319.jpg"
-  },
-  {
-    "id": 6473,
-    "problem_id": 6320,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6320.jpg"
-  },
-  {
-    "id": 6474,
-    "problem_id": 6321,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6321.jpg"
-  },
-  {
-    "id": 6475,
-    "problem_id": 6322,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6322.jpg"
-  },
-  {
-    "id": 6476,
-    "problem_id": 6323,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6323.jpg"
-  },
-  {
-    "id": 6477,
-    "problem_id": 6324,
-    "problem": "line R S, line S T, line R Q, line Q T, line R S, line S T, line R Q, line Q T\nFind m \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6324.jpg"
-  },
-  {
-    "id": 6478,
-    "problem_id": 6325,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle KJM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6325.jpg"
-  },
-  {
-    "id": 6480,
-    "problem_id": 6326,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle KJM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6326.jpg"
-  },
-  {
-    "id": 6481,
-    "problem_id": 6327,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle KJM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6327.jpg"
-  },
-  {
-    "id": 6482,
-    "problem_id": 6328,
-    "problem": "line K L, line M L, line J M, line J K, line K L, line M L, line J M, line J K\nSolve for the measure of \\angle KJM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6328.jpg"
-  },
-  {
-    "id": 6483,
-    "problem_id": 6329,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6329.jpg"
-  },
-  {
-    "id": 6484,
-    "problem_id": 6330,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6330.jpg"
-  },
-  {
-    "id": 6485,
-    "problem_id": 6331,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6331.jpg"
-  },
-  {
-    "id": 6486,
-    "problem_id": 6332,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6332.jpg"
-  },
-  {
-    "id": 6487,
-    "problem_id": 6333,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6333.jpg"
-  },
-  {
-    "id": 6488,
-    "problem_id": 6334,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6334.jpg"
-  },
-  {
-    "id": 6489,
-    "problem_id": 6335,
-    "problem": "line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6335.jpg"
-  },
-  {
-    "id": 6490,
-    "problem_id": 6336,
-    "problem": "line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6336.jpg"
-  },
-  {
-    "id": 6491,
-    "problem_id": 6337,
-    "problem": "line A D E, line C E, line C D, line B C, line B A, line A D E, line C E, line C D, line B C, line B A\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6337.jpg"
-  },
-  {
-    "id": 6492,
-    "problem_id": 6338,
-    "problem": "line A B, line B D, line C D, line A C, line A B, line B D, line C D, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6338.jpg"
-  },
-  {
-    "id": 6493,
-    "problem_id": 6339,
-    "problem": "line D C B, line A C E, \\odot C lieson A D E B, line D C B, line A C E, \\odot C lieson A D E B\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6339.jpg"
-  },
-  {
-    "id": 6494,
-    "problem_id": 6340,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6340.jpg"
-  },
-  {
-    "id": 6495,
-    "problem_id": 6341,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6341.jpg"
-  },
-  {
-    "id": 6496,
-    "problem_id": 6342,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6342.jpg"
-  },
-  {
-    "id": 6497,
-    "problem_id": 6343,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6343.jpg"
-  },
-  {
-    "id": 6498,
-    "problem_id": 6344,
-    "problem": "line X Y Z, line X Y Z\nFind the measurement of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6344.jpg"
-  },
-  {
-    "id": 6499,
-    "problem_id": 6345,
-    "problem": "line F A D B I, line J C D, line K G D, line H E D, line F A D B I, line J C D, line K G D, line H E D\nGiven that DE \\perp DG and AB \\perp DC. If m \\angle 3 = 15, what is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6345.jpg"
-  },
-  {
-    "id": 6500,
-    "problem_id": 6346,
-    "problem": "line F A D B I, line J C D, line K G D, line H E D, line F A D B I, line J C D, line K G D, line H E D\nGiven that DE \\perp DG and AB \\perp DC. If m \\angle 3 = 15, what is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6346.jpg"
-  },
-  {
-    "id": 6501,
-    "problem_id": 6347,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6347.jpg"
-  },
-  {
-    "id": 6502,
-    "problem_id": 6348,
-    "problem": "line A D, line C D, line B C, line B A, line A D, line C D, line B C, line B A\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6348.jpg"
-  },
-  {
-    "id": 6503,
-    "problem_id": 6349,
-    "problem": "line D E, line G F, line E F, line D G, line E G, line D E, line G F, line E F, line D G, line E G\nFind the value of x for which DEFG is a rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6349.jpg"
-  },
-  {
-    "id": 6504,
-    "problem_id": 6350,
-    "problem": "line D E, line G F, line E F, line D G, line E G, line D E, line G F, line E F, line D G, line E G\nFind the value of x for which DEFG is a rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6350.jpg"
-  },
-  {
-    "id": 6505,
-    "problem_id": 6351,
-    "problem": "line D E, line G F, line E F, line D G, line E G, line D E, line G F, line E F, line D G, line E G\nFind the value of x for which DEFG is a rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6351.jpg"
-  },
-  {
-    "id": 6506,
-    "problem_id": 6352,
-    "problem": "line D E, line G F, line E F, line D G, line E G, line D E, line G F, line E F, line D G, line E G\nFind the value of x for which DEFG is a rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6352.jpg"
-  },
-  {
-    "id": 6507,
-    "problem_id": 6353,
-    "problem": "line D E, line G F, line E F, line D G, line E G, line D E, line G F, line E F, line D G, line E G\nFind the value of x for which DEFG is a rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6353.jpg"
-  },
-  {
-    "id": 6508,
-    "problem_id": 6354,
-    "problem": "line D E, line G F, line E F, line D G, line E G, line D E, line G F, line E F, line D G, line E G\nFind the value of x for which DEFG is a rectangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6354.jpg"
-  },
-  {
-    "id": 6509,
-    "problem_id": 6355,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the length of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6355.jpg"
-  },
-  {
-    "id": 6510,
-    "problem_id": 6356,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the length of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6356.jpg"
-  },
-  {
-    "id": 6511,
-    "problem_id": 6357,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find the length of CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6357.jpg"
-  },
-  {
-    "id": 6512,
-    "problem_id": 6358,
-    "problem": "line A B, line B C, line D C, line A D, line B E D, line A E C, line A B, line B C, line D C, line A D, line B E D, line A E C\nQuadrilateral ABCD is a rectangle. Find m \\angle ABD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6358.jpg"
-  },
-  {
-    "id": 6513,
-    "problem_id": 6359,
-    "problem": "line A B C, line A E D, line C D, line B E, line A B C, line A E D, line C D, line B E\nEach pair of polygons is similar. Find BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6359.jpg"
-  },
-  {
-    "id": 6514,
-    "problem_id": 6360,
-    "problem": "line A B C, line A E D, line C D, line B E, line A B C, line A E D, line C D, line B E\nEach pair of polygons is similar. Find BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6360.jpg"
-  },
-  {
-    "id": 6515,
-    "problem_id": 6361,
-    "problem": "line A B C, line A E D, line C D, line B E, line A B C, line A E D, line C D, line B E\nEach pair of polygons is similar. Find BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6361.jpg"
-  },
-  {
-    "id": 6516,
-    "problem_id": 6362,
-    "problem": "line Q T S B, line A P U Q, line Q V R C, line S R, line P S, line T V, line U T, line Q T S B, line A P U Q, line Q V R C, line S R, line P S, line T V, line U T\nGiven that UT = TV and m \\angle PQS = 42, find m \\angle VTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6362.jpg"
-  },
-  {
-    "id": 6517,
-    "problem_id": 6363,
-    "problem": "line Q T S B, line A P U Q, line Q V R C, line S R, line P S, line T V, line U T, line Q T S B, line A P U Q, line Q V R C, line S R, line P S, line T V, line U T\nGiven that UT = TV and m \\angle PQS = 42, find m \\angle VTS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6363.jpg"
-  },
-  {
-    "id": 6518,
-    "problem_id": 6364,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nExpress \\tan B as ratio.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6364.jpg"
-  },
-  {
-    "id": 6519,
-    "problem_id": 6365,
-    "problem": "line A B E, line C D E, line A C, line B D, line A B E, line C D E, line A C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6365.jpg"
-  },
-  {
-    "id": 6520,
-    "problem_id": 6366,
-    "problem": "line A B E, line C D E, line A C, line B D, line A B E, line C D E, line A C, line B D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6366.jpg"
-  },
-  {
-    "id": 6521,
-    "problem_id": 6367,
-    "problem": "line d lieson A C E F, line b lieson D E H I, line a lieson B C J K, line c lieson L J H G, line d lieson A C E F, line b lieson D E H I, line a lieson B C J K, line c lieson L J H G\nline a \\parallel line b, line c \\parallel line d, and m \\angle 4 = 57. Find the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6367.jpg"
-  },
-  {
-    "id": 6522,
-    "problem_id": 6368,
-    "problem": "line A C D, line B C E, line A E, line D E, line B A, line B D, \\odot C lieson B A E D, line A C D, line B C E, line A E, line D E, line B A, line B D, \\odot C lieson B A E D\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6368.jpg"
-  },
-  {
-    "id": 6523,
-    "problem_id": 6369,
-    "problem": "line D E, line E F, line G F, line D G, \\odot A lieson D G F E, line D E, line E F, line G F, line D G, \\odot A lieson D G F E\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6369.jpg"
-  },
-  {
-    "id": 6524,
-    "problem_id": 6370,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6370.jpg"
-  },
-  {
-    "id": 6525,
-    "problem_id": 6371,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6371.jpg"
-  },
-  {
-    "id": 6526,
-    "problem_id": 6372,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6372.jpg"
-  },
-  {
-    "id": 6527,
-    "problem_id": 6373,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6373.jpg"
-  },
-  {
-    "id": 6528,
-    "problem_id": 6374,
-    "problem": "line E D, line E A B, line C B, line C A, line D A, line E D, line E A B, line C B, line C A, line D A\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6374.jpg"
-  },
-  {
-    "id": 6529,
-    "problem_id": 6375,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6375.jpg"
-  },
-  {
-    "id": 6530,
-    "problem_id": 6376,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6376.jpg"
-  },
-  {
-    "id": 6531,
-    "problem_id": 6377,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6377.jpg"
-  },
-  {
-    "id": 6532,
-    "problem_id": 6378,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6378.jpg"
-  },
-  {
-    "id": 6533,
-    "problem_id": 6379,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is BC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6379.jpg"
-  },
-  {
-    "id": 6534,
-    "problem_id": 6380,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6380.jpg"
-  },
-  {
-    "id": 6535,
-    "problem_id": 6381,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6381.jpg"
-  },
-  {
-    "id": 6536,
-    "problem_id": 6382,
-    "problem": "line A C D, line B A, line B D, line B C, line A C D, line B A, line B D, line B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6382.jpg"
-  },
-  {
-    "id": 6537,
-    "problem_id": 6383,
-    "problem": "line S R, line Q R, line P Q, line P S, line S R, line Q R, line P Q, line P S\nPQRS is a parallelogram. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6383.jpg"
-  },
-  {
-    "id": 6538,
-    "problem_id": 6384,
-    "problem": "line S R, line Q R, line P Q, line P S, line S R, line Q R, line P Q, line P S\nPQRS is a parallelogram. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6384.jpg"
-  },
-  {
-    "id": 6539,
-    "problem_id": 6385,
-    "problem": "line A B, line D A, line D B, line D C, line B C, line A B, line D A, line D B, line D C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6385.jpg"
-  },
-  {
-    "id": 6540,
-    "problem_id": 6386,
-    "problem": "line A B, line D A, line D B, line D C, line B C, line A B, line D A, line D B, line D C, line B C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6386.jpg"
-  },
-  {
-    "id": 6542,
-    "problem_id": 6387,
-    "problem": "line A K B, \\odot K lieson A B, line A K B, \\odot K lieson A B\nWhat is the area of \\odot K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6387.jpg"
-  },
-  {
-    "id": 6543,
-    "problem_id": 6388,
-    "problem": "line A K B, \\odot K lieson A B, line A K B, \\odot K lieson A B\nWhat is the area of \\odot K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6388.jpg"
-  },
-  {
-    "id": 6544,
-    "problem_id": 6389,
-    "problem": "line A K B, \\odot K lieson A B, line A K B, \\odot K lieson A B\nWhat is the area of \\odot K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6389.jpg"
-  },
-  {
-    "id": 6545,
-    "problem_id": 6390,
-    "problem": "line A K B, \\odot K lieson A B, line A K B, \\odot K lieson A B\nWhat is the area of \\odot K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6390.jpg"
-  },
-  {
-    "id": 6546,
-    "problem_id": 6391,
-    "problem": "line A K B, \\odot K lieson A B, line A K B, \\odot K lieson A B\nWhat is the area of \\odot K?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6391.jpg"
-  },
-  {
-    "id": 6547,
-    "problem_id": 6392,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6392.jpg"
-  },
-  {
-    "id": 6548,
-    "problem_id": 6393,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6393.jpg"
-  },
-  {
-    "id": 6549,
-    "problem_id": 6394,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6394.jpg"
-  },
-  {
-    "id": 6550,
-    "problem_id": 6395,
-    "problem": "line P A B Q, line R Q, line R B, line S A, line S P, line S R, line P A B Q, line R Q, line R B, line S A, line S P, line S R\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6395.jpg"
-  },
-  {
-    "id": 6551,
-    "problem_id": 6396,
-    "problem": "line A D, line A B C, line B D, line C D, line A D, line A B C, line B D, line C D\nFind v.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6396.jpg"
-  },
-  {
-    "id": 6552,
-    "problem_id": 6397,
-    "problem": "line D A, line A B C, line D B, line D C, line D A, line A B C, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6397.jpg"
-  },
-  {
-    "id": 6553,
-    "problem_id": 6398,
-    "problem": "line D A, line A B C, line D B, line D C, line D A, line A B C, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6398.jpg"
-  },
-  {
-    "id": 6554,
-    "problem_id": 6399,
-    "problem": "line D A, line A B C, line D B, line D C, line D A, line A B C, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6399.jpg"
-  },
-  {
-    "id": 6555,
-    "problem_id": 6400,
-    "problem": "line D A, line A B C, line D B, line D C, line D A, line A B C, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6400.jpg"
-  },
-  {
-    "id": 6556,
-    "problem_id": 6401,
-    "problem": "line D A, line A B C, line D B, line D C, line D A, line A B C, line D B, line D C\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6401.jpg"
-  },
-  {
-    "id": 6557,
-    "problem_id": 6402,
-    "problem": "line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F, line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6402.jpg"
-  },
-  {
-    "id": 6558,
-    "problem_id": 6403,
-    "problem": "line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F, line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6403.jpg"
-  },
-  {
-    "id": 6559,
-    "problem_id": 6404,
-    "problem": "line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F, line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6404.jpg"
-  },
-  {
-    "id": 6560,
-    "problem_id": 6405,
-    "problem": "line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F, line A D, line A C, line B A, line B D C, line E G, line E F, line H E, line H G F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6405.jpg"
-  },
-  {
-    "id": 6562,
-    "problem_id": 6406,
-    "problem": "line C D, \\odot C lieson A B D, line C D, \\odot C lieson A B D\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6406.jpg"
-  },
-  {
-    "id": 6563,
-    "problem_id": 6407,
-    "problem": "line C D, \\odot C lieson A B D, line C D, \\odot C lieson A B D\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6407.jpg"
-  },
-  {
-    "id": 6564,
-    "problem_id": 6408,
-    "problem": "line C D, \\odot C lieson A B D, line C D, \\odot C lieson A B D\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6408.jpg"
-  },
-  {
-    "id": 6565,
-    "problem_id": 6409,
-    "problem": "line C D, \\odot C lieson A B D, line C D, \\odot C lieson A B D\nFind the length of \\widehat AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6409.jpg"
-  },
-  {
-    "id": 6566,
-    "problem_id": 6410,
-    "problem": "line P Q, line Q A S, line S R, line P A R, \\odot B lieson P S R Q, line P Q, line Q A S, line S R, line P A R, \\odot B lieson P S R Q\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6410.jpg"
-  },
-  {
-    "id": 6567,
-    "problem_id": 6411,
-    "problem": "line C D A, line A E B, line C F B, line C G, line G F, line D G, line A G, line G E, line G B, line C D A, line A E B, line C F B, line C G, line G F, line D G, line A G, line G E, line G B\nDG = 2x-7 and EG = x+4. What is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6411.jpg"
-  },
-  {
-    "id": 6568,
-    "problem_id": 6412,
-    "problem": "line C D A, line A E B, line C F B, line C G, line G F, line D G, line A G, line G E, line G B, line C D A, line A E B, line C F B, line C G, line G F, line D G, line A G, line G E, line G B\nDG = 2x-7 and EG = x+4. What is FG?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6412.jpg"
-  },
-  {
-    "id": 6569,
-    "problem_id": 6413,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6413.jpg"
-  },
-  {
-    "id": 6570,
-    "problem_id": 6414,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6414.jpg"
-  },
-  {
-    "id": 6571,
-    "problem_id": 6415,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6415.jpg"
-  },
-  {
-    "id": 6572,
-    "problem_id": 6416,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6416.jpg"
-  },
-  {
-    "id": 6573,
-    "problem_id": 6417,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6417.jpg"
-  },
-  {
-    "id": 6574,
-    "problem_id": 6418,
-    "problem": "line K L, line M L, line J L, line K J, line J M, line K L, line M L, line J L, line K J, line J M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6418.jpg"
-  },
-  {
-    "id": 6575,
-    "problem_id": 6419,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6419.jpg"
-  },
-  {
-    "id": 6576,
-    "problem_id": 6420,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of DC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6420.jpg"
-  },
-  {
-    "id": 6577,
-    "problem_id": 6421,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 3 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6421.jpg"
-  },
-  {
-    "id": 6578,
-    "problem_id": 6422,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 3 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6422.jpg"
-  },
-  {
-    "id": 6579,
-    "problem_id": 6423,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 3 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6423.jpg"
-  },
-  {
-    "id": 6580,
-    "problem_id": 6424,
-    "problem": "line A B C, line E B D, \\odot B lieson E A D C, line A B C, line E B D, \\odot B lieson E A D C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6424.jpg"
-  },
-  {
-    "id": 6581,
-    "problem_id": 6425,
-    "problem": "line A B C, line E B D, \\odot B lieson E A D C, line A B C, line E B D, \\odot B lieson E A D C\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6425.jpg"
-  },
-  {
-    "id": 6582,
-    "problem_id": 6426,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6426.jpg"
-  },
-  {
-    "id": 6583,
-    "problem_id": 6427,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6427.jpg"
-  },
-  {
-    "id": 6584,
-    "problem_id": 6428,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6428.jpg"
-  },
-  {
-    "id": 6585,
-    "problem_id": 6429,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6429.jpg"
-  },
-  {
-    "id": 6586,
-    "problem_id": 6430,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6430.jpg"
-  },
-  {
-    "id": 6587,
-    "problem_id": 6431,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle DBA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6431.jpg"
-  },
-  {
-    "id": 6588,
-    "problem_id": 6432,
-    "problem": "line A D E, line B C E, line B A, line C D, line A D E, line B C E, line B A, line C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6432.jpg"
-  },
-  {
-    "id": 6589,
-    "problem_id": 6433,
-    "problem": "line A D E, line B C E, line B A, line C D, line A D E, line B C E, line B A, line C D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6433.jpg"
-  },
-  {
-    "id": 6590,
-    "problem_id": 6434,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6434.jpg"
-  },
-  {
-    "id": 6591,
-    "problem_id": 6435,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6435.jpg"
-  },
-  {
-    "id": 6592,
-    "problem_id": 6436,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6436.jpg"
-  },
-  {
-    "id": 6593,
-    "problem_id": 6437,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6437.jpg"
-  },
-  {
-    "id": 6594,
-    "problem_id": 6438,
-    "problem": "line B C F H, line D C A, line E F G, line B C F H, line D C A, line E F G\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6438.jpg"
-  },
-  {
-    "id": 6595,
-    "problem_id": 6439,
-    "problem": "line A B, line D C, line M L, line N P, line D A, line C B, line N M, line P L, line A B, line D C, line M L, line N P, line D A, line C B, line N M, line P L\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6439.jpg"
-  },
-  {
-    "id": 6596,
-    "problem_id": 6440,
-    "problem": "line A B, line D C, line M L, line N P, line D A, line C B, line N M, line P L, line A B, line D C, line M L, line N P, line D A, line C B, line N M, line P L\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6440.jpg"
-  },
-  {
-    "id": 6597,
-    "problem_id": 6441,
-    "problem": "line A B, line D C, line M L, line N P, line D A, line C B, line N M, line P L, line A B, line D C, line M L, line N P, line D A, line C B, line N M, line P L\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6441.jpg"
-  },
-  {
-    "id": 6598,
-    "problem_id": 6442,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6442.jpg"
-  },
-  {
-    "id": 6599,
-    "problem_id": 6443,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6443.jpg"
-  },
-  {
-    "id": 6600,
-    "problem_id": 6444,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6444.jpg"
-  },
-  {
-    "id": 6601,
-    "problem_id": 6445,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6445.jpg"
-  },
-  {
-    "id": 6602,
-    "problem_id": 6446,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6446.jpg"
-  },
-  {
-    "id": 6603,
-    "problem_id": 6447,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6447.jpg"
-  },
-  {
-    "id": 6604,
-    "problem_id": 6448,
-    "problem": "line A D, line A C B, line B D, line C D, line A D, line A C B, line B D, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6448.jpg"
-  },
-  {
-    "id": 6605,
-    "problem_id": 6449,
-    "problem": "line A D, line A C B, line B D, line C D, line A D, line A C B, line B D, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6449.jpg"
-  },
-  {
-    "id": 6606,
-    "problem_id": 6450,
-    "problem": "line A D, line A C B, line B D, line C D, line A D, line A C B, line B D, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6450.jpg"
-  },
-  {
-    "id": 6607,
-    "problem_id": 6451,
-    "problem": "line A D, line A C B, line B D, line C D, line A D, line A C B, line B D, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6451.jpg"
-  },
-  {
-    "id": 6608,
-    "problem_id": 6452,
-    "problem": "line A D, line A C B, line B D, line C D, line A D, line A C B, line B D, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6452.jpg"
-  },
-  {
-    "id": 6609,
-    "problem_id": 6453,
-    "problem": "line A D, line A C B, line B D, line C D, line A D, line A C B, line B D, line C D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6453.jpg"
-  },
-  {
-    "id": 6610,
-    "problem_id": 6454,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6454.jpg"
-  },
-  {
-    "id": 6611,
-    "problem_id": 6455,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6455.jpg"
-  },
-  {
-    "id": 6612,
-    "problem_id": 6456,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6456.jpg"
-  },
-  {
-    "id": 6613,
-    "problem_id": 6457,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6457.jpg"
-  },
-  {
-    "id": 6614,
-    "problem_id": 6458,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6458.jpg"
-  },
-  {
-    "id": 6615,
-    "problem_id": 6459,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6459.jpg"
-  },
-  {
-    "id": 6616,
-    "problem_id": 6460,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6460.jpg"
-  },
-  {
-    "id": 6617,
-    "problem_id": 6461,
-    "problem": "line C B A, line D C, line D B, line D A, line C B A, line D C, line D B, line D A\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6461.jpg"
-  },
-  {
-    "id": 6618,
-    "problem_id": 6462,
-    "problem": "line Q M, line P Q, \\odot A lieson P M Q, line Q M, line P Q, \\odot A lieson P M Q\nFind the measure of \\widehat QPM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6462.jpg"
-  },
-  {
-    "id": 6619,
-    "problem_id": 6463,
-    "problem": "line Q M, line P Q, \\odot A lieson P M Q, line Q M, line P Q, \\odot A lieson P M Q\nFind the measure of \\widehat QPM.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6463.jpg"
-  },
-  {
-    "id": 6620,
-    "problem_id": 6464,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6464.jpg"
-  },
-  {
-    "id": 6621,
-    "problem_id": 6465,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6465.jpg"
-  },
-  {
-    "id": 6622,
-    "problem_id": 6466,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6466.jpg"
-  },
-  {
-    "id": 6623,
-    "problem_id": 6467,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6467.jpg"
-  },
-  {
-    "id": 6624,
-    "problem_id": 6468,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6468.jpg"
-  },
-  {
-    "id": 6625,
-    "problem_id": 6469,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6469.jpg"
-  },
-  {
-    "id": 6626,
-    "problem_id": 6470,
-    "problem": "line C D, line B D, line C B, line C D, line B D, line C B\nFind m \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6470.jpg"
-  },
-  {
-    "id": 6627,
-    "problem_id": 6471,
-    "problem": "line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N, line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6471.jpg"
-  },
-  {
-    "id": 6628,
-    "problem_id": 6472,
-    "problem": "line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N, line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6472.jpg"
-  },
-  {
-    "id": 6629,
-    "problem_id": 6473,
-    "problem": "line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N, line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6473.jpg"
-  },
-  {
-    "id": 6630,
-    "problem_id": 6474,
-    "problem": "line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N, line H G F C A, line I J K L M, line B C L P, line D F K O, line E G J N\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6474.jpg"
-  },
-  {
-    "id": 6631,
-    "problem_id": 6475,
-    "problem": "line A E, line E B D, line A B C, line D C, line A E, line E B D, line A B C, line D C\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6475.jpg"
-  },
-  {
-    "id": 6632,
-    "problem_id": 6476,
-    "problem": "line A E, line E B D, line A B C, line D C, line A E, line E B D, line A B C, line D C\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6476.jpg"
-  },
-  {
-    "id": 6633,
-    "problem_id": 6477,
-    "problem": "line A E, line E B D, line A B C, line D C, line A E, line E B D, line A B C, line D C\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6477.jpg"
-  },
-  {
-    "id": 6634,
-    "problem_id": 6478,
-    "problem": "line A E, line E B D, line A B C, line D C, line A E, line E B D, line A B C, line D C\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6478.jpg"
-  },
-  {
-    "id": 6635,
-    "problem_id": 6479,
-    "problem": "line A D, line A B, line B C, line E D C, line A D, line A B, line B C, line E D C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6479.jpg"
-  },
-  {
-    "id": 6636,
-    "problem_id": 6480,
-    "problem": "line A D, line A B, line B C, line E D C, line A D, line A B, line B C, line E D C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6480.jpg"
-  },
-  {
-    "id": 6637,
-    "problem_id": 6481,
-    "problem": "line A D, line A B, line B C, line E D C, line A D, line A B, line B C, line E D C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6481.jpg"
-  },
-  {
-    "id": 6638,
-    "problem_id": 6482,
-    "problem": "line A D, line A B, line B C, line E D C, line A D, line A B, line B C, line E D C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6482.jpg"
-  },
-  {
-    "id": 6639,
-    "problem_id": 6483,
-    "problem": "line A D, line A B, line B C, line E D C, line A D, line A B, line B C, line E D C\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6483.jpg"
-  },
-  {
-    "id": 6640,
-    "problem_id": 6484,
-    "problem": "line B C D, line A D, line A B, \\odot B lieson C A, line B C D, line A D, line A B, \\odot B lieson C A\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6484.jpg"
-  },
-  {
-    "id": 6641,
-    "problem_id": 6485,
-    "problem": "line E J G, line E H, line F G, line F J H, line F E, line G H, line E J G, line E H, line F G, line F J H, line F E, line G H\nEFGH is a parallelogram. Find w.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6485.jpg"
-  },
-  {
-    "id": 6642,
-    "problem_id": 6486,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6486.jpg"
-  },
-  {
-    "id": 6643,
-    "problem_id": 6487,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6487.jpg"
-  },
-  {
-    "id": 6644,
-    "problem_id": 6488,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6488.jpg"
-  },
-  {
-    "id": 6645,
-    "problem_id": 6489,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6489.jpg"
-  },
-  {
-    "id": 6646,
-    "problem_id": 6490,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6490.jpg"
-  },
-  {
-    "id": 6647,
-    "problem_id": 6491,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6491.jpg"
-  },
-  {
-    "id": 6648,
-    "problem_id": 6492,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6492.jpg"
-  },
-  {
-    "id": 6649,
-    "problem_id": 6493,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6493.jpg"
-  },
-  {
-    "id": 6650,
-    "problem_id": 6494,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind EF in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6494.jpg"
-  },
-  {
-    "id": 6651,
-    "problem_id": 6495,
-    "problem": "line A D, line D F C, line B C, line A E B, line E F, line A D, line D F C, line B C, line A E B, line E F\nFind EF in the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6495.jpg"
-  },
-  {
-    "id": 6652,
-    "problem_id": 6496,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind the measure of \\widehat YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6496.jpg"
-  },
-  {
-    "id": 6653,
-    "problem_id": 6497,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind the measure of \\widehat YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6497.jpg"
-  },
-  {
-    "id": 6654,
-    "problem_id": 6498,
-    "problem": "line Y W, line Y Z, \\odot A lieson W Z Y, line Y W, line Y Z, \\odot A lieson W Z Y\nFind the measure of \\widehat YZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6498.jpg"
-  },
-  {
-    "id": 6655,
-    "problem_id": 6499,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6499.jpg"
-  },
-  {
-    "id": 6656,
-    "problem_id": 6500,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6500.jpg"
-  },
-  {
-    "id": 6657,
-    "problem_id": 6501,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6501.jpg"
-  },
-  {
-    "id": 6658,
-    "problem_id": 6502,
-    "problem": "line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z, line W P Y, line Y Z, line X P Z, line X Y, line X W, line W Z\nUse \\parallelogram WXYZ to find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6502.jpg"
-  },
-  {
-    "id": 6659,
-    "problem_id": 6503,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6503.jpg"
-  },
-  {
-    "id": 6660,
-    "problem_id": 6504,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6504.jpg"
-  },
-  {
-    "id": 6661,
-    "problem_id": 6505,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6505.jpg"
-  },
-  {
-    "id": 6662,
-    "problem_id": 6506,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6506.jpg"
-  },
-  {
-    "id": 6663,
-    "problem_id": 6507,
-    "problem": "line B C, line A B, line A C, line B C, line A B, line A C\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6507.jpg"
-  },
-  {
-    "id": 6664,
-    "problem_id": 6508,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6508.jpg"
-  },
-  {
-    "id": 6665,
-    "problem_id": 6509,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6509.jpg"
-  },
-  {
-    "id": 6666,
-    "problem_id": 6510,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6510.jpg"
-  },
-  {
-    "id": 6667,
-    "problem_id": 6511,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6511.jpg"
-  },
-  {
-    "id": 6668,
-    "problem_id": 6512,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6512.jpg"
-  },
-  {
-    "id": 6669,
-    "problem_id": 6513,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6513.jpg"
-  },
-  {
-    "id": 6670,
-    "problem_id": 6514,
-    "problem": "line A B C D, line A B C D\nFind the length of CA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6514.jpg"
-  },
-  {
-    "id": 6671,
-    "problem_id": 6515,
-    "problem": "line A D H, line B D E F, line C E G, line A D H, line B D E F, line C E G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6515.jpg"
-  },
-  {
-    "id": 6672,
-    "problem_id": 6516,
-    "problem": "line A D H, line B D E F, line C E G, line A D H, line B D E F, line C E G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6516.jpg"
-  },
-  {
-    "id": 6673,
-    "problem_id": 6517,
-    "problem": "line A D H, line B D E F, line C E G, line A D H, line B D E F, line C E G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6517.jpg"
-  },
-  {
-    "id": 6674,
-    "problem_id": 6518,
-    "problem": "line A D H, line B D E F, line C E G, line A D H, line B D E F, line C E G\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6518.jpg"
-  },
-  {
-    "id": 6675,
-    "problem_id": 6519,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6519.jpg"
-  },
-  {
-    "id": 6676,
-    "problem_id": 6520,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6520.jpg"
-  },
-  {
-    "id": 6677,
-    "problem_id": 6521,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6521.jpg"
-  },
-  {
-    "id": 6678,
-    "problem_id": 6522,
-    "problem": "line B A, line C A, line B C, line B A, line C A, line B C\nFind the perimeter of triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6522.jpg"
-  },
-  {
-    "id": 6679,
-    "problem_id": 6523,
-    "problem": "line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B, line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6523.jpg"
-  },
-  {
-    "id": 6680,
-    "problem_id": 6524,
-    "problem": "line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B, line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6524.jpg"
-  },
-  {
-    "id": 6681,
-    "problem_id": 6525,
-    "problem": "line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B, line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6525.jpg"
-  },
-  {
-    "id": 6682,
-    "problem_id": 6526,
-    "problem": "line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B, line E G, line F G, line C F, line A C, line A B, line B E, line D E, \\odot D lieson A C F G E B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6526.jpg"
-  },
-  {
-    "id": 6683,
-    "problem_id": 6527,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6527.jpg"
-  },
-  {
-    "id": 6684,
-    "problem_id": 6528,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6528.jpg"
-  },
-  {
-    "id": 6685,
-    "problem_id": 6529,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6529.jpg"
-  },
-  {
-    "id": 6686,
-    "problem_id": 6530,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6530.jpg"
-  },
-  {
-    "id": 6687,
-    "problem_id": 6531,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6531.jpg"
-  },
-  {
-    "id": 6688,
-    "problem_id": 6532,
-    "problem": "line A B, line A C, line C B, line A B, line A C, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6532.jpg"
-  },
-  {
-    "id": 6689,
-    "problem_id": 6533,
-    "problem": "line M A N, line L B N, line L C M, \\odot P lieson C A B, line M A N, line L B N, line L C M, \\odot P lieson C A B\n\\odot P is inscribed in equilateral triangle LMN. What is the radius of \\odot P?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6533.jpg"
-  },
-  {
-    "id": 6690,
-    "problem_id": 6534,
-    "problem": "line M A N, line L B N, line L C M, \\odot P lieson C A B, line M A N, line L B N, line L C M, \\odot P lieson C A B\n\\odot P is inscribed in equilateral triangle LMN. What is the radius of \\odot P?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6534.jpg"
-  },
-  {
-    "id": 6691,
-    "problem_id": 6535,
-    "problem": "line A B, line B D, line D H, line F G H, line C F, line A C, line E G, line A B, line B D, line D H, line F G H, line C F, line A C, line E G\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6535.jpg"
-  },
-  {
-    "id": 6692,
-    "problem_id": 6536,
-    "problem": "line A B, line B D, line D H, line F G H, line C F, line A C, line E G, line A B, line B D, line D H, line F G H, line C F, line A C, line E G\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6536.jpg"
-  },
-  {
-    "id": 6693,
-    "problem_id": 6537,
-    "problem": "line A B, line B D, line D H, line F G H, line C F, line A C, line E G, line A B, line B D, line D H, line F G H, line C F, line A C, line E G\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6537.jpg"
-  },
-  {
-    "id": 6694,
-    "problem_id": 6538,
-    "problem": "line A B, line B D, line D H, line F G H, line C F, line A C, line E G, line A B, line B D, line D H, line F G H, line C F, line A C, line E G\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6538.jpg"
-  },
-  {
-    "id": 6695,
-    "problem_id": 6539,
-    "problem": "line A B, line B D, line D H, line F G H, line C F, line A C, line E G, line A B, line B D, line D H, line F G H, line C F, line A C, line E G\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6539.jpg"
-  },
-  {
-    "id": 6696,
-    "problem_id": 6540,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6540.jpg"
-  },
-  {
-    "id": 6697,
-    "problem_id": 6541,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6541.jpg"
-  },
-  {
-    "id": 6698,
-    "problem_id": 6542,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6542.jpg"
-  },
-  {
-    "id": 6699,
-    "problem_id": 6543,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6543.jpg"
-  },
-  {
-    "id": 6700,
-    "problem_id": 6544,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6544.jpg"
-  },
-  {
-    "id": 6701,
-    "problem_id": 6545,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6545.jpg"
-  },
-  {
-    "id": 6702,
-    "problem_id": 6546,
-    "problem": "line P Q R, line P Q R\nFind the measurement of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6546.jpg"
-  },
-  {
-    "id": 6703,
-    "problem_id": 6547,
-    "problem": "line B A, line A C E, line D E, line B D, line B C, line B A, line A C E, line D E, line B D, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6547.jpg"
-  },
-  {
-    "id": 6704,
-    "problem_id": 6548,
-    "problem": "line B A, line A C E, line D E, line B D, line B C, line B A, line A C E, line D E, line B D, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6548.jpg"
-  },
-  {
-    "id": 6705,
-    "problem_id": 6549,
-    "problem": "line B A, line A C E, line D E, line B D, line B C, line B A, line A C E, line D E, line B D, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6549.jpg"
-  },
-  {
-    "id": 6706,
-    "problem_id": 6550,
-    "problem": "line B A, line A C E, line D E, line B D, line B C, line B A, line A C E, line D E, line B D, line B C\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6550.jpg"
-  },
-  {
-    "id": 6707,
-    "problem_id": 6551,
-    "problem": "line R S, line R A T, line S T, \\odot R lieson A S, line R S, line R A T, line S T, \\odot R lieson A S\nThe segment is tangent to the circle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6551.jpg"
-  },
-  {
-    "id": 6708,
-    "problem_id": 6552,
-    "problem": "line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B, line C B A, line A D F, line C E F, line C D, line B D, \\odot G lieson C E D B\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6552.jpg"
-  },
-  {
-    "id": 6709,
-    "problem_id": 6553,
-    "problem": "line B A, line D A, line C B, line C D E, line B A, line D A, line C B, line C D E\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6553.jpg"
-  },
-  {
-    "id": 6710,
-    "problem_id": 6554,
-    "problem": "line B A, line D A, line C B, line C D E, line B A, line D A, line C B, line C D E\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6554.jpg"
-  },
-  {
-    "id": 6711,
-    "problem_id": 6555,
-    "problem": "line B A, line D A, line C B, line C D E, line B A, line D A, line C B, line C D E\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6555.jpg"
-  },
-  {
-    "id": 6712,
-    "problem_id": 6556,
-    "problem": "line B A, line D A, line C B, line C D E, line B A, line D A, line C B, line C D E\nFind the value of the variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6556.jpg"
-  },
-  {
-    "id": 6713,
-    "problem_id": 6557,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6557.jpg"
-  },
-  {
-    "id": 6714,
-    "problem_id": 6558,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6558.jpg"
-  },
-  {
-    "id": 6715,
-    "problem_id": 6559,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6559.jpg"
-  },
-  {
-    "id": 6716,
-    "problem_id": 6560,
-    "problem": "line B C D, line A C, line A B, line B C D, line A C, line A B\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6560.jpg"
-  },
-  {
-    "id": 6717,
-    "problem_id": 6561,
-    "problem": "line A F, line B E, line C A, line E D, line B D, line C F, line A F, line B E, line C A, line E D, line B D, line C F\n\\triangle ACF \\sim \\triangle EDB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6561.jpg"
-  },
-  {
-    "id": 6718,
-    "problem_id": 6562,
-    "problem": "line A F, line B E, line C A, line E D, line B D, line C F, line A F, line B E, line C A, line E D, line B D, line C F\n\\triangle ACF \\sim \\triangle EDB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6562.jpg"
-  },
-  {
-    "id": 6719,
-    "problem_id": 6563,
-    "problem": "line A F, line B E, line C A, line E D, line B D, line C F, line A F, line B E, line C A, line E D, line B D, line C F\n\\triangle ACF \\sim \\triangle EDB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6563.jpg"
-  },
-  {
-    "id": 6720,
-    "problem_id": 6564,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind \\tan A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6564.jpg"
-  },
-  {
-    "id": 6721,
-    "problem_id": 6565,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind \\tan A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6565.jpg"
-  },
-  {
-    "id": 6722,
-    "problem_id": 6566,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind \\tan A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6566.jpg"
-  },
-  {
-    "id": 6723,
-    "problem_id": 6567,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind \\tan A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6567.jpg"
-  },
-  {
-    "id": 6724,
-    "problem_id": 6568,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6568.jpg"
-  },
-  {
-    "id": 6725,
-    "problem_id": 6569,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6569.jpg"
-  },
-  {
-    "id": 6726,
-    "problem_id": 6570,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6570.jpg"
-  },
-  {
-    "id": 6727,
-    "problem_id": 6571,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6571.jpg"
-  },
-  {
-    "id": 6728,
-    "problem_id": 6572,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6572.jpg"
-  },
-  {
-    "id": 6729,
-    "problem_id": 6573,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6573.jpg"
-  },
-  {
-    "id": 6730,
-    "problem_id": 6574,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6574.jpg"
-  },
-  {
-    "id": 6731,
-    "problem_id": 6575,
-    "problem": "line A C, line B C, line A B, \\odot B lieson C A, line A C, line B C, line A B, \\odot B lieson C A\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6575.jpg"
-  },
-  {
-    "id": 6732,
-    "problem_id": 6576,
-    "problem": "line A C, line B C, line A B, \\odot B lieson C A, line A C, line B C, line A B, \\odot B lieson C A\nFind the shaded area.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6576.jpg"
-  },
-  {
-    "id": 6733,
-    "problem_id": 6577,
-    "problem": "line D P C, line B N C, line A M B, line A L D, \\odot Q lieson M L P N, line D P C, line B N C, line A M B, line A L D, \\odot Q lieson M L P N\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6577.jpg"
-  },
-  {
-    "id": 6734,
-    "problem_id": 6578,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6578.jpg"
-  },
-  {
-    "id": 6735,
-    "problem_id": 6579,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6579.jpg"
-  },
-  {
-    "id": 6736,
-    "problem_id": 6580,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6580.jpg"
-  },
-  {
-    "id": 6737,
-    "problem_id": 6581,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6581.jpg"
-  },
-  {
-    "id": 6738,
-    "problem_id": 6582,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6582.jpg"
-  },
-  {
-    "id": 6739,
-    "problem_id": 6583,
-    "problem": "line D A, line A B C, line D B, line D C, line D A, line A B C, line D B, line D C\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6583.jpg"
-  },
-  {
-    "id": 6740,
-    "problem_id": 6584,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6584.jpg"
-  },
-  {
-    "id": 6741,
-    "problem_id": 6585,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6585.jpg"
-  },
-  {
-    "id": 6742,
-    "problem_id": 6586,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6586.jpg"
-  },
-  {
-    "id": 6743,
-    "problem_id": 6587,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6587.jpg"
-  },
-  {
-    "id": 6744,
-    "problem_id": 6588,
-    "problem": "line A C, line C D, line B D, line A B, line A F D, line B F, line A C, line C D, line B D, line A B, line A F D, line B F\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6588.jpg"
-  },
-  {
-    "id": 6745,
-    "problem_id": 6589,
-    "problem": "line A Y Z, line X Y, line X W, line C W Z, line B X Z, line A Y Z, line X Y, line X W, line C W Z, line B X Z\nFind XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6589.jpg"
-  },
-  {
-    "id": 6746,
-    "problem_id": 6590,
-    "problem": "line A Y Z, line X Y, line X W, line C W Z, line B X Z, line A Y Z, line X Y, line X W, line C W Z, line B X Z\nFind XY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6590.jpg"
-  },
-  {
-    "id": 6747,
-    "problem_id": 6591,
-    "problem": "line A B, line B C, \\odot D lieson A C B, line A B, line B C, \\odot D lieson A C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6591.jpg"
-  },
-  {
-    "id": 6748,
-    "problem_id": 6592,
-    "problem": "line A B, line B C, \\odot D lieson A C B, line A B, line B C, \\odot D lieson A C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6592.jpg"
-  },
-  {
-    "id": 6749,
-    "problem_id": 6593,
-    "problem": "line A B, line B C, \\odot D lieson A C B, line A B, line B C, \\odot D lieson A C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6593.jpg"
-  },
-  {
-    "id": 6750,
-    "problem_id": 6594,
-    "problem": "line D E F, line H G F, line D J G, line E J H, \\odot A lieson D H G E, line D E F, line H G F, line D J G, line E J H, \\odot A lieson D H G E\nFind m \\widehat GE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6594.jpg"
-  },
-  {
-    "id": 6751,
-    "problem_id": 6595,
-    "problem": "line B Q R, line C P R, line R S A, line B Q R, line C P R, line R S A\nRQ bisects \\angle PRS. What is the measure of \\angle QRS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6595.jpg"
-  },
-  {
-    "id": 6752,
-    "problem_id": 6596,
-    "problem": "line M N, line M P T, line N Q T, line P Q, line M N, line M P T, line N Q T, line P Q\nIf MN \\parallel PQ, use a proportion to find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6596.jpg"
-  },
-  {
-    "id": 6753,
-    "problem_id": 6597,
-    "problem": "line M N, line M P T, line N Q T, line P Q, line M N, line M P T, line N Q T, line P Q\nIf MN \\parallel PQ, use a proportion to find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6597.jpg"
-  },
-  {
-    "id": 6754,
-    "problem_id": 6598,
-    "problem": "line M N, line M P T, line N Q T, line P Q, line M N, line M P T, line N Q T, line P Q\nIf MN \\parallel PQ, use a proportion to find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6598.jpg"
-  },
-  {
-    "id": 6755,
-    "problem_id": 6599,
-    "problem": "line M N, line M P T, line N Q T, line P Q, line M N, line M P T, line N Q T, line P Q\nIf MN \\parallel PQ, use a proportion to find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6599.jpg"
-  },
-  {
-    "id": 6756,
-    "problem_id": 6600,
-    "problem": "line A B C, line D B, line D A, line A B C, line D B, line D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6600.jpg"
-  },
-  {
-    "id": 6757,
-    "problem_id": 6601,
-    "problem": "line A B C, line D B, line D A, line A B C, line D B, line D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6601.jpg"
-  },
-  {
-    "id": 6758,
-    "problem_id": 6602,
-    "problem": "line A B C, line D B, line D A, line A B C, line D B, line D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6602.jpg"
-  },
-  {
-    "id": 6759,
-    "problem_id": 6603,
-    "problem": "line A B C, line D B, line D A, line A B C, line D B, line D A\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6603.jpg"
-  },
-  {
-    "id": 6760,
-    "problem_id": 6604,
-    "problem": "line A B C, line D C, line A E D, line E B, line A B C, line D C, line A E D, line E B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6604.jpg"
-  },
-  {
-    "id": 6761,
-    "problem_id": 6605,
-    "problem": "line A B C, line D C, line A E D, line E B, line A B C, line D C, line A E D, line E B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6605.jpg"
-  },
-  {
-    "id": 6762,
-    "problem_id": 6606,
-    "problem": "line A B C, line D C, line A E D, line E B, line A B C, line D C, line A E D, line E B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6606.jpg"
-  },
-  {
-    "id": 6763,
-    "problem_id": 6607,
-    "problem": "line A B C, line D C, line A E D, line E B, line A B C, line D C, line A E D, line E B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6607.jpg"
-  },
-  {
-    "id": 6764,
-    "problem_id": 6608,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6608.jpg"
-  },
-  {
-    "id": 6765,
-    "problem_id": 6609,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6609.jpg"
-  },
-  {
-    "id": 6766,
-    "problem_id": 6610,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6610.jpg"
-  },
-  {
-    "id": 6767,
-    "problem_id": 6611,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6611.jpg"
-  },
-  {
-    "id": 6768,
-    "problem_id": 6612,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6612.jpg"
-  },
-  {
-    "id": 6769,
-    "problem_id": 6613,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6613.jpg"
-  },
-  {
-    "id": 6770,
-    "problem_id": 6614,
-    "problem": "line D B, line D C, line A B C, line D B, line D C, line A B C\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6614.jpg"
-  },
-  {
-    "id": 6771,
-    "problem_id": 6615,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6615.jpg"
-  },
-  {
-    "id": 6772,
-    "problem_id": 6616,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6616.jpg"
-  },
-  {
-    "id": 6773,
-    "problem_id": 6617,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6617.jpg"
-  },
-  {
-    "id": 6774,
-    "problem_id": 6618,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6618.jpg"
-  },
-  {
-    "id": 6775,
-    "problem_id": 6619,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6619.jpg"
-  },
-  {
-    "id": 6776,
-    "problem_id": 6620,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6620.jpg"
-  },
-  {
-    "id": 6777,
-    "problem_id": 6621,
-    "problem": "line A C E, line D C, line B C F, line A C E, line D C, line B C F\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6621.jpg"
-  },
-  {
-    "id": 6778,
-    "problem_id": 6622,
-    "problem": "line A C E, line D C B, line D E, line A B, line A D, line B E, line A C E, line D C B, line D E, line A B, line A D, line B E\nFind the measure of \\angle 3 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6622.jpg"
-  },
-  {
-    "id": 6779,
-    "problem_id": 6623,
-    "problem": "line A C E, line D C B, line D E, line A B, line A D, line B E, line A C E, line D C B, line D E, line A B, line A D, line B E\nFind the measure of \\angle 3 in special parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6623.jpg"
-  },
-  {
-    "id": 6780,
-    "problem_id": 6624,
-    "problem": "line C Y A, line B X A, line B C, line X Y, line C Y A, line B X A, line B C, line X Y\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6624.jpg"
-  },
-  {
-    "id": 6781,
-    "problem_id": 6625,
-    "problem": "line C Y A, line B X A, line B C, line X Y, line C Y A, line B X A, line B C, line X Y\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6625.jpg"
-  },
-  {
-    "id": 6782,
-    "problem_id": 6626,
-    "problem": "line C Y A, line B X A, line B C, line X Y, line C Y A, line B X A, line B C, line X Y\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6626.jpg"
-  },
-  {
-    "id": 6783,
-    "problem_id": 6627,
-    "problem": "line C Y A, line B X A, line B C, line X Y, line C Y A, line B X A, line B C, line X Y\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6627.jpg"
-  },
-  {
-    "id": 6784,
-    "problem_id": 6628,
-    "problem": "line C Y A, line B X A, line B C, line X Y, line C Y A, line B X A, line B C, line X Y\nFind AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6628.jpg"
-  },
-  {
-    "id": 6785,
-    "problem_id": 6629,
-    "problem": "line B C D, line E D, line A E, line A B, line E C, line B C D, line E D, line A E, line A B, line E C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6629.jpg"
-  },
-  {
-    "id": 6786,
-    "problem_id": 6630,
-    "problem": "line B C D, line E D, line A E, line A B, line E C, line B C D, line E D, line A E, line A B, line E C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6630.jpg"
-  },
-  {
-    "id": 6787,
-    "problem_id": 6631,
-    "problem": "line B C D, line E D, line A E, line A B, line E C, line B C D, line E D, line A E, line A B, line E C\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6631.jpg"
-  },
-  {
-    "id": 6788,
-    "problem_id": 6632,
-    "problem": "line H G F E D, line I J K L M, line C E L N, line B F K O, line A G J P, line H G F E D, line I J K L M, line C E L N, line B F K O, line A G J P\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6632.jpg"
-  },
-  {
-    "id": 6789,
-    "problem_id": 6633,
-    "problem": "line H G F E D, line I J K L M, line C E L N, line B F K O, line A G J P, line H G F E D, line I J K L M, line C E L N, line B F K O, line A G J P\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6633.jpg"
-  },
-  {
-    "id": 6790,
-    "problem_id": 6634,
-    "problem": "line H G F E D, line I J K L M, line C E L N, line B F K O, line A G J P, line H G F E D, line I J K L M, line C E L N, line B F K O, line A G J P\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6634.jpg"
-  },
-  {
-    "id": 6791,
-    "problem_id": 6635,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nWhat is RP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6635.jpg"
-  },
-  {
-    "id": 6792,
-    "problem_id": 6636,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6636.jpg"
-  },
-  {
-    "id": 6793,
-    "problem_id": 6637,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6637.jpg"
-  },
-  {
-    "id": 6794,
-    "problem_id": 6638,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6638.jpg"
-  },
-  {
-    "id": 6795,
-    "problem_id": 6639,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6639.jpg"
-  },
-  {
-    "id": 6796,
-    "problem_id": 6640,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6640.jpg"
-  },
-  {
-    "id": 6797,
-    "problem_id": 6641,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6641.jpg"
-  },
-  {
-    "id": 6798,
-    "problem_id": 6642,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind x so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6642.jpg"
-  },
-  {
-    "id": 6800,
-    "problem_id": 6643,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is area of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6643.jpg"
-  },
-  {
-    "id": 6801,
-    "problem_id": 6644,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is area of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6644.jpg"
-  },
-  {
-    "id": 6803,
-    "problem_id": 6645,
-    "problem": "line F D A, line C B, line D E, line A E B, line D C, line F C, line F D A, line C B, line D E, line A E B, line D C, line F C\nFor \\parallelogram ABCD, what is area of ABCD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6645.jpg"
-  },
-  {
-    "id": 6804,
-    "problem_id": 6646,
-    "problem": "line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D, line A B, line G B H, line I E H, line F C G, line F D I, \\odot A lieson C B E D\nFind the area of the square. Assume that the polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6646.jpg"
-  },
-  {
-    "id": 6805,
-    "problem_id": 6647,
-    "problem": "line P Q, line P M, line Q M, line P Q, line P M, line Q M\nWhat is the measure of \\angle M?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6647.jpg"
-  },
-  {
-    "id": 6806,
-    "problem_id": 6648,
-    "problem": "line P Q, line P M, line Q M, line P Q, line P M, line Q M\nWhat is the measure of \\angle M?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6648.jpg"
-  },
-  {
-    "id": 6807,
-    "problem_id": 6649,
-    "problem": "line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W, line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W\nIf quadrilateral ABCD \\sim quadrilateral WXYZ. What is the perimeter of WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6649.jpg"
-  },
-  {
-    "id": 6808,
-    "problem_id": 6650,
-    "problem": "line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W, line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W\nIf quadrilateral ABCD \\sim quadrilateral WXYZ. What is the perimeter of WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6650.jpg"
-  },
-  {
-    "id": 6809,
-    "problem_id": 6651,
-    "problem": "line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W, line A D, line W Z, line X Y, line B C, line Y Z, line C D, line B A, line X W\nIf quadrilateral ABCD \\sim quadrilateral WXYZ. What is the perimeter of WXYZ?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6651.jpg"
-  },
-  {
-    "id": 6810,
-    "problem_id": 6652,
-    "problem": "line R S T, line R V U, line T U, line S V, line R S T, line R V U, line T U, line S V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6652.jpg"
-  },
-  {
-    "id": 6811,
-    "problem_id": 6653,
-    "problem": "line R S T, line R V U, line T U, line S V, line R S T, line R V U, line T U, line S V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6653.jpg"
-  },
-  {
-    "id": 6812,
-    "problem_id": 6654,
-    "problem": "line R S T, line R V U, line T U, line S V, line R S T, line R V U, line T U, line S V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6654.jpg"
-  },
-  {
-    "id": 6813,
-    "problem_id": 6655,
-    "problem": "line R S T, line R V U, line T U, line S V, line R S T, line R V U, line T U, line S V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6655.jpg"
-  },
-  {
-    "id": 6814,
-    "problem_id": 6656,
-    "problem": "line R S T, line R V U, line T U, line S V, line R S T, line R V U, line T U, line S V\nFind ST.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6656.jpg"
-  },
-  {
-    "id": 6815,
-    "problem_id": 6657,
-    "problem": "line K B M, line J B L, \\odot A lieson J M L K, line K B M, line J B L, \\odot A lieson J M L K\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6657.jpg"
-  },
-  {
-    "id": 6816,
-    "problem_id": 6658,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable x for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6658.jpg"
-  },
-  {
-    "id": 6817,
-    "problem_id": 6659,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable x for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6659.jpg"
-  },
-  {
-    "id": 6818,
-    "problem_id": 6660,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable x for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6660.jpg"
-  },
-  {
-    "id": 6819,
-    "problem_id": 6661,
-    "problem": "line C D, line B A, line A D, line B C, line C D, line B A, line A D, line B C\nFind the value of variable x for which ABCD must be a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6661.jpg"
-  },
-  {
-    "id": 6820,
-    "problem_id": 6662,
-    "problem": "line A D F G E B, line C B, line C E, line C G, line C F, line C D, line A C, line A D F G E B, line C B, line C E, line C G, line C F, line C D, line A C\n\\triangle ABC is isosceles, \\triangle DCE is equilateral, and \\triangle FCG is isosceles. Find the measure of the \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6662.jpg"
-  },
-  {
-    "id": 6821,
-    "problem_id": 6663,
-    "problem": "line B C, line P C, line B A P, \\odot P lieson A C, line B C, line P C, line B A P, \\odot P lieson A C\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6663.jpg"
-  },
-  {
-    "id": 6822,
-    "problem_id": 6664,
-    "problem": "line B C, line P C, line B A P, \\odot P lieson A C, line B C, line P C, line B A P, \\odot P lieson A C\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6664.jpg"
-  },
-  {
-    "id": 6823,
-    "problem_id": 6665,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6665.jpg"
-  },
-  {
-    "id": 6824,
-    "problem_id": 6666,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6666.jpg"
-  },
-  {
-    "id": 6825,
-    "problem_id": 6667,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6667.jpg"
-  },
-  {
-    "id": 6826,
-    "problem_id": 6668,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6668.jpg"
-  },
-  {
-    "id": 6827,
-    "problem_id": 6669,
-    "problem": "line C B, line B D, line A C, line A B, line C D, line C B, line B D, line A C, line A B, line C D\nFind the measure of \\angle 1 for the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6669.jpg"
-  },
-  {
-    "id": 6828,
-    "problem_id": 6670,
-    "problem": "line E F, line F D G, line H G, line E C H, line C D, line E F, line F D G, line H G, line E C H, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6670.jpg"
-  },
-  {
-    "id": 6829,
-    "problem_id": 6671,
-    "problem": "line E F, line F D G, line H G, line E C H, line C D, line E F, line F D G, line H G, line E C H, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6671.jpg"
-  },
-  {
-    "id": 6830,
-    "problem_id": 6672,
-    "problem": "line E F, line F D G, line H G, line E C H, line C D, line E F, line F D G, line H G, line E C H, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6672.jpg"
-  },
-  {
-    "id": 6831,
-    "problem_id": 6673,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6673.jpg"
-  },
-  {
-    "id": 6832,
-    "problem_id": 6674,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6674.jpg"
-  },
-  {
-    "id": 6833,
-    "problem_id": 6675,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6675.jpg"
-  },
-  {
-    "id": 6834,
-    "problem_id": 6676,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6676.jpg"
-  },
-  {
-    "id": 6835,
-    "problem_id": 6677,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6677.jpg"
-  },
-  {
-    "id": 6836,
-    "problem_id": 6678,
-    "problem": "line C A, line A B, line C B, line C A, line A B, line C B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6678.jpg"
-  },
-  {
-    "id": 6837,
-    "problem_id": 6679,
-    "problem": "line A C F H, line p lieson D C B, line q lieson G F E, line A C F H, line p lieson D C B, line q lieson G F E\nFind x so that line p \\parallel line q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6679.jpg"
-  },
-  {
-    "id": 6838,
-    "problem_id": 6680,
-    "problem": "line A C F H, line p lieson D C B, line q lieson G F E, line A C F H, line p lieson D C B, line q lieson G F E\nFind x so that line p \\parallel line q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6680.jpg"
-  },
-  {
-    "id": 6839,
-    "problem_id": 6681,
-    "problem": "line A C F H, line p lieson D C B, line q lieson G F E, line A C F H, line p lieson D C B, line q lieson G F E\nFind x so that line p \\parallel line q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6681.jpg"
-  },
-  {
-    "id": 6840,
-    "problem_id": 6682,
-    "problem": "line A C F H, line p lieson D C B, line q lieson G F E, line A C F H, line p lieson D C B, line q lieson G F E\nFind x so that line p \\parallel line q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6682.jpg"
-  },
-  {
-    "id": 6841,
-    "problem_id": 6683,
-    "problem": "line A B D, line E B C, line A B D, line E B C\nm \\angle 9 = 2x-4, m \\angle 10 = 2x+4. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6683.jpg"
-  },
-  {
-    "id": 6842,
-    "problem_id": 6684,
-    "problem": "line A B D, line E B C, line A B D, line E B C\nm \\angle 9 = 2x-4, m \\angle 10 = 2x+4. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6684.jpg"
-  },
-  {
-    "id": 6843,
-    "problem_id": 6685,
-    "problem": "line A B D, line E B C, line A B D, line E B C\nm \\angle 9 = 2x-4, m \\angle 10 = 2x+4. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6685.jpg"
-  },
-  {
-    "id": 6844,
-    "problem_id": 6686,
-    "problem": "line L N, line L O M, line N M, line O N, line L N, line L O M, line N M, line O N\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6686.jpg"
-  },
-  {
-    "id": 6845,
-    "problem_id": 6687,
-    "problem": "line L N, line L O M, line N M, line O N, line L N, line L O M, line N M, line O N\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6687.jpg"
-  },
-  {
-    "id": 6846,
-    "problem_id": 6688,
-    "problem": "line L N, line L O M, line N M, line O N, line L N, line L O M, line N M, line O N\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6688.jpg"
-  },
-  {
-    "id": 6847,
-    "problem_id": 6689,
-    "problem": "line B A, line A C, line E C, line B E, line B D C, line A D E, line B A, line A C, line E C, line B E, line B D C, line A D E\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6689.jpg"
-  },
-  {
-    "id": 6848,
-    "problem_id": 6690,
-    "problem": "line B A, line A C, line E C, line B E, line B D C, line A D E, line B A, line A C, line E C, line B E, line B D C, line A D E\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6690.jpg"
-  },
-  {
-    "id": 6849,
-    "problem_id": 6691,
-    "problem": "line B A, line A C, line E C, line B E, line B D C, line A D E, line B A, line A C, line E C, line B E, line B D C, line A D E\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6691.jpg"
-  },
-  {
-    "id": 6850,
-    "problem_id": 6692,
-    "problem": "line B A, line A C, line E C, line B E, line B D C, line A D E, line B A, line A C, line E C, line B E, line B D C, line A D E\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6692.jpg"
-  },
-  {
-    "id": 6851,
-    "problem_id": 6693,
-    "problem": "line B A, line A C, line E C, line B E, line B D C, line A D E, line B A, line A C, line E C, line B E, line B D C, line A D E\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6693.jpg"
-  },
-  {
-    "id": 6852,
-    "problem_id": 6694,
-    "problem": "line B A, line A C, line E C, line B E, line B D C, line A D E, line B A, line A C, line E C, line B E, line B D C, line A D E\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6694.jpg"
-  },
-  {
-    "id": 6853,
-    "problem_id": 6695,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6695.jpg"
-  },
-  {
-    "id": 6854,
-    "problem_id": 6696,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6696.jpg"
-  },
-  {
-    "id": 6855,
-    "problem_id": 6697,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6697.jpg"
-  },
-  {
-    "id": 6856,
-    "problem_id": 6698,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6698.jpg"
-  },
-  {
-    "id": 6857,
-    "problem_id": 6699,
-    "problem": "line R A, line P A, line A Q, \\odot A lieson R Q P, line R A, line P A, line A Q, \\odot A lieson R Q P\nFind the value of variable x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6699.jpg"
-  },
-  {
-    "id": 6858,
-    "problem_id": 6700,
-    "problem": "line A D F, line C F, line F E, line C D E, line B A, line B C, line A D F, line C F, line F E, line C D E, line B A, line B C\nFind the area of the shaded figure in square inches.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6700.jpg"
-  },
-  {
-    "id": 6859,
-    "problem_id": 6701,
-    "problem": "line A D F, line C F, line F E, line C D E, line B A, line B C, line A D F, line C F, line F E, line C D E, line B A, line B C\nFind the area of the shaded figure in square inches.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6701.jpg"
-  },
-  {
-    "id": 6860,
-    "problem_id": 6702,
-    "problem": "line A D F, line C F, line F E, line C D E, line B A, line B C, line A D F, line C F, line F E, line C D E, line B A, line B C\nFind the area of the shaded figure in square inches.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6702.jpg"
-  },
-  {
-    "id": 6861,
-    "problem_id": 6703,
-    "problem": "line A D F, line C F, line F E, line C D E, line B A, line B C, line A D F, line C F, line F E, line C D E, line B A, line B C\nFind the area of the shaded figure in square inches.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6703.jpg"
-  },
-  {
-    "id": 6862,
-    "problem_id": 6704,
-    "problem": "line A D F, line C F, line F E, line C D E, line B A, line B C, line A D F, line C F, line F E, line C D E, line B A, line B C\nFind the area of the shaded figure in square inches.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6704.jpg"
-  },
-  {
-    "id": 6863,
-    "problem_id": 6705,
-    "problem": "line A D F, line C F, line F E, line C D E, line B A, line B C, line A D F, line C F, line F E, line C D E, line B A, line B C\nFind the area of the shaded figure in square inches.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6705.jpg"
-  },
-  {
-    "id": 6864,
-    "problem_id": 6706,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6706.jpg"
-  },
-  {
-    "id": 6865,
-    "problem_id": 6707,
-    "problem": "line P Q, line R Q, line P R, line P Q, line R Q, line P R\nSolve for p.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6707.jpg"
-  },
-  {
-    "id": 6866,
-    "problem_id": 6708,
-    "problem": "line C B, line B A, line C A, line C B, line B A, line C A\nDetermine the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6708.jpg"
-  },
-  {
-    "id": 6867,
-    "problem_id": 6709,
-    "problem": "line C B, line B A, line C A, line C B, line B A, line C A\nDetermine the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6709.jpg"
-  },
-  {
-    "id": 6868,
-    "problem_id": 6710,
-    "problem": "line C B, line B A, line C A, line C B, line B A, line C A\nDetermine the measure of \\angle B.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6710.jpg"
-  },
-  {
-    "id": 6870,
-    "problem_id": 6711,
-    "problem": "line R W T, line S V T, line R U S, line U V, line U W, line R W T, line S V T, line R U S, line U V, line U W\nFind m \\angle SVU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6711.jpg"
-  },
-  {
-    "id": 6872,
-    "problem_id": 6712,
-    "problem": "line R W T, line S V T, line R U S, line U V, line U W, line R W T, line S V T, line R U S, line U V, line U W\nFind m \\angle SVU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6712.jpg"
-  },
-  {
-    "id": 6873,
-    "problem_id": 6713,
-    "problem": "line R W T, line S V T, line R U S, line U V, line U W, line R W T, line S V T, line R U S, line U V, line U W\nFind m \\angle SVU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6713.jpg"
-  },
-  {
-    "id": 6874,
-    "problem_id": 6714,
-    "problem": "line R T, line S T, line S R, line R T, line S T, line S R\nWhat is the length of RS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6714.jpg"
-  },
-  {
-    "id": 6875,
-    "problem_id": 6715,
-    "problem": "line R T, line S T, line S R, line R T, line S T, line S R\nWhat is the length of RS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6715.jpg"
-  },
-  {
-    "id": 6876,
-    "problem_id": 6716,
-    "problem": "line R T, line S T, line S R, line R T, line S T, line S R\nWhat is the length of RS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6716.jpg"
-  },
-  {
-    "id": 6877,
-    "problem_id": 6717,
-    "problem": "line R T, line S T, line S R, line R T, line S T, line S R\nWhat is the length of RS?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6717.jpg"
-  },
-  {
-    "id": 6878,
-    "problem_id": 6718,
-    "problem": "line A B, line A C, line C B, line D F, line D E, line F E, line A B, line A C, line C B, line D F, line D E, line F E\nFind the measure of DF, if \\triangle DEF \\sim \\triangle ACB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6718.jpg"
-  },
-  {
-    "id": 6879,
-    "problem_id": 6719,
-    "problem": "line A B, line A C, line C B, line D F, line D E, line F E, line A B, line A C, line C B, line D F, line D E, line F E\nFind the measure of DF, if \\triangle DEF \\sim \\triangle ACB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6719.jpg"
-  },
-  {
-    "id": 6880,
-    "problem_id": 6720,
-    "problem": "line A B, line B C D E, line F E, line C G F, line A G D, line A B, line B C D E, line F E, line C G F, line A G D\nBD = x-1, CE = x+2. Find AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6720.jpg"
-  },
-  {
-    "id": 6881,
-    "problem_id": 6721,
-    "problem": "line A B, line B C D E, line F E, line C G F, line A G D, line A B, line B C D E, line F E, line C G F, line A G D\nBD = x-1, CE = x+2. Find AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6721.jpg"
-  },
-  {
-    "id": 6882,
-    "problem_id": 6722,
-    "problem": "line A B, line B C D E, line F E, line C G F, line A G D, line A B, line B C D E, line F E, line C G F, line A G D\nBD = x-1, CE = x+2. Find AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6722.jpg"
-  },
-  {
-    "id": 6883,
-    "problem_id": 6723,
-    "problem": "line A B, line B C D E, line F E, line C G F, line A G D, line A B, line B C D E, line F E, line C G F, line A G D\nBD = x-1, CE = x+2. Find AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6723.jpg"
-  },
-  {
-    "id": 6884,
-    "problem_id": 6724,
-    "problem": "line A B C, line D B, line D F, line F G, line E G, line B E, \\odot H lieson D F G E B, line A B C, line D B, line D F, line F G, line E G, line B E, \\odot H lieson D F G E B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6724.jpg"
-  },
-  {
-    "id": 6885,
-    "problem_id": 6725,
-    "problem": "line A B C, line D B, line D F, line F G, line E G, line B E, \\odot H lieson D F G E B, line A B C, line D B, line D F, line F G, line E G, line B E, \\odot H lieson D F G E B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6725.jpg"
-  },
-  {
-    "id": 6886,
-    "problem_id": 6726,
-    "problem": "line B C D, line B E, line B A, line E D, line A D, line A C E, line B C D, line B E, line B A, line E D, line A D, line A C E\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6726.jpg"
-  },
-  {
-    "id": 6887,
-    "problem_id": 6727,
-    "problem": "line B C D, line B E, line B A, line E D, line A D, line A C E, line B C D, line B E, line B A, line E D, line A D, line A C E\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6727.jpg"
-  },
-  {
-    "id": 6888,
-    "problem_id": 6728,
-    "problem": "line B C D, line B E, line B A, line E D, line A D, line A C E, line B C D, line B E, line B A, line E D, line A D, line A C E\nFind the area of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6728.jpg"
-  },
-  {
-    "id": 6889,
-    "problem_id": 6729,
-    "problem": "line A B, line B C, line D C, line A D, \\odot E lieson A D C B, line A B, line B C, line D C, line A D, \\odot E lieson A D C B\nA square is inscribed in a circle. What is the circumference of the circle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6729.jpg"
-  },
-  {
-    "id": 6890,
-    "problem_id": 6730,
-    "problem": "line A C, line C B, line C D, line A D B, line A C, line C B, line C D, line A D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6730.jpg"
-  },
-  {
-    "id": 6891,
-    "problem_id": 6731,
-    "problem": "line A C, line C B, line C D, line A D B, line A C, line C B, line C D, line A D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6731.jpg"
-  },
-  {
-    "id": 6892,
-    "problem_id": 6732,
-    "problem": "line A C, line C B, line C D, line A D B, line A C, line C B, line C D, line A D B\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6732.jpg"
-  },
-  {
-    "id": 6893,
-    "problem_id": 6733,
-    "problem": "line G J, line G K H, line J H, \\odot G lieson J K, line G J, line G K H, line J H, \\odot G lieson J K\nJH is tangent to \\odot G at J. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6733.jpg"
-  },
-  {
-    "id": 6894,
-    "problem_id": 6734,
-    "problem": "line G J, line G K H, line J H, \\odot G lieson J K, line G J, line G K H, line J H, \\odot G lieson J K\nJH is tangent to \\odot G at J. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6734.jpg"
-  },
-  {
-    "id": 6895,
-    "problem_id": 6735,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6735.jpg"
-  },
-  {
-    "id": 6896,
-    "problem_id": 6736,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6736.jpg"
-  },
-  {
-    "id": 6897,
-    "problem_id": 6737,
-    "problem": "line C A, line C B, line A B, line C A, line C B, line A B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6737.jpg"
-  },
-  {
-    "id": 6898,
-    "problem_id": 6738,
-    "problem": "line E C A, line E B, line A B, line D C B, line D E, line D A, line E C A, line E B, line A B, line D C B, line D E, line D A\nFind the value of x. Area = 48 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6738.jpg"
-  },
-  {
-    "id": 6899,
-    "problem_id": 6739,
-    "problem": "line E C A, line E B, line A B, line D C B, line D E, line D A, line E C A, line E B, line A B, line D C B, line D E, line D A\nFind the value of x. Area = 48 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6739.jpg"
-  },
-  {
-    "id": 6900,
-    "problem_id": 6740,
-    "problem": "line E C A, line E B, line A B, line D C B, line D E, line D A, line E C A, line E B, line A B, line D C B, line D E, line D A\nFind the value of x. Area = 48 in^{2}.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6740.jpg"
-  },
-  {
-    "id": 6901,
-    "problem_id": 6741,
-    "problem": "line C D E, line A C, line A E, line B E, line B D, line C D E, line A C, line A E, line B E, line B D\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6741.jpg"
-  },
-  {
-    "id": 6902,
-    "problem_id": 6742,
-    "problem": "line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D, line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6742.jpg"
-  },
-  {
-    "id": 6903,
-    "problem_id": 6743,
-    "problem": "line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D, line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6743.jpg"
-  },
-  {
-    "id": 6904,
-    "problem_id": 6744,
-    "problem": "line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D, line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6744.jpg"
-  },
-  {
-    "id": 6905,
-    "problem_id": 6745,
-    "problem": "line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D, line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6745.jpg"
-  },
-  {
-    "id": 6906,
-    "problem_id": 6746,
-    "problem": "line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D, line F A, line F E, line E A, line D A, line A C, line A B, line C B, line D C, line E D\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6746.jpg"
-  },
-  {
-    "id": 6907,
-    "problem_id": 6747,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nWhat is the value of n in the trapezoid?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6747.jpg"
-  },
-  {
-    "id": 6908,
-    "problem_id": 6748,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nWhat is the value of n in the trapezoid?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6748.jpg"
-  },
-  {
-    "id": 6909,
-    "problem_id": 6749,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6749.jpg"
-  },
-  {
-    "id": 6910,
-    "problem_id": 6750,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6750.jpg"
-  },
-  {
-    "id": 6911,
-    "problem_id": 6751,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6751.jpg"
-  },
-  {
-    "id": 6912,
-    "problem_id": 6752,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6752.jpg"
-  },
-  {
-    "id": 6913,
-    "problem_id": 6753,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6753.jpg"
-  },
-  {
-    "id": 6914,
-    "problem_id": 6754,
-    "problem": "line C B D, line A D, line A B, line C A, line C B D, line A D, line A B, line C A\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6754.jpg"
-  },
-  {
-    "id": 6915,
-    "problem_id": 6755,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 1 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6755.jpg"
-  },
-  {
-    "id": 6916,
-    "problem_id": 6756,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 1 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6756.jpg"
-  },
-  {
-    "id": 6918,
-    "problem_id": 6757,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 1 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6757.jpg"
-  },
-  {
-    "id": 6919,
-    "problem_id": 6758,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 1 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6758.jpg"
-  },
-  {
-    "id": 6920,
-    "problem_id": 6759,
-    "problem": "line G C, line A C, line G B A, line B C, line F G, line D F A, line D G, line G C, line A C, line G B A, line B C, line F G, line D F A, line D G\nFind the measure of \\angle 1 if m \\angle DGF = 53 and m \\angle AGC = 40.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6759.jpg"
-  },
-  {
-    "id": 6921,
-    "problem_id": 6760,
-    "problem": "line A E, line B C E, line A C D, line A B, line B D, line E D, line A E, line B C E, line A C D, line A B, line B D, line E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6760.jpg"
-  },
-  {
-    "id": 6922,
-    "problem_id": 6761,
-    "problem": "line A E, line B C E, line A C D, line A B, line B D, line E D, line A E, line B C E, line A C D, line A B, line B D, line E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6761.jpg"
-  },
-  {
-    "id": 6923,
-    "problem_id": 6762,
-    "problem": "line A E, line B C E, line A C D, line A B, line B D, line E D, line A E, line B C E, line A C D, line A B, line B D, line E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6762.jpg"
-  },
-  {
-    "id": 6924,
-    "problem_id": 6763,
-    "problem": "line A E, line B C E, line A C D, line A B, line B D, line E D, line A E, line B C E, line A C D, line A B, line B D, line E D\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6763.jpg"
-  },
-  {
-    "id": 6925,
-    "problem_id": 6764,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6764.jpg"
-  },
-  {
-    "id": 6926,
-    "problem_id": 6765,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6765.jpg"
-  },
-  {
-    "id": 6927,
-    "problem_id": 6766,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6766.jpg"
-  },
-  {
-    "id": 6928,
-    "problem_id": 6767,
-    "problem": "line R T, line S T, line R S, line R T, line S T, line R S\nFind the measure of \\angle T.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6767.jpg"
-  },
-  {
-    "id": 6929,
-    "problem_id": 6768,
-    "problem": "line A C, line A B D, line C B, line C D, line A C, line A B D, line C B, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6768.jpg"
-  },
-  {
-    "id": 6931,
-    "problem_id": 6769,
-    "problem": "line A C, line A B D, line C B, line C D, line A C, line A B D, line C B, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6769.jpg"
-  },
-  {
-    "id": 6932,
-    "problem_id": 6770,
-    "problem": "line A C, line A B D, line C B, line C D, line A C, line A B D, line C B, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6770.jpg"
-  },
-  {
-    "id": 6933,
-    "problem_id": 6771,
-    "problem": "line A C, line A B D, line C B, line C D, line A C, line A B D, line C B, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6771.jpg"
-  },
-  {
-    "id": 6934,
-    "problem_id": 6772,
-    "problem": "line A C, line A B D, line C B, line C D, line A C, line A B D, line C B, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6772.jpg"
-  },
-  {
-    "id": 6935,
-    "problem_id": 6773,
-    "problem": "line A C, line A B D, line C B, line C D, line A C, line A B D, line C B, line C D\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6773.jpg"
-  },
-  {
-    "id": 6936,
-    "problem_id": 6774,
-    "problem": "line A B, line B E, line E G, line F G, line C F, line A C, line D G, \\odot D lieson A C F G E B, line A B, line B E, line E G, line F G, line C F, line A C, line D G, \\odot D lieson A C F G E B\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6774.jpg"
-  },
-  {
-    "id": 6938,
-    "problem_id": 6775,
-    "problem": "line A B C, line F E C, line F B, line F A, line F D, line E D, line D C, line A B C, line F E C, line F B, line F A, line F D, line E D, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6775.jpg"
-  },
-  {
-    "id": 6939,
-    "problem_id": 6776,
-    "problem": "line A B C, line F E C, line F B, line F A, line F D, line E D, line D C, line A B C, line F E C, line F B, line F A, line F D, line E D, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6776.jpg"
-  },
-  {
-    "id": 6940,
-    "problem_id": 6777,
-    "problem": "line A B C, line F E C, line F B, line F A, line F D, line E D, line D C, line A B C, line F E C, line F B, line F A, line F D, line E D, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6777.jpg"
-  },
-  {
-    "id": 6941,
-    "problem_id": 6778,
-    "problem": "line A B C, line F E C, line F B, line F A, line F D, line E D, line D C, line A B C, line F E C, line F B, line F A, line F D, line E D, line D C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6778.jpg"
-  },
-  {
-    "id": 6942,
-    "problem_id": 6779,
-    "problem": "line C D, line A C, line A D, line C B, line C D, line A C, line A D, line C B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6779.jpg"
-  },
-  {
-    "id": 6943,
-    "problem_id": 6780,
-    "problem": "line C D, line A C, line A D, line C B, line C D, line A C, line A D, line C B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6780.jpg"
-  },
-  {
-    "id": 6944,
-    "problem_id": 6781,
-    "problem": "line C D, line A C, line A D, line C B, line C D, line A C, line A D, line C B\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6781.jpg"
-  },
-  {
-    "id": 6945,
-    "problem_id": 6782,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\cos L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6782.jpg"
-  },
-  {
-    "id": 6946,
-    "problem_id": 6783,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\cos L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6783.jpg"
-  },
-  {
-    "id": 6947,
-    "problem_id": 6784,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\cos L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6784.jpg"
-  },
-  {
-    "id": 6948,
-    "problem_id": 6785,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\cos L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6785.jpg"
-  },
-  {
-    "id": 6950,
-    "problem_id": 6786,
-    "problem": "line Q M, line P Q, \\odot A lieson P M Q, line Q M, line P Q, \\odot A lieson P M Q\nFind the measure of \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6786.jpg"
-  },
-  {
-    "id": 6951,
-    "problem_id": 6787,
-    "problem": "line Q M, line P Q, \\odot A lieson P M Q, line Q M, line P Q, \\odot A lieson P M Q\nFind the measure of \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6787.jpg"
-  },
-  {
-    "id": 6952,
-    "problem_id": 6788,
-    "problem": "line A B E, line E D, line C D, line B D, line A C, line A B E, line E D, line C D, line B D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6788.jpg"
-  },
-  {
-    "id": 6953,
-    "problem_id": 6789,
-    "problem": "line A B E, line E D, line C D, line B D, line A C, line A B E, line E D, line C D, line B D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6789.jpg"
-  },
-  {
-    "id": 6954,
-    "problem_id": 6790,
-    "problem": "line A B E, line E D, line C D, line B D, line A C, line A B E, line E D, line C D, line B D, line A C\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6790.jpg"
-  },
-  {
-    "id": 6955,
-    "problem_id": 6791,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6791.jpg"
-  },
-  {
-    "id": 6956,
-    "problem_id": 6792,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6792.jpg"
-  },
-  {
-    "id": 6957,
-    "problem_id": 6793,
-    "problem": "line A D E, line B C E, line A B, line D C, line A D E, line B C E, line A B, line D C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6793.jpg"
-  },
-  {
-    "id": 6958,
-    "problem_id": 6794,
-    "problem": "line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X, line Y A X, line W A Z, line Y Z, line X Z, line W Y, line W X\nQuadrilateral WXZY is a rectangle. Find the measure of \\angle 7 if m \\angle 1 = 30.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6794.jpg"
-  },
-  {
-    "id": 6959,
-    "problem_id": 6795,
-    "problem": "line G F A, line C G H B, \\odot D lieson F J G, line G F A, line C G H B, \\odot D lieson F J G\nFind m \\angle FGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6795.jpg"
-  },
-  {
-    "id": 6960,
-    "problem_id": 6796,
-    "problem": "line G F A, line C G H B, \\odot D lieson F J G, line G F A, line C G H B, \\odot D lieson F J G\nFind m \\angle FGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6796.jpg"
-  },
-  {
-    "id": 6961,
-    "problem_id": 6797,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6797.jpg"
-  },
-  {
-    "id": 6962,
-    "problem_id": 6798,
-    "problem": "line A B C, line C D, line B D, line A D, line A B C, line C D, line B D, line A D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6798.jpg"
-  },
-  {
-    "id": 6963,
-    "problem_id": 6799,
-    "problem": "line P Y, line P T, line T Y, line P Y, line P T, line T Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6799.jpg"
-  },
-  {
-    "id": 6964,
-    "problem_id": 6800,
-    "problem": "line P Y, line P T, line T Y, line P Y, line P T, line T Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6800.jpg"
-  },
-  {
-    "id": 6965,
-    "problem_id": 6801,
-    "problem": "line P Y, line P T, line T Y, line P Y, line P T, line T Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6801.jpg"
-  },
-  {
-    "id": 6966,
-    "problem_id": 6802,
-    "problem": "line P Y, line P T, line T Y, line P Y, line P T, line T Y\nWhat is m \\angle Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6802.jpg"
-  },
-  {
-    "id": 6967,
-    "problem_id": 6803,
-    "problem": "line E D, line D C, line A B C, line E A, line E F C, line D F B, line E D, line D C, line A B C, line E A, line E F C, line D F B\nWhat is FC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6803.jpg"
-  },
-  {
-    "id": 6968,
-    "problem_id": 6804,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6804.jpg"
-  },
-  {
-    "id": 6969,
-    "problem_id": 6805,
-    "problem": "line B C, line A D, line B A, line C D, line B C, line A D, line B A, line C D\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6805.jpg"
-  },
-  {
-    "id": 6970,
-    "problem_id": 6806,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6806.jpg"
-  },
-  {
-    "id": 6971,
-    "problem_id": 6807,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6807.jpg"
-  },
-  {
-    "id": 6972,
-    "problem_id": 6808,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6808.jpg"
-  },
-  {
-    "id": 6973,
-    "problem_id": 6809,
-    "problem": "line A B, \\odot A lieson B, line A B, \\odot A lieson B\nFind the circumference of \\odot A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6809.jpg"
-  },
-  {
-    "id": 6974,
-    "problem_id": 6810,
-    "problem": "line A B C, line D C, line D B, line E D, line E B, line E A, line A B C, line D C, line D B, line E D, line E B, line E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6810.jpg"
-  },
-  {
-    "id": 6975,
-    "problem_id": 6811,
-    "problem": "line A B C, line D C, line D B, line E D, line E B, line E A, line A B C, line D C, line D B, line E D, line E B, line E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6811.jpg"
-  },
-  {
-    "id": 6976,
-    "problem_id": 6812,
-    "problem": "line A B C, line D C, line D B, line E D, line E B, line E A, line A B C, line D C, line D B, line E D, line E B, line E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6812.jpg"
-  },
-  {
-    "id": 6977,
-    "problem_id": 6813,
-    "problem": "line A B C, line D C, line D B, line E D, line E B, line E A, line A B C, line D C, line D B, line E D, line E B, line E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6813.jpg"
-  },
-  {
-    "id": 6978,
-    "problem_id": 6814,
-    "problem": "line A B C, line D C, line D B, line E D, line E B, line E A, line A B C, line D C, line D B, line E D, line E B, line E A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6814.jpg"
-  },
-  {
-    "id": 6979,
-    "problem_id": 6815,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nFind the value of variable c in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6815.jpg"
-  },
-  {
-    "id": 6980,
-    "problem_id": 6816,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nFind the value of variable c in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6816.jpg"
-  },
-  {
-    "id": 6981,
-    "problem_id": 6817,
-    "problem": "line A B, line C D, line B D, line A C, line A B, line C D, line B D, line A C\nFind the value of variable c in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6817.jpg"
-  },
-  {
-    "id": 6982,
-    "problem_id": 6818,
-    "problem": "line H G, line E F, line F G, line H E, \\odot N lieson E H G F, line H G, line E F, line F G, line H E, \\odot N lieson E H G F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6818.jpg"
-  },
-  {
-    "id": 6983,
-    "problem_id": 6819,
-    "problem": "line H G, line E F, line F G, line H E, \\odot N lieson E H G F, line H G, line E F, line F G, line H E, \\odot N lieson E H G F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6819.jpg"
-  },
-  {
-    "id": 6984,
-    "problem_id": 6820,
-    "problem": "line H G, line E F, line F G, line H E, \\odot N lieson E H G F, line H G, line E F, line F G, line H E, \\odot N lieson E H G F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6820.jpg"
-  },
-  {
-    "id": 6985,
-    "problem_id": 6821,
-    "problem": "line H G, line E F, line F G, line H E, \\odot N lieson E H G F, line H G, line E F, line F G, line H E, \\odot N lieson E H G F\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6821.jpg"
-  },
-  {
-    "id": 6986,
-    "problem_id": 6822,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6822.jpg"
-  },
-  {
-    "id": 6987,
-    "problem_id": 6823,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6823.jpg"
-  },
-  {
-    "id": 6988,
-    "problem_id": 6824,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6824.jpg"
-  },
-  {
-    "id": 6989,
-    "problem_id": 6825,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6825.jpg"
-  },
-  {
-    "id": 6990,
-    "problem_id": 6826,
-    "problem": "line B D F J, line A D G H, line C G I, line E F G, line E D C, line B D F J, line A D G H, line C G I, line E F G, line E D C\nFind m \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6826.jpg"
-  },
-  {
-    "id": 6991,
-    "problem_id": 6827,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle HLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6827.jpg"
-  },
-  {
-    "id": 6992,
-    "problem_id": 6828,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle HLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6828.jpg"
-  },
-  {
-    "id": 6993,
-    "problem_id": 6829,
-    "problem": "line J H K, line L K, line L J, line L H, line J H K, line L K, line L J, line L H\nFind the measure of \\angle HLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6829.jpg"
-  },
-  {
-    "id": 6994,
-    "problem_id": 6830,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6830.jpg"
-  },
-  {
-    "id": 6995,
-    "problem_id": 6831,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6831.jpg"
-  },
-  {
-    "id": 6996,
-    "problem_id": 6832,
-    "problem": "line A B, line A C, line B C, line A B, line A C, line B C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6832.jpg"
-  },
-  {
-    "id": 6997,
-    "problem_id": 6833,
-    "problem": "line M H, line H J P, line M J Q, line P Q, line M H, line H J P, line M J Q, line P Q\n\\triangle MHJ \\cong \\triangle PQJ. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6833.jpg"
-  },
-  {
-    "id": 6998,
-    "problem_id": 6834,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6834.jpg"
-  },
-  {
-    "id": 6999,
-    "problem_id": 6835,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6835.jpg"
-  },
-  {
-    "id": 7000,
-    "problem_id": 6836,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6836.jpg"
-  },
-  {
-    "id": 7001,
-    "problem_id": 6837,
-    "problem": "line A B C, line D C, line A D, line D B, line A B C, line D C, line A D, line D B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6837.jpg"
-  },
-  {
-    "id": 7002,
-    "problem_id": 6838,
-    "problem": "line N Q M K, line P Q R, line L K, \\odot A lieson N R L M P, line N Q M K, line P Q R, line L K, \\odot A lieson N R L M P\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6838.jpg"
-  },
-  {
-    "id": 7003,
-    "problem_id": 6839,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the measure of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6839.jpg"
-  },
-  {
-    "id": 7004,
-    "problem_id": 6840,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the measure of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6840.jpg"
-  },
-  {
-    "id": 7005,
-    "problem_id": 6841,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the measure of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6841.jpg"
-  },
-  {
-    "id": 7006,
-    "problem_id": 6842,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the measure of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6842.jpg"
-  },
-  {
-    "id": 7007,
-    "problem_id": 6843,
-    "problem": "line E F, line E G, line X Y, line X Z, line F G, line Z Y, line E F, line E G, line X Y, line X Z, line F G, line Z Y\nEach pair of polygons is similar. Find the measure of XZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6843.jpg"
-  },
-  {
-    "id": 7008,
-    "problem_id": 6844,
-    "problem": "line C B, line A C, line A B, line C B, line A C, line A B\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6844.jpg"
-  },
-  {
-    "id": 7009,
-    "problem_id": 6845,
-    "problem": "line C B, line A C, line A B, line C B, line A C, line A B\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6845.jpg"
-  },
-  {
-    "id": 7010,
-    "problem_id": 6846,
-    "problem": "line C B, line A C, line A B, line C B, line A C, line A B\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6846.jpg"
-  },
-  {
-    "id": 7011,
-    "problem_id": 6847,
-    "problem": "line C B, line A C, line A B, line C B, line A C, line A B\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6847.jpg"
-  },
-  {
-    "id": 7012,
-    "problem_id": 6848,
-    "problem": "line C B, line A C, line A B, line C B, line A C, line A B\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6848.jpg"
-  },
-  {
-    "id": 7013,
-    "problem_id": 6849,
-    "problem": "line C B, line A C, line A B, line C B, line A C, line A B\nSolve for m \\angle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6849.jpg"
-  },
-  {
-    "id": 7014,
-    "problem_id": 6850,
-    "problem": "line E C B, line D C A, line E C B, line D C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6850.jpg"
-  },
-  {
-    "id": 7015,
-    "problem_id": 6851,
-    "problem": "line E C B, line D C A, line E C B, line D C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6851.jpg"
-  },
-  {
-    "id": 7016,
-    "problem_id": 6852,
-    "problem": "line E C B, line D C A, line E C B, line D C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6852.jpg"
-  },
-  {
-    "id": 7017,
-    "problem_id": 6853,
-    "problem": "line E C B, line D C A, line E C B, line D C A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6853.jpg"
-  },
-  {
-    "id": 7018,
-    "problem_id": 6854,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nWhat is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6854.jpg"
-  },
-  {
-    "id": 7019,
-    "problem_id": 6855,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nWhat is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6855.jpg"
-  },
-  {
-    "id": 7020,
-    "problem_id": 6856,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nWhat is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6856.jpg"
-  },
-  {
-    "id": 7021,
-    "problem_id": 6857,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nWhat is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6857.jpg"
-  },
-  {
-    "id": 7022,
-    "problem_id": 6858,
-    "problem": "line A B, line B C, line A C, line A B, line B C, line A C\nWhat is AB?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6858.jpg"
-  },
-  {
-    "id": 7023,
-    "problem_id": 6859,
-    "problem": "line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N, line Q R N, line M R P, line Q P, line M N, line M Q, line N P, \\odot R lieson M Q P N\nIn \\odot R, m \\widehat MN = 120. Solve for m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6859.jpg"
-  },
-  {
-    "id": 7024,
-    "problem_id": 6860,
-    "problem": "line J M, line K P M, line L M, line K L, line J K, line J P L, line J M, line K P M, line L M, line K L, line J K, line J P L\nFind JL, if KP = 4 and PM = 7.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6860.jpg"
-  },
-  {
-    "id": 7025,
-    "problem_id": 6861,
-    "problem": "line C A, line D A, line A B, line C A, line D A, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6861.jpg"
-  },
-  {
-    "id": 7026,
-    "problem_id": 6862,
-    "problem": "line C A, line D A, line A B, line C A, line D A, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6862.jpg"
-  },
-  {
-    "id": 7027,
-    "problem_id": 6863,
-    "problem": "line C A, line D A, line A B, line C A, line D A, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6863.jpg"
-  },
-  {
-    "id": 7028,
-    "problem_id": 6864,
-    "problem": "line C A, line D A, line A B, line C A, line D A, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6864.jpg"
-  },
-  {
-    "id": 7029,
-    "problem_id": 6865,
-    "problem": "line C A, line D A, line A B, line C A, line D A, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6865.jpg"
-  },
-  {
-    "id": 7030,
-    "problem_id": 6866,
-    "problem": "line C A, line D A, line A B, line C A, line D A, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6866.jpg"
-  },
-  {
-    "id": 7031,
-    "problem_id": 6867,
-    "problem": "line D E F G, line A C F I, line B C E H, line D E F G, line A C F I, line B C E H\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6867.jpg"
-  },
-  {
-    "id": 7032,
-    "problem_id": 6868,
-    "problem": "line D E F G, line A C F I, line B C E H, line D E F G, line A C F I, line B C E H\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6868.jpg"
-  },
-  {
-    "id": 7033,
-    "problem_id": 6869,
-    "problem": "line C D E, line A D, line B D, line C D E, line A D, line B D\nm \\angle 3 = 38, find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6869.jpg"
-  },
-  {
-    "id": 7034,
-    "problem_id": 6870,
-    "problem": "line C D E, line A D, line B D, line C D E, line A D, line B D\nm \\angle 3 = 38, find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6870.jpg"
-  },
-  {
-    "id": 7035,
-    "problem_id": 6871,
-    "problem": "line C D E, line A D, line B D, line C D E, line A D, line B D\nm \\angle 3 = 38, find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6871.jpg"
-  },
-  {
-    "id": 7036,
-    "problem_id": 6872,
-    "problem": "line C D E, line A D, line B D, line C D E, line A D, line B D\nm \\angle 3 = 38, find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6872.jpg"
-  },
-  {
-    "id": 7037,
-    "problem_id": 6873,
-    "problem": "line C D E, line A D, line B D, line C D E, line A D, line B D\nm \\angle 3 = 38, find the measure of \\angle 4.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6873.jpg"
-  },
-  {
-    "id": 7038,
-    "problem_id": 6874,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6874.jpg"
-  },
-  {
-    "id": 7039,
-    "problem_id": 6875,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nThe polygons are similar. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6875.jpg"
-  },
-  {
-    "id": 7040,
-    "problem_id": 6876,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nThe polygons are similar. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6876.jpg"
-  },
-  {
-    "id": 7041,
-    "problem_id": 6877,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nThe polygons are similar. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6877.jpg"
-  },
-  {
-    "id": 7042,
-    "problem_id": 6878,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nThe polygons are similar. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6878.jpg"
-  },
-  {
-    "id": 7043,
-    "problem_id": 6879,
-    "problem": "line A B C, line E C, line A D E, line D B, line A B C, line E C, line A D E, line D B\nThe polygons are similar. Solve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6879.jpg"
-  },
-  {
-    "id": 7044,
-    "problem_id": 6880,
-    "problem": "line A B, line E D B, line E C, line D C, line C B, line F A, line F E, line A B, line E D B, line E C, line D C, line C B, line F A, line F E\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6880.jpg"
-  },
-  {
-    "id": 7045,
-    "problem_id": 6881,
-    "problem": "line A B, line E D B, line E C, line D C, line C B, line F A, line F E, line A B, line E D B, line E C, line D C, line C B, line F A, line F E\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6881.jpg"
-  },
-  {
-    "id": 7046,
-    "problem_id": 6882,
-    "problem": "line A B, line E D B, line E C, line D C, line C B, line F A, line F E, line A B, line E D B, line E C, line D C, line C B, line F A, line F E\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6882.jpg"
-  },
-  {
-    "id": 7047,
-    "problem_id": 6883,
-    "problem": "line K L, line J L, line J K, line Z W, line Z Y, line W Y, line K L, line J L, line J K, line Z W, line Z Y, line W Y\n\\triangle JKL \\sim \\triangle WYZ. Find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6883.jpg"
-  },
-  {
-    "id": 7048,
-    "problem_id": 6884,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6884.jpg"
-  },
-  {
-    "id": 7049,
-    "problem_id": 6885,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nWhat is x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6885.jpg"
-  },
-  {
-    "id": 7050,
-    "problem_id": 6886,
-    "problem": "line A W X Y Z B, line A W X Y Z B\nFind the measurement of ZW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6886.jpg"
-  },
-  {
-    "id": 7051,
-    "problem_id": 6887,
-    "problem": "line A W X Y Z B, line A W X Y Z B\nFind the measurement of ZW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6887.jpg"
-  },
-  {
-    "id": 7052,
-    "problem_id": 6888,
-    "problem": "line A W X Y Z B, line A W X Y Z B\nFind the measurement of ZW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6888.jpg"
-  },
-  {
-    "id": 7053,
-    "problem_id": 6889,
-    "problem": "line A D H, line B E G, line F E D C, line A D H, line B E G, line F E D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6889.jpg"
-  },
-  {
-    "id": 7054,
-    "problem_id": 6890,
-    "problem": "line A D H, line B E G, line F E D C, line A D H, line B E G, line F E D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6890.jpg"
-  },
-  {
-    "id": 7055,
-    "problem_id": 6891,
-    "problem": "line A D H, line B E G, line F E D C, line A D H, line B E G, line F E D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6891.jpg"
-  },
-  {
-    "id": 7056,
-    "problem_id": 6892,
-    "problem": "line A D H, line B E G, line F E D C, line A D H, line B E G, line F E D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6892.jpg"
-  },
-  {
-    "id": 7057,
-    "problem_id": 6893,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6893.jpg"
-  },
-  {
-    "id": 7058,
-    "problem_id": 6894,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6894.jpg"
-  },
-  {
-    "id": 7059,
-    "problem_id": 6895,
-    "problem": "line H C E D I, line G A E B F, line H C E D I, line G A E B F\nSolve for y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6895.jpg"
-  },
-  {
-    "id": 7061,
-    "problem_id": 6896,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6896.jpg"
-  },
-  {
-    "id": 7062,
-    "problem_id": 6897,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6897.jpg"
-  },
-  {
-    "id": 7063,
-    "problem_id": 6898,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6898.jpg"
-  },
-  {
-    "id": 7064,
-    "problem_id": 6899,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6899.jpg"
-  },
-  {
-    "id": 7065,
-    "problem_id": 6900,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6900.jpg"
-  },
-  {
-    "id": 7066,
-    "problem_id": 6901,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6901.jpg"
-  },
-  {
-    "id": 7067,
-    "problem_id": 6902,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6902.jpg"
-  },
-  {
-    "id": 7068,
-    "problem_id": 6903,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6903.jpg"
-  },
-  {
-    "id": 7069,
-    "problem_id": 6904,
-    "problem": "line A E C, line D C, line B E D, line B C, line A D, line A B, line A E C, line D C, line B E D, line B C, line A D, line A B\nUse \\parallelogram ABCD to solve for d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6904.jpg"
-  },
-  {
-    "id": 7070,
-    "problem_id": 6905,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6905.jpg"
-  },
-  {
-    "id": 7071,
-    "problem_id": 6906,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6906.jpg"
-  },
-  {
-    "id": 7072,
-    "problem_id": 6907,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6907.jpg"
-  },
-  {
-    "id": 7074,
-    "problem_id": 6908,
-    "problem": "line B C, line A C, line A B, line B C, line A C, line A B\nFind the measure of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6908.jpg"
-  },
-  {
-    "id": 7075,
-    "problem_id": 6909,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6909.jpg"
-  },
-  {
-    "id": 7076,
-    "problem_id": 6910,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6910.jpg"
-  },
-  {
-    "id": 7077,
-    "problem_id": 6911,
-    "problem": "line R Q, line P Q, line M P, line M R, line R Q, line P Q, line M P, line M R\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6911.jpg"
-  },
-  {
-    "id": 7079,
-    "problem_id": 6912,
-    "problem": "line V T S, line Q R S, line Q V, line R T, line V T S, line Q R S, line Q V, line R T\nFind VT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6912.jpg"
-  },
-  {
-    "id": 7080,
-    "problem_id": 6913,
-    "problem": "line V T S, line Q R S, line Q V, line R T, line V T S, line Q R S, line Q V, line R T\nFind VT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6913.jpg"
-  },
-  {
-    "id": 7081,
-    "problem_id": 6914,
-    "problem": "line V T S, line Q R S, line Q V, line R T, line V T S, line Q R S, line Q V, line R T\nFind VT.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6914.jpg"
-  },
-  {
-    "id": 7082,
-    "problem_id": 6915,
-    "problem": "line B I H, line A I J K E, line C J G, line D K F, line B I H, line A I J K E, line C J G, line D K F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6915.jpg"
-  },
-  {
-    "id": 7083,
-    "problem_id": 6916,
-    "problem": "line B I H, line A I J K E, line C J G, line D K F, line B I H, line A I J K E, line C J G, line D K F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6916.jpg"
-  },
-  {
-    "id": 7084,
-    "problem_id": 6917,
-    "problem": "line B I H, line A I J K E, line C J G, line D K F, line B I H, line A I J K E, line C J G, line D K F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6917.jpg"
-  },
-  {
-    "id": 7085,
-    "problem_id": 6918,
-    "problem": "line B I H, line A I J K E, line C J G, line D K F, line B I H, line A I J K E, line C J G, line D K F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6918.jpg"
-  },
-  {
-    "id": 7086,
-    "problem_id": 6919,
-    "problem": "line B I H, line A I J K E, line C J G, line D K F, line B I H, line A I J K E, line C J G, line D K F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6919.jpg"
-  },
-  {
-    "id": 7087,
-    "problem_id": 6920,
-    "problem": "line B I H, line A I J K E, line C J G, line D K F, line B I H, line A I J K E, line C J G, line D K F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6920.jpg"
-  },
-  {
-    "id": 7088,
-    "problem_id": 6921,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6921.jpg"
-  },
-  {
-    "id": 7089,
-    "problem_id": 6922,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6922.jpg"
-  },
-  {
-    "id": 7090,
-    "problem_id": 6923,
-    "problem": "line A B C, line D C, line D B, line D A, line A B C, line D C, line D B, line D A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6923.jpg"
-  },
-  {
-    "id": 7091,
-    "problem_id": 6924,
-    "problem": "line Z W Y, line Z X, line W X, line Y X, line Z W Y, line Z X, line W X, line Y X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6924.jpg"
-  },
-  {
-    "id": 7092,
-    "problem_id": 6925,
-    "problem": "line Z W Y, line Z X, line W X, line Y X, line Z W Y, line Z X, line W X, line Y X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6925.jpg"
-  },
-  {
-    "id": 7093,
-    "problem_id": 6926,
-    "problem": "line Z W Y, line Z X, line W X, line Y X, line Z W Y, line Z X, line W X, line Y X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6926.jpg"
-  },
-  {
-    "id": 7094,
-    "problem_id": 6927,
-    "problem": "line Z W Y, line Z X, line W X, line Y X, line Z W Y, line Z X, line W X, line Y X\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6927.jpg"
-  },
-  {
-    "id": 7095,
-    "problem_id": 6928,
-    "problem": "line A B D, line B C, \\odot E lieson B C, line A B D, line B C, \\odot E lieson B C\nWhat is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6928.jpg"
-  },
-  {
-    "id": 7096,
-    "problem_id": 6929,
-    "problem": "line T Z V, line X Y V, line U W V, line T Y W, line U X T, line U Y Z, line T Z V, line X Y V, line U W V, line T Y W, line U X T, line U Y Z\nIn \\triangle TUV, Y is the centroid. If YU = 9, find ZY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6929.jpg"
-  },
-  {
-    "id": 7097,
-    "problem_id": 6930,
-    "problem": "line G F, line D E F, line H E, line C H G, line C D, line G F, line D E F, line H E, line C H G, line C D\nRefer to trapezoid CDFG with median HE. Let WX be the median of CDEH. Find WX.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6930.jpg"
-  },
-  {
-    "id": 7098,
-    "problem_id": 6931,
-    "problem": "line S T C, line D V U, line B R V, line R S A, line T U E, line S T C, line D V U, line B R V, line R S A, line T U E\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6931.jpg"
-  },
-  {
-    "id": 7099,
-    "problem_id": 6932,
-    "problem": "line S T C, line D V U, line B R V, line R S A, line T U E, line S T C, line D V U, line B R V, line R S A, line T U E\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6932.jpg"
-  },
-  {
-    "id": 7100,
-    "problem_id": 6933,
-    "problem": "line S T C, line D V U, line B R V, line R S A, line T U E, line S T C, line D V U, line B R V, line R S A, line T U E\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6933.jpg"
-  },
-  {
-    "id": 7101,
-    "problem_id": 6934,
-    "problem": "line S T C, line D V U, line B R V, line R S A, line T U E, line S T C, line D V U, line B R V, line R S A, line T U E\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6934.jpg"
-  },
-  {
-    "id": 7102,
-    "problem_id": 6935,
-    "problem": "line S T C, line D V U, line B R V, line R S A, line T U E, line S T C, line D V U, line B R V, line R S A, line T U E\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6935.jpg"
-  },
-  {
-    "id": 7103,
-    "problem_id": 6936,
-    "problem": "line S T C, line D V U, line B R V, line R S A, line T U E, line S T C, line D V U, line B R V, line R S A, line T U E\nFind a.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6936.jpg"
-  },
-  {
-    "id": 7104,
-    "problem_id": 6937,
-    "problem": "line P R M, line R Q, line N R, \\odot R lieson N M Q P, line P R M, line R Q, line N R, \\odot R lieson N M Q P\nPM is a diameter of \\odot R. Find m \\widehat MQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6937.jpg"
-  },
-  {
-    "id": 7105,
-    "problem_id": 6938,
-    "problem": "line P R M, line R Q, line N R, \\odot R lieson N M Q P, line P R M, line R Q, line N R, \\odot R lieson N M Q P\nPM is a diameter of \\odot R. Find m \\widehat MQ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6938.jpg"
-  },
-  {
-    "id": 7106,
-    "problem_id": 6939,
-    "problem": "line A D G, line E D C, line B D F, line A D G, line E D C, line B D F\nWhat is the measure of \\angle 2?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6939.jpg"
-  },
-  {
-    "id": 7107,
-    "problem_id": 6940,
-    "problem": "line B E, line B F, line E F, line A C, line A D, line C D, line B E, line B F, line E F, line A C, line A D, line C D\n\\triangle BEF and \\triangle ACD are similar. What is the ratio of the areas from the \\triangle BEF to the \\triangle ACD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6940.jpg"
-  },
-  {
-    "id": 7108,
-    "problem_id": 6941,
-    "problem": "line O A Q, line P Q, line P O, \\odot O lieson A P, line O A Q, line P Q, line P O, \\odot O lieson A P\nIn the circle, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6941.jpg"
-  },
-  {
-    "id": 7109,
-    "problem_id": 6942,
-    "problem": "line O A Q, line P Q, line P O, \\odot O lieson A P, line O A Q, line P Q, line P O, \\odot O lieson A P\nIn the circle, what is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6942.jpg"
-  },
-  {
-    "id": 7110,
-    "problem_id": 6943,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6943.jpg"
-  },
-  {
-    "id": 7111,
-    "problem_id": 6944,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6944.jpg"
-  },
-  {
-    "id": 7112,
-    "problem_id": 6945,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6945.jpg"
-  },
-  {
-    "id": 7113,
-    "problem_id": 6946,
-    "problem": "line A C D, line A B, line B D, line B C, line A C D, line A B, line B D, line B C\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6946.jpg"
-  },
-  {
-    "id": 7114,
-    "problem_id": 6947,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6947.jpg"
-  },
-  {
-    "id": 7115,
-    "problem_id": 6948,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6948.jpg"
-  },
-  {
-    "id": 7116,
-    "problem_id": 6949,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6949.jpg"
-  },
-  {
-    "id": 7117,
-    "problem_id": 6950,
-    "problem": "line R Q, line R P, line Q P, line R Q, line R P, line Q P\nSolve for m \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6950.jpg"
-  },
-  {
-    "id": 7119,
-    "problem_id": 6951,
-    "problem": "line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J, line y lieson B E H L, line z lieson A D I K, line w lieson F E D C, line x lieson G H I J\nm \\angle 12 = 64. Find the measure of \\angle 9.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6951.jpg"
-  },
-  {
-    "id": 7120,
-    "problem_id": 6952,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind m \\angle EDF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6952.jpg"
-  },
-  {
-    "id": 7121,
-    "problem_id": 6953,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6953.jpg"
-  },
-  {
-    "id": 7122,
-    "problem_id": 6954,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6954.jpg"
-  },
-  {
-    "id": 7123,
-    "problem_id": 6955,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6955.jpg"
-  },
-  {
-    "id": 7124,
-    "problem_id": 6956,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6956.jpg"
-  },
-  {
-    "id": 7125,
-    "problem_id": 6957,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6957.jpg"
-  },
-  {
-    "id": 7126,
-    "problem_id": 6958,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6958.jpg"
-  },
-  {
-    "id": 7127,
-    "problem_id": 6959,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6959.jpg"
-  },
-  {
-    "id": 7128,
-    "problem_id": 6960,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6960.jpg"
-  },
-  {
-    "id": 7129,
-    "problem_id": 6961,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6961.jpg"
-  },
-  {
-    "id": 7130,
-    "problem_id": 6962,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6962.jpg"
-  },
-  {
-    "id": 7131,
-    "problem_id": 6963,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6963.jpg"
-  },
-  {
-    "id": 7132,
-    "problem_id": 6964,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6964.jpg"
-  },
-  {
-    "id": 7133,
-    "problem_id": 6965,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6965.jpg"
-  },
-  {
-    "id": 7134,
-    "problem_id": 6966,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6966.jpg"
-  },
-  {
-    "id": 7135,
-    "problem_id": 6967,
-    "problem": "line A B, line C D, line A C, line B D, line A B, line C D, line A C, line B D\nFind the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6967.jpg"
-  },
-  {
-    "id": 7136,
-    "problem_id": 6968,
-    "problem": "line r lieson A C G, line E C D F, line s lieson B D H, line r lieson A C G, line E C D F, line s lieson B D H\nFind x so that line r \\parallel line s.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6968.jpg"
-  },
-  {
-    "id": 7137,
-    "problem_id": 6969,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6969.jpg"
-  },
-  {
-    "id": 7138,
-    "problem_id": 6970,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6970.jpg"
-  },
-  {
-    "id": 7139,
-    "problem_id": 6971,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6971.jpg"
-  },
-  {
-    "id": 7140,
-    "problem_id": 6972,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6972.jpg"
-  },
-  {
-    "id": 7141,
-    "problem_id": 6973,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6973.jpg"
-  },
-  {
-    "id": 7142,
-    "problem_id": 6974,
-    "problem": "line A D, line B C D, line B A, line A C, line A D, line B C D, line B A, line A C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6974.jpg"
-  },
-  {
-    "id": 7143,
-    "problem_id": 6975,
-    "problem": "line B C, line B A, line A C, line C D, line A D, line B C, line B A, line A C, line C D, line A D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6975.jpg"
-  },
-  {
-    "id": 7144,
-    "problem_id": 6976,
-    "problem": "line B C, line B A, line A C, line C D, line A D, line B C, line B A, line A C, line C D, line A D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6976.jpg"
-  },
-  {
-    "id": 7145,
-    "problem_id": 6977,
-    "problem": "line B C, line B A, line A C, line C D, line A D, line B C, line B A, line A C, line C D, line A D\nFind the value of m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6977.jpg"
-  },
-  {
-    "id": 7147,
-    "problem_id": 6978,
-    "problem": "line P Q, line R S P, line R Q, line S Q, line P Q, line R S P, line R Q, line S Q\nFind x in \\triangle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6978.jpg"
-  },
-  {
-    "id": 7148,
-    "problem_id": 6979,
-    "problem": "line P Q, line R S P, line R Q, line S Q, line P Q, line R S P, line R Q, line S Q\nFind x in \\triangle PQR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6979.jpg"
-  },
-  {
-    "id": 7149,
-    "problem_id": 6980,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6980.jpg"
-  },
-  {
-    "id": 7150,
-    "problem_id": 6981,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6981.jpg"
-  },
-  {
-    "id": 7151,
-    "problem_id": 6982,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6982.jpg"
-  },
-  {
-    "id": 7152,
-    "problem_id": 6983,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6983.jpg"
-  },
-  {
-    "id": 7153,
-    "problem_id": 6984,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6984.jpg"
-  },
-  {
-    "id": 7154,
-    "problem_id": 6985,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6985.jpg"
-  },
-  {
-    "id": 7155,
-    "problem_id": 6986,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6986.jpg"
-  },
-  {
-    "id": 7156,
-    "problem_id": 6987,
-    "problem": "line G K, line K H, line G H, line G K, line K H, line G H\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6987.jpg"
-  },
-  {
-    "id": 7157,
-    "problem_id": 6988,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6988.jpg"
-  },
-  {
-    "id": 7158,
-    "problem_id": 6989,
-    "problem": "line A B, line C B, line C A, line A B, line C B, line C A\nWhat is the perimeter of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6989.jpg"
-  },
-  {
-    "id": 7159,
-    "problem_id": 6990,
-    "problem": "line T S, line Q T, line R S, line Q R, line T S, line Q T, line R S, line Q R\nFor isosceles trapezoid QRST, find the measure of \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6990.jpg"
-  },
-  {
-    "id": 7160,
-    "problem_id": 6991,
-    "problem": "line H G, line F G, line E F, line E H, line H G, line F G, line E F, line E H\nEFGH is a kite. What is m \\angle G?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6991.jpg"
-  },
-  {
-    "id": 7161,
-    "problem_id": 6992,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6992.jpg"
-  },
-  {
-    "id": 7162,
-    "problem_id": 6993,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6993.jpg"
-  },
-  {
-    "id": 7163,
-    "problem_id": 6994,
-    "problem": "line D A, line D C, line C B, line A B, line D A, line D C, line C B, line A B\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6994.jpg"
-  },
-  {
-    "id": 7164,
-    "problem_id": 6995,
-    "problem": "line X Y, line Z Y, line X Z, line X Y, line Z Y, line X Z\nWhat is the value of \\cos Y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6995.jpg"
-  },
-  {
-    "id": 7165,
-    "problem_id": 6996,
-    "problem": "line Q T S, line P T R, line P Q, line S R, \\odot A lieson P S R Q, line Q T S, line P T R, line P Q, line S R, \\odot A lieson P S R Q\nWhat is the measure of \\angle TSR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6996.jpg"
-  },
-  {
-    "id": 7166,
-    "problem_id": 6997,
-    "problem": "line A E, line E D, line E C, \\odot E lieson A D C B, line A E, line E D, line E C, \\odot E lieson A D C B\nFind m \\widehat AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6997.jpg"
-  },
-  {
-    "id": 7167,
-    "problem_id": 6998,
-    "problem": "line A E, line E D, line E C, \\odot E lieson A D C B, line A E, line E D, line E C, \\odot E lieson A D C B\nFind m \\widehat AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6998.jpg"
-  },
-  {
-    "id": 7168,
-    "problem_id": 6999,
-    "problem": "line A E, line E D, line E C, \\odot E lieson A D C B, line A E, line E D, line E C, \\odot E lieson A D C B\nFind m \\widehat AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/6999.jpg"
-  },
-  {
-    "id": 7169,
-    "problem_id": 7000,
-    "problem": "line A E, line E D, line E C, \\odot E lieson A D C B, line A E, line E D, line E C, \\odot E lieson A D C B\nFind m \\widehat AD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7000.jpg"
-  },
-  {
-    "id": 7170,
-    "problem_id": 7001,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. Find the scale factor from polygon ABCD to polygon EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7001.jpg"
-  },
-  {
-    "id": 7171,
-    "problem_id": 7002,
-    "problem": "line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D, line G F, line G H, line F E, line B A, line B C, line H E, line C D, line A D\nEach pair of polygons is similar. Find the scale factor from polygon ABCD to polygon EFGH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7002.jpg"
-  },
-  {
-    "id": 7172,
-    "problem_id": 7003,
-    "problem": "line B A, line A D, line C A, line B C D, line B A, line A D, line C A, line B C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7003.jpg"
-  },
-  {
-    "id": 7173,
-    "problem_id": 7004,
-    "problem": "line B A, line A D, line C A, line B C D, line B A, line A D, line C A, line B C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7004.jpg"
-  },
-  {
-    "id": 7174,
-    "problem_id": 7005,
-    "problem": "line B A, line A D, line C A, line B C D, line B A, line A D, line C A, line B C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7005.jpg"
-  },
-  {
-    "id": 7175,
-    "problem_id": 7006,
-    "problem": "line B A, line A D, line C A, line B C D, line B A, line A D, line C A, line B C D\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7006.jpg"
-  },
-  {
-    "id": 7176,
-    "problem_id": 7007,
-    "problem": "line A B F, line E D C, line O D, line O B, \\odot O lieson E C F A, line A B F, line E D C, line O D, line O B, \\odot O lieson E C F A\nFind the diameter of circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7007.jpg"
-  },
-  {
-    "id": 7177,
-    "problem_id": 7008,
-    "problem": "line Z Y, line X Y, line W X, line W Z, line Z Y, line X Y, line W X, line W Z\nUse parallelogram WXYZ to find m \\angle WZY.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7008.jpg"
-  },
-  {
-    "id": 7178,
-    "problem_id": 7009,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7009.jpg"
-  },
-  {
-    "id": 7179,
-    "problem_id": 7010,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7010.jpg"
-  },
-  {
-    "id": 7181,
-    "problem_id": 7011,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7011.jpg"
-  },
-  {
-    "id": 7182,
-    "problem_id": 7012,
-    "problem": "line S T, line R S, line R T P, line S T, line R S, line R T P\n\\triangle RST is a right triangle. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7012.jpg"
-  },
-  {
-    "id": 7183,
-    "problem_id": 7013,
-    "problem": "line S T, line R S, line R T P, line S T, line R S, line R T P\n\\triangle RST is a right triangle. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7013.jpg"
-  },
-  {
-    "id": 7184,
-    "problem_id": 7014,
-    "problem": "line S T, line R S, line R T P, line S T, line R S, line R T P\n\\triangle RST is a right triangle. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7014.jpg"
-  },
-  {
-    "id": 7185,
-    "problem_id": 7015,
-    "problem": "line S T, line R S, line R T P, line S T, line R S, line R T P\n\\triangle RST is a right triangle. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7015.jpg"
-  },
-  {
-    "id": 7187,
-    "problem_id": 7016,
-    "problem": "line S T, line R S, line R T P, line S T, line R S, line R T P\n\\triangle RST is a right triangle. Find m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7016.jpg"
-  },
-  {
-    "id": 7188,
-    "problem_id": 7017,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7017.jpg"
-  },
-  {
-    "id": 7189,
-    "problem_id": 7018,
-    "problem": "line A D, line A B C, line C D, line B D, line A D, line A B C, line C D, line B D\nSolve for z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7018.jpg"
-  },
-  {
-    "id": 7190,
-    "problem_id": 7019,
-    "problem": "line I E O A J, line F B O, line G C O, line H D O, line I E O A J, line F B O, line G C O, line H D O\nm \\angle AOB = 6x+5, m \\angle BOC = 4x-2, m \\angle AOC = 8x+21. Find the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7019.jpg"
-  },
-  {
-    "id": 7191,
-    "problem_id": 7020,
-    "problem": "line A B, line C A, line D A, line D C B, line A B, line C A, line D A, line D C B\nFind the value of the variable m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7020.jpg"
-  },
-  {
-    "id": 7192,
-    "problem_id": 7021,
-    "problem": "line A B, line C A, line D A, line D C B, line A B, line C A, line D A, line D C B\nFind the value of the variable m.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7021.jpg"
-  },
-  {
-    "id": 7193,
-    "problem_id": 7022,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7022.jpg"
-  },
-  {
-    "id": 7194,
-    "problem_id": 7023,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7023.jpg"
-  },
-  {
-    "id": 7195,
-    "problem_id": 7024,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7024.jpg"
-  },
-  {
-    "id": 7196,
-    "problem_id": 7025,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7025.jpg"
-  },
-  {
-    "id": 7197,
-    "problem_id": 7026,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7026.jpg"
-  },
-  {
-    "id": 7198,
-    "problem_id": 7027,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7027.jpg"
-  },
-  {
-    "id": 7199,
-    "problem_id": 7028,
-    "problem": "line B D, line B C, line C D, line B D, line B C, line C D\nFind BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7028.jpg"
-  },
-  {
-    "id": 7200,
-    "problem_id": 7029,
-    "problem": "line B D, line B C, line C D, line B D, line B C, line C D\nFind BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7029.jpg"
-  },
-  {
-    "id": 7201,
-    "problem_id": 7030,
-    "problem": "line B D, line B C, line C D, line B D, line B C, line C D\nFind BD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7030.jpg"
-  },
-  {
-    "id": 7202,
-    "problem_id": 7031,
-    "problem": "line A E C, line D E B, line A B, line C B, line D A, line D C, line A E C, line D E B, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7031.jpg"
-  },
-  {
-    "id": 7203,
-    "problem_id": 7032,
-    "problem": "line A E C, line D E B, line A B, line C B, line D A, line D C, line A E C, line D E B, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7032.jpg"
-  },
-  {
-    "id": 7204,
-    "problem_id": 7033,
-    "problem": "line A E C, line D E B, line A B, line C B, line D A, line D C, line A E C, line D E B, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7033.jpg"
-  },
-  {
-    "id": 7205,
-    "problem_id": 7034,
-    "problem": "line A E C, line D E B, line A B, line C B, line D A, line D C, line A E C, line D E B, line A B, line C B, line D A, line D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7034.jpg"
-  },
-  {
-    "id": 7206,
-    "problem_id": 7035,
-    "problem": "line A P, line B P, line P C, \\odot P lieson A D C B, line A P, line B P, line P C, \\odot P lieson A D C B\nFind the measure of \\widehat ADB for \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7035.jpg"
-  },
-  {
-    "id": 7207,
-    "problem_id": 7036,
-    "problem": "line A P, line B P, line P C, \\odot P lieson A D C B, line A P, line B P, line P C, \\odot P lieson A D C B\nFind the measure of \\widehat ADB for \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7036.jpg"
-  },
-  {
-    "id": 7208,
-    "problem_id": 7037,
-    "problem": "line A P, line B P, line P C, \\odot P lieson A D C B, line A P, line B P, line P C, \\odot P lieson A D C B\nFind the measure of \\widehat ADB for \\odot P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7037.jpg"
-  },
-  {
-    "id": 7209,
-    "problem_id": 7038,
-    "problem": "line A D B, line B C, line A C, \\odot D lieson A C B, line A D B, line B C, line A C, \\odot D lieson A C B\nThe triangle is inscribed in \\odot D. Find the radius of \\odot D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7038.jpg"
-  },
-  {
-    "id": 7210,
-    "problem_id": 7039,
-    "problem": "line A D B, line B C, line A C, \\odot D lieson A C B, line A D B, line B C, line A C, \\odot D lieson A C B\nThe triangle is inscribed in \\odot D. Find the radius of \\odot D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7039.jpg"
-  },
-  {
-    "id": 7211,
-    "problem_id": 7040,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7040.jpg"
-  },
-  {
-    "id": 7212,
-    "problem_id": 7041,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7041.jpg"
-  },
-  {
-    "id": 7213,
-    "problem_id": 7042,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7042.jpg"
-  },
-  {
-    "id": 7214,
-    "problem_id": 7043,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7043.jpg"
-  },
-  {
-    "id": 7215,
-    "problem_id": 7044,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7044.jpg"
-  },
-  {
-    "id": 7216,
-    "problem_id": 7045,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7045.jpg"
-  },
-  {
-    "id": 7217,
-    "problem_id": 7046,
-    "problem": "line A T, \\odot T lieson A, line A T, \\odot T lieson A\nWhat is the circumference of \\odot T?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7046.jpg"
-  },
-  {
-    "id": 7218,
-    "problem_id": 7047,
-    "problem": "line A B, line C A, line C D B, \\odot D lieson C A B, line A B, line C A, line C D B, \\odot D lieson C A B\nFind the exact diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7047.jpg"
-  },
-  {
-    "id": 7219,
-    "problem_id": 7048,
-    "problem": "line A B, line C A, line C D B, \\odot D lieson C A B, line A B, line C A, line C D B, \\odot D lieson C A B\nFind the exact diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7048.jpg"
-  },
-  {
-    "id": 7220,
-    "problem_id": 7049,
-    "problem": "line A B, line C A, line C D B, \\odot D lieson C A B, line A B, line C A, line C D B, \\odot D lieson C A B\nFind the exact diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7049.jpg"
-  },
-  {
-    "id": 7221,
-    "problem_id": 7050,
-    "problem": "line A B, line C A, line C D B, \\odot D lieson C A B, line A B, line C A, line C D B, \\odot D lieson C A B\nFind the exact diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7050.jpg"
-  },
-  {
-    "id": 7222,
-    "problem_id": 7051,
-    "problem": "line A B, line C A, line C D B, \\odot D lieson C A B, line A B, line C A, line C D B, \\odot D lieson C A B\nFind the exact diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7051.jpg"
-  },
-  {
-    "id": 7223,
-    "problem_id": 7052,
-    "problem": "line B E D, line C D, line A D, line C E A, line B A, line B C, line B E D, line C D, line A D, line C E A, line B A, line B C\nWhat is the length of CD in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7052.jpg"
-  },
-  {
-    "id": 7224,
-    "problem_id": 7053,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle ABC of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7053.jpg"
-  },
-  {
-    "id": 7225,
-    "problem_id": 7054,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle ABC of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7054.jpg"
-  },
-  {
-    "id": 7226,
-    "problem_id": 7055,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle ABC of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7055.jpg"
-  },
-  {
-    "id": 7227,
-    "problem_id": 7056,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle ABC of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7056.jpg"
-  },
-  {
-    "id": 7228,
-    "problem_id": 7057,
-    "problem": "line B C, line D C, line A B, line A D, line B C, line D C, line A B, line A D\nSolve for the measure of \\angle ABC of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7057.jpg"
-  },
-  {
-    "id": 7229,
-    "problem_id": 7058,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind the area of square WXYZ. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7058.jpg"
-  },
-  {
-    "id": 7230,
-    "problem_id": 7059,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7059.jpg"
-  },
-  {
-    "id": 7231,
-    "problem_id": 7060,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7060.jpg"
-  },
-  {
-    "id": 7232,
-    "problem_id": 7061,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7061.jpg"
-  },
-  {
-    "id": 7233,
-    "problem_id": 7062,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7062.jpg"
-  },
-  {
-    "id": 7234,
-    "problem_id": 7063,
-    "problem": "line R S, line P S, line Q P, line Q R, line R S, line P S, line Q P, line Q R\nUse parallelogram to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7063.jpg"
-  },
-  {
-    "id": 7235,
-    "problem_id": 7064,
-    "problem": "line T P D, line P C, line P B, \\odot P lieson T B D C, line T P D, line P C, line P B, \\odot P lieson T B D C\nFind the measure of \\widehat CD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7064.jpg"
-  },
-  {
-    "id": 7236,
-    "problem_id": 7065,
-    "problem": "line A B, line B C D, line E D, line A E, line A C, line A B, line B C D, line E D, line A E, line A C\nFind the perimeter of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7065.jpg"
-  },
-  {
-    "id": 7237,
-    "problem_id": 7066,
-    "problem": "line G F B, line A F E D, line I H E C, line F H, line G F B, line A F E D, line I H E C, line F H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7066.jpg"
-  },
-  {
-    "id": 7238,
-    "problem_id": 7067,
-    "problem": "line G F B, line A F E D, line I H E C, line F H, line G F B, line A F E D, line I H E C, line F H\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7067.jpg"
-  },
-  {
-    "id": 7239,
-    "problem_id": 7068,
-    "problem": "line D E B, line C E A, line D C, line D A, line A B, line C B, line D E B, line C E A, line D C, line D A, line A B, line C B\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7068.jpg"
-  },
-  {
-    "id": 7241,
-    "problem_id": 7069,
-    "problem": "line D E B, line C E A, line D C, line D A, line A B, line C B, line D E B, line C E A, line D C, line D A, line A B, line C B\nFind the area of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7069.jpg"
-  },
-  {
-    "id": 7242,
-    "problem_id": 7070,
-    "problem": "line M H L, line K J L, line K P M, line P J, line J H, line P H, line M H L, line K J L, line K P M, line P J, line J H, line P H\nJH, JP, and PH are midsegments of \\triangle KLM. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7070.jpg"
-  },
-  {
-    "id": 7243,
-    "problem_id": 7071,
-    "problem": "line M N, line N P, line R P, line M R, line M Q P, line R Q N, line M N, line N P, line R P, line M R, line M Q P, line R Q N\nUse parallelogram MNPR to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7071.jpg"
-  },
-  {
-    "id": 7244,
-    "problem_id": 7072,
-    "problem": "line M N, line N P, line R P, line M R, line M Q P, line R Q N, line M N, line N P, line R P, line M R, line M Q P, line R Q N\nUse parallelogram MNPR to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7072.jpg"
-  },
-  {
-    "id": 7245,
-    "problem_id": 7073,
-    "problem": "line M N, line N P, line R P, line M R, line M Q P, line R Q N, line M N, line N P, line R P, line M R, line M Q P, line R Q N\nUse parallelogram MNPR to find y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7073.jpg"
-  },
-  {
-    "id": 7246,
-    "problem_id": 7074,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 8 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7074.jpg"
-  },
-  {
-    "id": 7247,
-    "problem_id": 7075,
-    "problem": "line B C, line D E F C, line D A, line A E B, line B F G, line B C, line D E F C, line D A, line A E B, line B F G\nFind the measure of \\angle 8 if AB \\perp BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7075.jpg"
-  },
-  {
-    "id": 7248,
-    "problem_id": 7076,
-    "problem": "line P Q R, line P Q R\nQ is the midpoint of PR. What is RP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7076.jpg"
-  },
-  {
-    "id": 7249,
-    "problem_id": 7077,
-    "problem": "line P Q R, line P Q R\nQ is the midpoint of PR. What is RP?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7077.jpg"
-  },
-  {
-    "id": 7250,
-    "problem_id": 7078,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind x in parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7078.jpg"
-  },
-  {
-    "id": 7251,
-    "problem_id": 7079,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind x in parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7079.jpg"
-  },
-  {
-    "id": 7252,
-    "problem_id": 7080,
-    "problem": "line A E B, line A D, line D C, line B C, line D B, line E D, line A E B, line A D, line D C, line B C, line D B, line E D\nFind x in parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7080.jpg"
-  },
-  {
-    "id": 7253,
-    "problem_id": 7081,
-    "problem": "line T U V, line T U V\nU is the midpoint of TV. What is TU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7081.jpg"
-  },
-  {
-    "id": 7254,
-    "problem_id": 7082,
-    "problem": "line T U V, line T U V\nU is the midpoint of TV. What is TU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7082.jpg"
-  },
-  {
-    "id": 7255,
-    "problem_id": 7083,
-    "problem": "line T U V, line T U V\nU is the midpoint of TV. What is TU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7083.jpg"
-  },
-  {
-    "id": 7256,
-    "problem_id": 7084,
-    "problem": "line T U V, line T U V\nU is the midpoint of TV. What is TU?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7084.jpg"
-  },
-  {
-    "id": 7257,
-    "problem_id": 7085,
-    "problem": "line A C D, line B C E, line A C D, line B C E\nWhat is the value of x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7085.jpg"
-  },
-  {
-    "id": 7258,
-    "problem_id": 7086,
-    "problem": "line G N A, line E N B, line E G, line A B, line G N A, line E N B, line E G, line A B\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7086.jpg"
-  },
-  {
-    "id": 7259,
-    "problem_id": 7087,
-    "problem": "line G N A, line E N B, line E G, line A B, line G N A, line E N B, line E G, line A B\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7087.jpg"
-  },
-  {
-    "id": 7260,
-    "problem_id": 7088,
-    "problem": "line G N A, line E N B, line E G, line A B, line G N A, line E N B, line E G, line A B\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7088.jpg"
-  },
-  {
-    "id": 7261,
-    "problem_id": 7089,
-    "problem": "line G N A, line E N B, line E G, line A B, line G N A, line E N B, line E G, line A B\nFind the measure of \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7089.jpg"
-  },
-  {
-    "id": 7263,
-    "problem_id": 7090,
-    "problem": "line J L, line M L, line K M J, line K L, line J L, line M L, line K M J, line K L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7090.jpg"
-  },
-  {
-    "id": 7264,
-    "problem_id": 7091,
-    "problem": "line J L, line M L, line K M J, line K L, line J L, line M L, line K M J, line K L\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7091.jpg"
-  },
-  {
-    "id": 7265,
-    "problem_id": 7092,
-    "problem": "line A E, line E D, line A B C, line C D, line E B, line A E, line E D, line A B C, line C D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7092.jpg"
-  },
-  {
-    "id": 7266,
-    "problem_id": 7093,
-    "problem": "line A E, line E D, line A B C, line C D, line E B, line A E, line E D, line A B C, line C D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7093.jpg"
-  },
-  {
-    "id": 7267,
-    "problem_id": 7094,
-    "problem": "line A E, line E D, line A B C, line C D, line E B, line A E, line E D, line A B C, line C D, line E B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7094.jpg"
-  },
-  {
-    "id": 7268,
-    "problem_id": 7095,
-    "problem": "line A C F, line B C, line B D, line D E, line C E, \\odot D lieson B E C, line A C F, line B C, line B D, line D E, line C E, \\odot D lieson B E C\nWhat is b? Lines that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7095.jpg"
-  },
-  {
-    "id": 7269,
-    "problem_id": 7096,
-    "problem": "line W Z, line Z Y, line W X, line X Y, line W Z, line Z Y, line W X, line X Y\nFind the value of b if WZYX is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7096.jpg"
-  },
-  {
-    "id": 7270,
-    "problem_id": 7097,
-    "problem": "line W Z, line Z Y, line W X, line X Y, line W Z, line Z Y, line W X, line X Y\nFind the value of b if WZYX is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7097.jpg"
-  },
-  {
-    "id": 7271,
-    "problem_id": 7098,
-    "problem": "line P R, line Q R, line Q P, line P R, line Q R, line Q P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7098.jpg"
-  },
-  {
-    "id": 7272,
-    "problem_id": 7099,
-    "problem": "line P R, line Q R, line Q P, line P R, line Q R, line Q P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7099.jpg"
-  },
-  {
-    "id": 7273,
-    "problem_id": 7100,
-    "problem": "line P R, line Q R, line Q P, line P R, line Q R, line Q P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7100.jpg"
-  },
-  {
-    "id": 7274,
-    "problem_id": 7101,
-    "problem": "line P R, line Q R, line Q P, line P R, line Q R, line Q P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7101.jpg"
-  },
-  {
-    "id": 7275,
-    "problem_id": 7102,
-    "problem": "line A C, line B C, line B A, line D A, line D B, line A C, line B C, line B A, line D A, line D B\nFind the perimeter of the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7102.jpg"
-  },
-  {
-    "id": 7276,
-    "problem_id": 7103,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7103.jpg"
-  },
-  {
-    "id": 7277,
-    "problem_id": 7104,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7104.jpg"
-  },
-  {
-    "id": 7278,
-    "problem_id": 7105,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7105.jpg"
-  },
-  {
-    "id": 7279,
-    "problem_id": 7106,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7106.jpg"
-  },
-  {
-    "id": 7280,
-    "problem_id": 7107,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7107.jpg"
-  },
-  {
-    "id": 7281,
-    "problem_id": 7108,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7108.jpg"
-  },
-  {
-    "id": 7282,
-    "problem_id": 7109,
-    "problem": "line A B, line B D, line A D, line C D, line B C, line A B, line B D, line A D, line C D, line B C\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7109.jpg"
-  },
-  {
-    "id": 7283,
-    "problem_id": 7110,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7110.jpg"
-  },
-  {
-    "id": 7284,
-    "problem_id": 7111,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7111.jpg"
-  },
-  {
-    "id": 7285,
-    "problem_id": 7112,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7112.jpg"
-  },
-  {
-    "id": 7286,
-    "problem_id": 7113,
-    "problem": "line D B A, line E B C, line D B A, line E B C\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7113.jpg"
-  },
-  {
-    "id": 7287,
-    "problem_id": 7114,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7114.jpg"
-  },
-  {
-    "id": 7288,
-    "problem_id": 7115,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7115.jpg"
-  },
-  {
-    "id": 7289,
-    "problem_id": 7116,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7116.jpg"
-  },
-  {
-    "id": 7290,
-    "problem_id": 7117,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7117.jpg"
-  },
-  {
-    "id": 7291,
-    "problem_id": 7118,
-    "problem": "line A B, line B D, line C D, line C A, line A D, line A B, line B D, line C D, line C A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7118.jpg"
-  },
-  {
-    "id": 7292,
-    "problem_id": 7119,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7119.jpg"
-  },
-  {
-    "id": 7293,
-    "problem_id": 7120,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7120.jpg"
-  },
-  {
-    "id": 7294,
-    "problem_id": 7121,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7121.jpg"
-  },
-  {
-    "id": 7295,
-    "problem_id": 7122,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7122.jpg"
-  },
-  {
-    "id": 7296,
-    "problem_id": 7123,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7123.jpg"
-  },
-  {
-    "id": 7297,
-    "problem_id": 7124,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7124.jpg"
-  },
-  {
-    "id": 7298,
-    "problem_id": 7125,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle K.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7125.jpg"
-  },
-  {
-    "id": 7299,
-    "problem_id": 7126,
-    "problem": "line D S U C, line B T U F, line A R S E, line D S U C, line B T U F, line A R S E\nFind m \\angle RSU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7126.jpg"
-  },
-  {
-    "id": 7300,
-    "problem_id": 7127,
-    "problem": "line D S U C, line B T U F, line A R S E, line D S U C, line B T U F, line A R S E\nFind m \\angle RSU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7127.jpg"
-  },
-  {
-    "id": 7301,
-    "problem_id": 7128,
-    "problem": "line D S U C, line B T U F, line A R S E, line D S U C, line B T U F, line A R S E\nFind m \\angle RSU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7128.jpg"
-  },
-  {
-    "id": 7302,
-    "problem_id": 7129,
-    "problem": "line D S U C, line B T U F, line A R S E, line D S U C, line B T U F, line A R S E\nFind m \\angle RSU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7129.jpg"
-  },
-  {
-    "id": 7303,
-    "problem_id": 7130,
-    "problem": "line D S U C, line B T U F, line A R S E, line D S U C, line B T U F, line A R S E\nFind m \\angle RSU.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7130.jpg"
-  },
-  {
-    "id": 7304,
-    "problem_id": 7131,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle AOD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7131.jpg"
-  },
-  {
-    "id": 7305,
-    "problem_id": 7132,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle AOD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7132.jpg"
-  },
-  {
-    "id": 7306,
-    "problem_id": 7133,
-    "problem": "line F A O, line O E J, line O B G, line O C H, line O D I, line F A O, line O E J, line O B G, line O C H, line O D I\nFind m \\angle AOD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7133.jpg"
-  },
-  {
-    "id": 7307,
-    "problem_id": 7134,
-    "problem": "line B D, line A C, line A B, line C D, line B D, line A C, line A B, line C D\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7134.jpg"
-  },
-  {
-    "id": 7308,
-    "problem_id": 7135,
-    "problem": "line B D, line A C, line A B, line C D, line B D, line A C, line A B, line C D\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7135.jpg"
-  },
-  {
-    "id": 7309,
-    "problem_id": 7136,
-    "problem": "line B D, line A C, line A B, line C D, line B D, line A C, line A B, line C D\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7136.jpg"
-  },
-  {
-    "id": 7310,
-    "problem_id": 7137,
-    "problem": "line B D, line A C, line A B, line C D, line B D, line A C, line A B, line C D\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7137.jpg"
-  },
-  {
-    "id": 7311,
-    "problem_id": 7138,
-    "problem": "line B D, line A C, line A B, line C D, line B D, line A C, line A B, line C D\nWhat is y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7138.jpg"
-  },
-  {
-    "id": 7312,
-    "problem_id": 7139,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind DF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7139.jpg"
-  },
-  {
-    "id": 7313,
-    "problem_id": 7140,
-    "problem": "line Q R, line X Y, line P S, line Q X P, line R Y S, line Q R, line X Y, line P S, line Q X P, line R Y S\nFind the measure of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7140.jpg"
-  },
-  {
-    "id": 7314,
-    "problem_id": 7141,
-    "problem": "line Q R, line X Y, line P S, line Q X P, line R Y S, line Q R, line X Y, line P S, line Q X P, line R Y S\nFind the measure of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7141.jpg"
-  },
-  {
-    "id": 7315,
-    "problem_id": 7142,
-    "problem": "line Q R, line X Y, line P S, line Q X P, line R Y S, line Q R, line X Y, line P S, line Q X P, line R Y S\nFind the measure of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7142.jpg"
-  },
-  {
-    "id": 7316,
-    "problem_id": 7143,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 5?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7143.jpg"
-  },
-  {
-    "id": 7317,
-    "problem_id": 7144,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 5?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7144.jpg"
-  },
-  {
-    "id": 7318,
-    "problem_id": 7145,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 5?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7145.jpg"
-  },
-  {
-    "id": 7319,
-    "problem_id": 7146,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 5?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7146.jpg"
-  },
-  {
-    "id": 7320,
-    "problem_id": 7147,
-    "problem": "line B A, line B C D, line B E, line A C E, line A D, line D E, line B A, line B C D, line B E, line A C E, line A D, line D E\nWhat is the measure of \\angle 5?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7147.jpg"
-  },
-  {
-    "id": 7321,
-    "problem_id": 7148,
-    "problem": "line B Q D, line A Q C, \\odot Q lieson B A D C, line B Q D, line A Q C, \\odot Q lieson B A D C\nFind m \\widehat BC of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7148.jpg"
-  },
-  {
-    "id": 7322,
-    "problem_id": 7149,
-    "problem": "line B Q D, line A Q C, \\odot Q lieson B A D C, line B Q D, line A Q C, \\odot Q lieson B A D C\nFind m \\widehat BC of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7149.jpg"
-  },
-  {
-    "id": 7323,
-    "problem_id": 7150,
-    "problem": "line F A B C G, line H D B, line B E I, line F A B C G, line H D B, line B E I\nFind m \\angle DBC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7150.jpg"
-  },
-  {
-    "id": 7324,
-    "problem_id": 7151,
-    "problem": "line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C, line m lieson A S U E, line n lieson B T V D, line l lieson F R S T C\nFind m \\angle RSU so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7151.jpg"
-  },
-  {
-    "id": 7325,
-    "problem_id": 7152,
-    "problem": "line C D E, line C B F, \\odot G lieson B D A, line C D E, line C B F, \\odot G lieson B D A\nFind the measure of \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7152.jpg"
-  },
-  {
-    "id": 7326,
-    "problem_id": 7153,
-    "problem": "line C D E, line C B F, \\odot G lieson B D A, line C D E, line C B F, \\odot G lieson B D A\nFind the measure of \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7153.jpg"
-  },
-  {
-    "id": 7327,
-    "problem_id": 7154,
-    "problem": "line A D E, line A C F, line A B G, line B C, line D C, line A D E, line A C F, line A B G, line B C, line D C\nm \\angle BAC = 38, BC = DC = 5, find m \\angle ACD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7154.jpg"
-  },
-  {
-    "id": 7328,
-    "problem_id": 7155,
-    "problem": "line A D E, line A C F, line A B G, line B C, line D C, line A D E, line A C F, line A B G, line B C, line D C\nm \\angle BAC = 38, BC = DC = 5, find m \\angle ACD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7155.jpg"
-  },
-  {
-    "id": 7329,
-    "problem_id": 7156,
-    "problem": "line A D E, line A C F, line A B G, line B C, line D C, line A D E, line A C F, line A B G, line B C, line D C\nm \\angle BAC = 38, BC = DC = 5, find m \\angle ACD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7156.jpg"
-  },
-  {
-    "id": 7330,
-    "problem_id": 7157,
-    "problem": "line A D E, line A C F, line A B G, line B C, line D C, line A D E, line A C F, line A B G, line B C, line D C\nm \\angle BAC = 38, BC = DC = 5, find m \\angle ACD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7157.jpg"
-  },
-  {
-    "id": 7331,
-    "problem_id": 7158,
-    "problem": "line E Q K, line E H, line E N, line H K, line H Q N, line N K, line E Q K, line E H, line E N, line H K, line H Q N, line N K\nIn rhombus EHKN, m \\angle NQK = 7z+6, and m \\angle ENQ = 5z+1. Find the measure of \\angle EQN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7158.jpg"
-  },
-  {
-    "id": 7332,
-    "problem_id": 7159,
-    "problem": "line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O, line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7159.jpg"
-  },
-  {
-    "id": 7333,
-    "problem_id": 7160,
-    "problem": "line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O, line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7160.jpg"
-  },
-  {
-    "id": 7334,
-    "problem_id": 7161,
-    "problem": "line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O, line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7161.jpg"
-  },
-  {
-    "id": 7335,
-    "problem_id": 7162,
-    "problem": "line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O, line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7162.jpg"
-  },
-  {
-    "id": 7336,
-    "problem_id": 7163,
-    "problem": "line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O, line C E L N, line I J K L M, line H G F E D, line A G J P, line B F K O\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7163.jpg"
-  },
-  {
-    "id": 7337,
-    "problem_id": 7164,
-    "problem": "line D C A, line A B E, line D E, line C B, line D C A, line A B E, line D E, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7164.jpg"
-  },
-  {
-    "id": 7338,
-    "problem_id": 7165,
-    "problem": "line D C A, line A B E, line D E, line C B, line D C A, line A B E, line D E, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7165.jpg"
-  },
-  {
-    "id": 7339,
-    "problem_id": 7166,
-    "problem": "line D C A, line A B E, line D E, line C B, line D C A, line A B E, line D E, line C B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7166.jpg"
-  },
-  {
-    "id": 7340,
-    "problem_id": 7167,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7167.jpg"
-  },
-  {
-    "id": 7341,
-    "problem_id": 7168,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7168.jpg"
-  },
-  {
-    "id": 7342,
-    "problem_id": 7169,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7169.jpg"
-  },
-  {
-    "id": 7343,
-    "problem_id": 7170,
-    "problem": "line A D, line B A, line B C, line C D, line A D, line B A, line B C, line C D\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7170.jpg"
-  },
-  {
-    "id": 7344,
-    "problem_id": 7171,
-    "problem": "line Q R P, line Q N, line N P, line N R, line Q R P, line Q N, line N P, line N R\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7171.jpg"
-  },
-  {
-    "id": 7345,
-    "problem_id": 7172,
-    "problem": "line Q R P, line Q N, line N P, line N R, line Q R P, line Q N, line N P, line N R\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7172.jpg"
-  },
-  {
-    "id": 7346,
-    "problem_id": 7173,
-    "problem": "line Q R P, line Q N, line N P, line N R, line Q R P, line Q N, line N P, line N R\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7173.jpg"
-  },
-  {
-    "id": 7347,
-    "problem_id": 7174,
-    "problem": "line Q R P, line Q N, line N P, line N R, line Q R P, line Q N, line N P, line N R\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7174.jpg"
-  },
-  {
-    "id": 7348,
-    "problem_id": 7175,
-    "problem": "line A C D, line B C E, \\odot F lieson B A E D, line A C D, line B C E, \\odot F lieson B A E D\nFind x. Assume that segments that appear to be tangent are tangent.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7175.jpg"
-  },
-  {
-    "id": 7349,
-    "problem_id": 7176,
-    "problem": "line Q S, line P T, line Q P, line S T, line Q S, line P T, line Q P, line S T\nFind x so that PQST is isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7176.jpg"
-  },
-  {
-    "id": 7350,
-    "problem_id": 7177,
-    "problem": "line Q S, line P T, line Q P, line S T, line Q S, line P T, line Q P, line S T\nFind x so that PQST is isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7177.jpg"
-  },
-  {
-    "id": 7351,
-    "problem_id": 7178,
-    "problem": "line Q S, line P T, line Q P, line S T, line Q S, line P T, line Q P, line S T\nFind x so that PQST is isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7178.jpg"
-  },
-  {
-    "id": 7352,
-    "problem_id": 7179,
-    "problem": "line Q S, line P T, line Q P, line S T, line Q S, line P T, line Q P, line S T\nFind x so that PQST is isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7179.jpg"
-  },
-  {
-    "id": 7353,
-    "problem_id": 7180,
-    "problem": "line Q S, line P T, line Q P, line S T, line Q S, line P T, line Q P, line S T\nFind x so that PQST is isosceles trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7180.jpg"
-  },
-  {
-    "id": 7354,
-    "problem_id": 7181,
-    "problem": "line A B, line D C, line A D, line B C, line A B, line D C, line A D, line B C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7181.jpg"
-  },
-  {
-    "id": 7355,
-    "problem_id": 7182,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7182.jpg"
-  },
-  {
-    "id": 7356,
-    "problem_id": 7183,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7183.jpg"
-  },
-  {
-    "id": 7357,
-    "problem_id": 7184,
-    "problem": "line A B C, \\odot B lieson A C, line A B C, \\odot B lieson A C\nFind the area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7184.jpg"
-  },
-  {
-    "id": 7358,
-    "problem_id": 7185,
-    "problem": "line A C F H, line E F G, line B C D, line A C F H, line E F G, line B C D\nFind m \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7185.jpg"
-  },
-  {
-    "id": 7359,
-    "problem_id": 7186,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7186.jpg"
-  },
-  {
-    "id": 7360,
-    "problem_id": 7187,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7187.jpg"
-  },
-  {
-    "id": 7361,
-    "problem_id": 7188,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7188.jpg"
-  },
-  {
-    "id": 7362,
-    "problem_id": 7189,
-    "problem": "line A B C, line D C, line D B, line A D, line A B C, line D C, line D B, line A D\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7189.jpg"
-  },
-  {
-    "id": 7364,
-    "problem_id": 7190,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7190.jpg"
-  },
-  {
-    "id": 7365,
-    "problem_id": 7191,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind m \\angle J.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7191.jpg"
-  },
-  {
-    "id": 7366,
-    "problem_id": 7192,
-    "problem": "line A C, line X Z, line A B, line X Y, line B C, line Y Z, line A C, line X Z, line A B, line X Y, line B C, line Y Z\n\\triangle ABC \\sim \\triangle XYZ. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7192.jpg"
-  },
-  {
-    "id": 7367,
-    "problem_id": 7193,
-    "problem": "line H K F, line E K G, line H G, line F G, line E H, line E F, line H K F, line E K G, line H G, line F G, line E H, line E F\nQuadrilateral EFGH is a rectangle. Find m \\angle HEF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7193.jpg"
-  },
-  {
-    "id": 7368,
-    "problem_id": 7194,
-    "problem": "line H K F, line E K G, line H G, line F G, line E H, line E F, line H K F, line E K G, line H G, line F G, line E H, line E F\nQuadrilateral EFGH is a rectangle. Find m \\angle HEF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7194.jpg"
-  },
-  {
-    "id": 7369,
-    "problem_id": 7195,
-    "problem": "line A B, line B F, line D E F, line A D, line C E, line A B, line B F, line D E F, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7195.jpg"
-  },
-  {
-    "id": 7370,
-    "problem_id": 7196,
-    "problem": "line A B, line B F, line D E F, line A D, line C E, line A B, line B F, line D E F, line A D, line C E\nFind the perimeter of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7196.jpg"
-  },
-  {
-    "id": 7371,
-    "problem_id": 7197,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind WX. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7197.jpg"
-  },
-  {
-    "id": 7372,
-    "problem_id": 7198,
-    "problem": "line W X, line Z Y, line W Z, line X Y, line W X, line Z Y, line W Z, line X Y\nFind WX. Perimeter = 14 miles.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7198.jpg"
-  },
-  {
-    "id": 7374,
-    "problem_id": 7199,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\tan X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7199.jpg"
-  },
-  {
-    "id": 7375,
-    "problem_id": 7200,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\tan X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7200.jpg"
-  },
-  {
-    "id": 7376,
-    "problem_id": 7201,
-    "problem": "line V W, line W X, line V X, line V W, line W X, line V X\nExpress the ratio of \\tan X.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7201.jpg"
-  },
-  {
-    "id": 7377,
-    "problem_id": 7202,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7202.jpg"
-  },
-  {
-    "id": 7378,
-    "problem_id": 7203,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7203.jpg"
-  },
-  {
-    "id": 7379,
-    "problem_id": 7204,
-    "problem": "line Q R, line S R, line P S, line P Q, line Q R, line S R, line P S, line P Q\nFind m \\angle Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7204.jpg"
-  },
-  {
-    "id": 7380,
-    "problem_id": 7205,
-    "problem": "line E G F, line E D, line D G, line D F, line E G F, line E D, line D G, line D F\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7205.jpg"
-  },
-  {
-    "id": 7381,
-    "problem_id": 7206,
-    "problem": "line E G F, line E D, line D G, line D F, line E G F, line E D, line D G, line D F\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7206.jpg"
-  },
-  {
-    "id": 7382,
-    "problem_id": 7207,
-    "problem": "line E G F, line E D, line D G, line D F, line E G F, line E D, line D G, line D F\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7207.jpg"
-  },
-  {
-    "id": 7383,
-    "problem_id": 7208,
-    "problem": "line E G F, line E D, line D G, line D F, line E G F, line E D, line D G, line D F\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7208.jpg"
-  },
-  {
-    "id": 7384,
-    "problem_id": 7209,
-    "problem": "line E G F, line E D, line D G, line D F, line E G F, line E D, line D G, line D F\nFind the measure of \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7209.jpg"
-  },
-  {
-    "id": 7385,
-    "problem_id": 7210,
-    "problem": "line B D, line A C, line D C, line B A, line B D, line A C, line D C, line B A\nFind the value of variable s in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7210.jpg"
-  },
-  {
-    "id": 7386,
-    "problem_id": 7211,
-    "problem": "line B D, line A C, line D C, line B A, line B D, line A C, line D C, line B A\nFind the value of variable s in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7211.jpg"
-  },
-  {
-    "id": 7387,
-    "problem_id": 7212,
-    "problem": "line F A H, line E A G, line E H, line E F, line F G, line G H, line F A H, line E A G, line E H, line E F, line F G, line G H\nFind HE in the kite.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7212.jpg"
-  },
-  {
-    "id": 7388,
-    "problem_id": 7213,
-    "problem": "line D E C, line B C, line A D, line A F B, line F E, line D E C, line B C, line A D, line A F B, line F E\nTrapezoid ABCD has an area of 750 square meters. Find the height of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7213.jpg"
-  },
-  {
-    "id": 7389,
-    "problem_id": 7214,
-    "problem": "line D E C, line B C, line A D, line A F B, line F E, line D E C, line B C, line A D, line A F B, line F E\nTrapezoid ABCD has an area of 750 square meters. Find the height of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7214.jpg"
-  },
-  {
-    "id": 7390,
-    "problem_id": 7215,
-    "problem": "line D E C, line B C, line A D, line A F B, line F E, line D E C, line B C, line A D, line A F B, line F E\nTrapezoid ABCD has an area of 750 square meters. Find the height of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7215.jpg"
-  },
-  {
-    "id": 7391,
-    "problem_id": 7216,
-    "problem": "line D E C, line B C, line A D, line A F B, line F E, line D E C, line B C, line A D, line A F B, line F E\nTrapezoid ABCD has an area of 750 square meters. Find the height of ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7216.jpg"
-  },
-  {
-    "id": 7392,
-    "problem_id": 7217,
-    "problem": "line A D F G, line E F, line E D, line C D B, line C A, line A B, line A D F G, line E F, line E D, line C D B, line C A, line A B\nFind the measure of \\angle 2 if m \\angle 4 = m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7217.jpg"
-  },
-  {
-    "id": 7393,
-    "problem_id": 7218,
-    "problem": "line A D F G, line E F, line E D, line C D B, line C A, line A B, line A D F G, line E F, line E D, line C D B, line C A, line A B\nFind the measure of \\angle 2 if m \\angle 4 = m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7218.jpg"
-  },
-  {
-    "id": 7394,
-    "problem_id": 7219,
-    "problem": "line A B, line C B, \\odot D lieson C A B, line A B, line C B, \\odot D lieson C A B\nFind m \\widehat AC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7219.jpg"
-  },
-  {
-    "id": 7395,
-    "problem_id": 7220,
-    "problem": "line A L H, line B K D H, line H E F C, line L D, line L E, line A L H, line B K D H, line H E F C, line L D, line L E\nFind m \\angle KHL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7220.jpg"
-  },
-  {
-    "id": 7396,
-    "problem_id": 7221,
-    "problem": "line A L H, line B K D H, line H E F C, line L D, line L E, line A L H, line B K D H, line H E F C, line L D, line L E\nFind m \\angle KHL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7221.jpg"
-  },
-  {
-    "id": 7397,
-    "problem_id": 7222,
-    "problem": "line D B, line D C, line A B, line A D, line B C, line D B, line D C, line A B, line A D, line B C\nFind the measure of DB in rectangle ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7222.jpg"
-  },
-  {
-    "id": 7398,
-    "problem_id": 7223,
-    "problem": "line D B, line D C, line A B, line A D, line B C, line D B, line D C, line A B, line A D, line B C\nFind the measure of DB in rectangle ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7223.jpg"
-  },
-  {
-    "id": 7399,
-    "problem_id": 7224,
-    "problem": "line G I, line G H, line H I, line G I, line G H, line H I\nWhat is IH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7224.jpg"
-  },
-  {
-    "id": 7400,
-    "problem_id": 7225,
-    "problem": "line G I, line G H, line H I, line G I, line G H, line H I\nWhat is IH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7225.jpg"
-  },
-  {
-    "id": 7401,
-    "problem_id": 7226,
-    "problem": "line G I, line G H, line H I, line G I, line G H, line H I\nWhat is IH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7226.jpg"
-  },
-  {
-    "id": 7402,
-    "problem_id": 7227,
-    "problem": "line G I, line G H, line H I, line G I, line G H, line H I\nWhat is IH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7227.jpg"
-  },
-  {
-    "id": 7403,
-    "problem_id": 7228,
-    "problem": "line G I, line G H, line H I, line G I, line G H, line H I\nWhat is IH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7228.jpg"
-  },
-  {
-    "id": 7404,
-    "problem_id": 7229,
-    "problem": "line G I, line G H, line H I, line G I, line G H, line H I\nWhat is IH?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7229.jpg"
-  },
-  {
-    "id": 7405,
-    "problem_id": 7230,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7230.jpg"
-  },
-  {
-    "id": 7406,
-    "problem_id": 7231,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7231.jpg"
-  },
-  {
-    "id": 7407,
-    "problem_id": 7232,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7232.jpg"
-  },
-  {
-    "id": 7408,
-    "problem_id": 7233,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7233.jpg"
-  },
-  {
-    "id": 7409,
-    "problem_id": 7234,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7234.jpg"
-  },
-  {
-    "id": 7410,
-    "problem_id": 7235,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7235.jpg"
-  },
-  {
-    "id": 7411,
-    "problem_id": 7236,
-    "problem": "line C P B, line A P, \\odot P lieson A C B, line C P B, line A P, \\odot P lieson A C B\nWhat is the radius?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7236.jpg"
-  },
-  {
-    "id": 7412,
-    "problem_id": 7237,
-    "problem": "line A B C, line C D, line B D, line A B C, line C D, line B D\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7237.jpg"
-  },
-  {
-    "id": 7413,
-    "problem_id": 7238,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7238.jpg"
-  },
-  {
-    "id": 7414,
-    "problem_id": 7239,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7239.jpg"
-  },
-  {
-    "id": 7415,
-    "problem_id": 7240,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7240.jpg"
-  },
-  {
-    "id": 7416,
-    "problem_id": 7241,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7241.jpg"
-  },
-  {
-    "id": 7417,
-    "problem_id": 7242,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7242.jpg"
-  },
-  {
-    "id": 7418,
-    "problem_id": 7243,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7243.jpg"
-  },
-  {
-    "id": 7419,
-    "problem_id": 7244,
-    "problem": "line R Q, line R P, \\odot R lieson Q P, line R Q, line R P, \\odot R lieson Q P\nFind the circumference of \\odot R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7244.jpg"
-  },
-  {
-    "id": 7420,
-    "problem_id": 7245,
-    "problem": "line A C, line C D, line D E, line F E, line B F, line B A, line A C, line C D, line D E, line F E, line B F, line B A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7245.jpg"
-  },
-  {
-    "id": 7421,
-    "problem_id": 7246,
-    "problem": "line A C, line C D, line D E, line F E, line B F, line B A, line A C, line C D, line D E, line F E, line B F, line B A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7246.jpg"
-  },
-  {
-    "id": 7422,
-    "problem_id": 7247,
-    "problem": "line A C, line C D, line D E, line F E, line B F, line B A, line A C, line C D, line D E, line F E, line B F, line B A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7247.jpg"
-  },
-  {
-    "id": 7423,
-    "problem_id": 7248,
-    "problem": "line A C, line C D, line D E, line F E, line B F, line B A, line A C, line C D, line D E, line F E, line B F, line B A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7248.jpg"
-  },
-  {
-    "id": 7424,
-    "problem_id": 7249,
-    "problem": "line A C, line C D, line D E, line F E, line B F, line B A, line A C, line C D, line D E, line F E, line B F, line B A\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7249.jpg"
-  },
-  {
-    "id": 7425,
-    "problem_id": 7250,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7250.jpg"
-  },
-  {
-    "id": 7426,
-    "problem_id": 7251,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7251.jpg"
-  },
-  {
-    "id": 7427,
-    "problem_id": 7252,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7252.jpg"
-  },
-  {
-    "id": 7428,
-    "problem_id": 7253,
-    "problem": "line C E B, line F E, line D E, line A F C, line A D B, line C E B, line F E, line D E, line A F C, line A D B\nFind DE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7253.jpg"
-  },
-  {
-    "id": 7429,
-    "problem_id": 7254,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7254.jpg"
-  },
-  {
-    "id": 7430,
-    "problem_id": 7255,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7255.jpg"
-  },
-  {
-    "id": 7431,
-    "problem_id": 7256,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7256.jpg"
-  },
-  {
-    "id": 7432,
-    "problem_id": 7257,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7257.jpg"
-  },
-  {
-    "id": 7433,
-    "problem_id": 7258,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nFind the area of \\odot Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7258.jpg"
-  },
-  {
-    "id": 7434,
-    "problem_id": 7259,
-    "problem": "line R T, line S T, line R S, line E G, line G F, line E F, line R T, line S T, line R S, line E G, line G F, line E F\nEach pair of polygons is similar. Find EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7259.jpg"
-  },
-  {
-    "id": 7435,
-    "problem_id": 7260,
-    "problem": "line R T, line S T, line R S, line E G, line G F, line E F, line R T, line S T, line R S, line E G, line G F, line E F\nEach pair of polygons is similar. Find EG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7260.jpg"
-  },
-  {
-    "id": 7436,
-    "problem_id": 7261,
-    "problem": "line P S R, line Q U R, line Q T P, \\odot A lieson T S U, line P S R, line Q U R, line Q T P, \\odot A lieson T S U\nThe \\triangle QPR is circumscribed about the circle. Find the perimeter of \\triangle QPR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7261.jpg"
-  },
-  {
-    "id": 7437,
-    "problem_id": 7262,
-    "problem": "line P S R, line Q U R, line Q T P, \\odot A lieson T S U, line P S R, line Q U R, line Q T P, \\odot A lieson T S U\nThe \\triangle QPR is circumscribed about the circle. Find the perimeter of \\triangle QPR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7262.jpg"
-  },
-  {
-    "id": 7438,
-    "problem_id": 7263,
-    "problem": "line T A S, line R C S, line B V S, line T B R, line R V, line T V, line A V, line V C, line T A S, line R C S, line B V S, line T B R, line R V, line T V, line A V, line V C\nThe perpendicular bisectors of \\triangle RST meet at V. Find the length of VR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7263.jpg"
-  },
-  {
-    "id": 7439,
-    "problem_id": 7264,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7264.jpg"
-  },
-  {
-    "id": 7440,
-    "problem_id": 7265,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7265.jpg"
-  },
-  {
-    "id": 7441,
-    "problem_id": 7266,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7266.jpg"
-  },
-  {
-    "id": 7442,
-    "problem_id": 7267,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7267.jpg"
-  },
-  {
-    "id": 7443,
-    "problem_id": 7268,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7268.jpg"
-  },
-  {
-    "id": 7444,
-    "problem_id": 7269,
-    "problem": "line K L, line J K, line J M, line M L, line K L, line J K, line J M, line M L\nFind m \\angle M.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7269.jpg"
-  },
-  {
-    "id": 7445,
-    "problem_id": 7270,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7270.jpg"
-  },
-  {
-    "id": 7446,
-    "problem_id": 7271,
-    "problem": "line B D, line A C D, line A B, line C B, line B D, line A C D, line A B, line C B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7271.jpg"
-  },
-  {
-    "id": 7447,
-    "problem_id": 7272,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of sector DEF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7272.jpg"
-  },
-  {
-    "id": 7448,
-    "problem_id": 7273,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the area of sector DEF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7273.jpg"
-  },
-  {
-    "id": 7449,
-    "problem_id": 7274,
-    "problem": "line H C N, line M N, line M H, line M C, line A B M, line S B E, \\odot M lieson S H N E A, line H C N, line M N, line M H, line M C, line A B M, line S B E, \\odot M lieson S H N E A\nFind m \\widehat ES.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7274.jpg"
-  },
-  {
-    "id": 7450,
-    "problem_id": 7275,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7275.jpg"
-  },
-  {
-    "id": 7451,
-    "problem_id": 7276,
-    "problem": "line A B, line B E C, line D C, line A D, line D E, line A B, line B E C, line D C, line A D, line D E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7276.jpg"
-  },
-  {
-    "id": 7452,
-    "problem_id": 7277,
-    "problem": "line A B, line B E C, line D C, line A D, line D E, line A B, line B E C, line D C, line A D, line D E\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7277.jpg"
-  },
-  {
-    "id": 7453,
-    "problem_id": 7278,
-    "problem": "line F A H, line J H, line F G, line H G, \\odot A lieson F J H G, line F A H, line J H, line F G, line H G, \\odot A lieson F J H G\nSolve for m \\widehat JGF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7278.jpg"
-  },
-  {
-    "id": 7454,
-    "problem_id": 7279,
-    "problem": "line F A H, line J H, line F G, line H G, \\odot A lieson F J H G, line F A H, line J H, line F G, line H G, \\odot A lieson F J H G\nSolve for m \\widehat JGF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7279.jpg"
-  },
-  {
-    "id": 7455,
-    "problem_id": 7280,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of GC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7280.jpg"
-  },
-  {
-    "id": 7456,
-    "problem_id": 7281,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of GC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7281.jpg"
-  },
-  {
-    "id": 7457,
-    "problem_id": 7282,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of GC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7282.jpg"
-  },
-  {
-    "id": 7458,
-    "problem_id": 7283,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of GC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7283.jpg"
-  },
-  {
-    "id": 7459,
-    "problem_id": 7284,
-    "problem": "line B A, line B G C, line A D F C, line A E, line G F E, line B D, line B A, line B G C, line A D F C, line A E, line G F E, line B D\nWhat is the length of GC?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7284.jpg"
-  },
-  {
-    "id": 7460,
-    "problem_id": 7285,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7285.jpg"
-  },
-  {
-    "id": 7461,
-    "problem_id": 7286,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7286.jpg"
-  },
-  {
-    "id": 7462,
-    "problem_id": 7287,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7287.jpg"
-  },
-  {
-    "id": 7463,
-    "problem_id": 7288,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7288.jpg"
-  },
-  {
-    "id": 7464,
-    "problem_id": 7289,
-    "problem": "line C D, line A C, line B D, line A B, line C D, line A C, line B D, line A B\nFor what value of x is the rhombus?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7289.jpg"
-  },
-  {
-    "id": 7465,
-    "problem_id": 7290,
-    "problem": "line H L J, line H K G, line G M J, line H X, line G X, line X J, line X M, line K X, line X L, line H L J, line H K G, line G M J, line H X, line G X, line X J, line X M, line K X, line X L\nKX, LX, and MX are the perpendicular bisectors of \\triangle GHJ. Find XJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7290.jpg"
-  },
-  {
-    "id": 7466,
-    "problem_id": 7291,
-    "problem": "line H L J, line H K G, line G M J, line H X, line G X, line X J, line X M, line K X, line X L, line H L J, line H K G, line G M J, line H X, line G X, line X J, line X M, line K X, line X L\nKX, LX, and MX are the perpendicular bisectors of \\triangle GHJ. Find XJ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7291.jpg"
-  },
-  {
-    "id": 7468,
-    "problem_id": 7292,
-    "problem": "line C D, line A B C, line A D, line B D, line C D, line A B C, line A D, line B D\nSolve for the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7292.jpg"
-  },
-  {
-    "id": 7469,
-    "problem_id": 7293,
-    "problem": "line C D, line A B C, line A D, line B D, line C D, line A B C, line A D, line B D\nSolve for the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7293.jpg"
-  },
-  {
-    "id": 7470,
-    "problem_id": 7294,
-    "problem": "line C D, line A B C, line A D, line B D, line C D, line A B C, line A D, line B D\nSolve for the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7294.jpg"
-  },
-  {
-    "id": 7471,
-    "problem_id": 7295,
-    "problem": "line E D, line B D, line A B, line A E, line A C D, \\odot C lieson A E D B, line E D, line B D, line A B, line A E, line A C D, \\odot C lieson A E D B\nFind the exact area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7295.jpg"
-  },
-  {
-    "id": 7472,
-    "problem_id": 7296,
-    "problem": "line E D, line B D, line A B, line A E, line A C D, \\odot C lieson A E D B, line E D, line B D, line A B, line A E, line A C D, \\odot C lieson A E D B\nFind the exact area of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7296.jpg"
-  },
-  {
-    "id": 7473,
-    "problem_id": 7297,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7297.jpg"
-  },
-  {
-    "id": 7475,
-    "problem_id": 7298,
-    "problem": "line A B, line A F, line F E, line E D, line C D, line B C, line A B, line A F, line F E, line E D, line C D, line B C\nFind m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7298.jpg"
-  },
-  {
-    "id": 7476,
-    "problem_id": 7299,
-    "problem": "line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R, line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R\nQS is a diameter of \\odot V. Find m \\widehat STP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7299.jpg"
-  },
-  {
-    "id": 7477,
-    "problem_id": 7300,
-    "problem": "line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R, line Q V S, line P V, line R V, line V T, \\odot V lieson Q P T S R\nQS is a diameter of \\odot V. Find m \\widehat STP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7300.jpg"
-  },
-  {
-    "id": 7478,
-    "problem_id": 7301,
-    "problem": "line E D, line E F, \\odot E lieson F D, line E D, line E F, \\odot E lieson F D\nFind the length of \\widehat FD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7301.jpg"
-  },
-  {
-    "id": 7479,
-    "problem_id": 7302,
-    "problem": "line T R, line P R, line P T, line T R, line P R, line P T\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7302.jpg"
-  },
-  {
-    "id": 7480,
-    "problem_id": 7303,
-    "problem": "line T R, line P R, line P T, line T R, line P R, line P T\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7303.jpg"
-  },
-  {
-    "id": 7481,
-    "problem_id": 7304,
-    "problem": "line T R, line P R, line P T, line T R, line P R, line P T\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7304.jpg"
-  },
-  {
-    "id": 7482,
-    "problem_id": 7305,
-    "problem": "line T R, line P R, line P T, line T R, line P R, line P T\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7305.jpg"
-  },
-  {
-    "id": 7483,
-    "problem_id": 7306,
-    "problem": "line T R, line P R, line P T, line T R, line P R, line P T\nFind m \\angle R.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7306.jpg"
-  },
-  {
-    "id": 7484,
-    "problem_id": 7307,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7307.jpg"
-  },
-  {
-    "id": 7485,
-    "problem_id": 7308,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7308.jpg"
-  },
-  {
-    "id": 7486,
-    "problem_id": 7309,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7309.jpg"
-  },
-  {
-    "id": 7487,
-    "problem_id": 7310,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7310.jpg"
-  },
-  {
-    "id": 7488,
-    "problem_id": 7311,
-    "problem": "line A W X Y Z B, line J I Y, line J H X, line C G H I Z, line A W X Y Z B, line J I Y, line J H X, line C G H I Z\nIf IJ / XJ = HJ / YJ, m \\angle WXJ = 130 and m \\angle WZG = 20, find m \\angle JHI.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7311.jpg"
-  },
-  {
-    "id": 7489,
-    "problem_id": 7312,
-    "problem": "line b lieson E F G, line a lieson B C D, line c lieson A C F H, line b lieson E F G, line a lieson B C D, line c lieson A C F H\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7312.jpg"
-  },
-  {
-    "id": 7490,
-    "problem_id": 7313,
-    "problem": "line b lieson E F G, line a lieson B C D, line c lieson A C F H, line b lieson E F G, line a lieson B C D, line c lieson A C F H\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7313.jpg"
-  },
-  {
-    "id": 7491,
-    "problem_id": 7314,
-    "problem": "line b lieson E F G, line a lieson B C D, line c lieson A C F H, line b lieson E F G, line a lieson B C D, line c lieson A C F H\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7314.jpg"
-  },
-  {
-    "id": 7492,
-    "problem_id": 7315,
-    "problem": "line b lieson E F G, line a lieson B C D, line c lieson A C F H, line b lieson E F G, line a lieson B C D, line c lieson A C F H\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7315.jpg"
-  },
-  {
-    "id": 7493,
-    "problem_id": 7316,
-    "problem": "line b lieson E F G, line a lieson B C D, line c lieson A C F H, line b lieson E F G, line a lieson B C D, line c lieson A C F H\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7316.jpg"
-  },
-  {
-    "id": 7496,
-    "problem_id": 7317,
-    "problem": "line E F G, line B C G, line A D F, line A E, line A B, line C D, line E F G, line B C G, line A D F, line A E, line A B, line C D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7317.jpg"
-  },
-  {
-    "id": 7497,
-    "problem_id": 7318,
-    "problem": "line E F G, line B C G, line A D F, line A E, line A B, line C D, line E F G, line B C G, line A D F, line A E, line A B, line C D\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7318.jpg"
-  },
-  {
-    "id": 7498,
-    "problem_id": 7319,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7319.jpg"
-  },
-  {
-    "id": 7499,
-    "problem_id": 7320,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7320.jpg"
-  },
-  {
-    "id": 7500,
-    "problem_id": 7321,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7321.jpg"
-  },
-  {
-    "id": 7501,
-    "problem_id": 7322,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7322.jpg"
-  },
-  {
-    "id": 7502,
-    "problem_id": 7323,
-    "problem": "line A B C, line D C, line B D, line A D, line A B C, line D C, line B D, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7323.jpg"
-  },
-  {
-    "id": 7503,
-    "problem_id": 7324,
-    "problem": "line A D E I, line G E F H, line B D C, line A D E I, line G E F H, line B D C\nFind m \\angle DEF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7324.jpg"
-  },
-  {
-    "id": 7504,
-    "problem_id": 7325,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7325.jpg"
-  },
-  {
-    "id": 7505,
-    "problem_id": 7326,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7326.jpg"
-  },
-  {
-    "id": 7506,
-    "problem_id": 7327,
-    "problem": "line R S, line S T P, line R Q P, line Q T, line R S, line S T P, line R Q P, line Q T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7327.jpg"
-  },
-  {
-    "id": 7507,
-    "problem_id": 7328,
-    "problem": "line R S, line S T P, line R Q P, line Q T, line R S, line S T P, line R Q P, line Q T\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7328.jpg"
-  },
-  {
-    "id": 7508,
-    "problem_id": 7329,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is the measure of \\angle 3 in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7329.jpg"
-  },
-  {
-    "id": 7509,
-    "problem_id": 7330,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is the measure of \\angle 3 in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7330.jpg"
-  },
-  {
-    "id": 7510,
-    "problem_id": 7331,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is the measure of \\angle 3 in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7331.jpg"
-  },
-  {
-    "id": 7511,
-    "problem_id": 7332,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is the measure of \\angle 3 in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7332.jpg"
-  },
-  {
-    "id": 7512,
-    "problem_id": 7333,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is the measure of \\angle 3 in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7333.jpg"
-  },
-  {
-    "id": 7513,
-    "problem_id": 7334,
-    "problem": "line A D, line E D, line B E, line B A, line A C E, line B C D, line A D, line E D, line B E, line B A, line A C E, line B C D\nWhat is the measure of \\angle 3 in the kite?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7334.jpg"
-  },
-  {
-    "id": 7514,
-    "problem_id": 7335,
-    "problem": "line D B A, line A C, line D E C, line B E, line D B A, line A C, line D E C, line B E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7335.jpg"
-  },
-  {
-    "id": 7515,
-    "problem_id": 7336,
-    "problem": "line D B A, line A C, line D E C, line B E, line D B A, line A C, line D E C, line B E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7336.jpg"
-  },
-  {
-    "id": 7516,
-    "problem_id": 7337,
-    "problem": "line D B A, line A C, line D E C, line B E, line D B A, line A C, line D E C, line B E\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7337.jpg"
-  },
-  {
-    "id": 7517,
-    "problem_id": 7338,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7338.jpg"
-  },
-  {
-    "id": 7518,
-    "problem_id": 7339,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7339.jpg"
-  },
-  {
-    "id": 7519,
-    "problem_id": 7340,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7340.jpg"
-  },
-  {
-    "id": 7520,
-    "problem_id": 7341,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7341.jpg"
-  },
-  {
-    "id": 7521,
-    "problem_id": 7342,
-    "problem": "line B C, line B D, line B A, line A C, line D C, line B C, line B D, line B A, line A C, line D C\nFind the measure of \\angle 5 in the rhombus.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7342.jpg"
-  },
-  {
-    "id": 7522,
-    "problem_id": 7343,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7343.jpg"
-  },
-  {
-    "id": 7523,
-    "problem_id": 7344,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7344.jpg"
-  },
-  {
-    "id": 7524,
-    "problem_id": 7345,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7345.jpg"
-  },
-  {
-    "id": 7525,
-    "problem_id": 7346,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7346.jpg"
-  },
-  {
-    "id": 7526,
-    "problem_id": 7347,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7347.jpg"
-  },
-  {
-    "id": 7527,
-    "problem_id": 7348,
-    "problem": "line F H, line G H, line F G, line F H, line G H, line F G\nFind m \\angle H.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7348.jpg"
-  },
-  {
-    "id": 7528,
-    "problem_id": 7349,
-    "problem": "line T Y Z, line T W, line W Z, line Y W, line T Y Z, line T W, line W Z, line Y W\nFind WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7349.jpg"
-  },
-  {
-    "id": 7529,
-    "problem_id": 7350,
-    "problem": "line T Y Z, line T W, line W Z, line Y W, line T Y Z, line T W, line W Z, line Y W\nFind WZ.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7350.jpg"
-  },
-  {
-    "id": 7530,
-    "problem_id": 7351,
-    "problem": "line D E, line B E, line C B, line A C D, line A B, line D E, line B E, line C B, line A C D, line A B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7351.jpg"
-  },
-  {
-    "id": 7531,
-    "problem_id": 7352,
-    "problem": "line D E, line B E, line C B, line A C D, line A B, line D E, line B E, line C B, line A C D, line A B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7352.jpg"
-  },
-  {
-    "id": 7532,
-    "problem_id": 7353,
-    "problem": "line D E, line B E, line C B, line A C D, line A B, line D E, line B E, line C B, line A C D, line A B\nFind the area of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7353.jpg"
-  },
-  {
-    "id": 7533,
-    "problem_id": 7354,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7354.jpg"
-  },
-  {
-    "id": 7534,
-    "problem_id": 7355,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7355.jpg"
-  },
-  {
-    "id": 7535,
-    "problem_id": 7356,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7356.jpg"
-  },
-  {
-    "id": 7536,
-    "problem_id": 7357,
-    "problem": "line B C D, line A D, line A B, line A C, line B C D, line A D, line A B, line A C\nDetermine the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7357.jpg"
-  },
-  {
-    "id": 7537,
-    "problem_id": 7358,
-    "problem": "line R A S, line Q A P, \\odot P lieson R S Q, line R A S, line Q A P, \\odot P lieson R S Q\nFind RS.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7358.jpg"
-  },
-  {
-    "id": 7538,
-    "problem_id": 7359,
-    "problem": "line P S, line P X Q, line X Y, line Q R, line R Y S, line P S, line P X Q, line X Y, line Q R, line R Y S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7359.jpg"
-  },
-  {
-    "id": 7539,
-    "problem_id": 7360,
-    "problem": "line P S, line P X Q, line X Y, line Q R, line R Y S, line P S, line P X Q, line X Y, line Q R, line R Y S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7360.jpg"
-  },
-  {
-    "id": 7540,
-    "problem_id": 7361,
-    "problem": "line P S, line P X Q, line X Y, line Q R, line R Y S, line P S, line P X Q, line X Y, line Q R, line R Y S\nFind QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7361.jpg"
-  },
-  {
-    "id": 7543,
-    "problem_id": 7362,
-    "problem": "line E F A, line C D E, line E G B, line E F A, line C D E, line E G B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7362.jpg"
-  },
-  {
-    "id": 7544,
-    "problem_id": 7363,
-    "problem": "line E F A, line C D E, line E G B, line E F A, line C D E, line E G B\nFind m \\angle FED.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7363.jpg"
-  },
-  {
-    "id": 7545,
-    "problem_id": 7364,
-    "problem": "line A C, line A D B, line C B, line C D, line A C, line A D B, line C B, line C D\nIf D is the midpoint of AB, find the length of AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7364.jpg"
-  },
-  {
-    "id": 7546,
-    "problem_id": 7365,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nWhat is the length of QR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7365.jpg"
-  },
-  {
-    "id": 7547,
-    "problem_id": 7366,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nWhat is the length of QR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7366.jpg"
-  },
-  {
-    "id": 7548,
-    "problem_id": 7367,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nWhat is the length of QR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7367.jpg"
-  },
-  {
-    "id": 7549,
-    "problem_id": 7368,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nWhat is the length of QR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7368.jpg"
-  },
-  {
-    "id": 7550,
-    "problem_id": 7369,
-    "problem": "line P Q, line P S R, line Q R, line S Q, line P Q, line P S R, line Q R, line S Q\nWhat is the length of QR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7369.jpg"
-  },
-  {
-    "id": 7551,
-    "problem_id": 7370,
-    "problem": "line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F, line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7370.jpg"
-  },
-  {
-    "id": 7552,
-    "problem_id": 7371,
-    "problem": "line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F, line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7371.jpg"
-  },
-  {
-    "id": 7553,
-    "problem_id": 7372,
-    "problem": "line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F, line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7372.jpg"
-  },
-  {
-    "id": 7554,
-    "problem_id": 7373,
-    "problem": "line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F, line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7373.jpg"
-  },
-  {
-    "id": 7555,
-    "problem_id": 7374,
-    "problem": "line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F, line D C, line G E, line G H, line G A, line B C, line F C, line A E H, line B D F\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7374.jpg"
-  },
-  {
-    "id": 7556,
-    "problem_id": 7375,
-    "problem": "line G A J, line G H, \\odot A lieson G J H, line G A J, line G H, \\odot A lieson G J H\nFind m \\widehat GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7375.jpg"
-  },
-  {
-    "id": 7557,
-    "problem_id": 7376,
-    "problem": "line G A J, line G H, \\odot A lieson G J H, line G A J, line G H, \\odot A lieson G J H\nFind m \\widehat GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7376.jpg"
-  },
-  {
-    "id": 7558,
-    "problem_id": 7377,
-    "problem": "line G A J, line G H, \\odot A lieson G J H, line G A J, line G H, \\odot A lieson G J H\nFind m \\widehat GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7377.jpg"
-  },
-  {
-    "id": 7559,
-    "problem_id": 7378,
-    "problem": "line G A J, line G H, \\odot A lieson G J H, line G A J, line G H, \\odot A lieson G J H\nFind m \\widehat GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7378.jpg"
-  },
-  {
-    "id": 7560,
-    "problem_id": 7379,
-    "problem": "line J L N, line M N, line J K M, line K L, line J L N, line M N, line J K M, line K L\nKL \\parallel MN. Find the measure of JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7379.jpg"
-  },
-  {
-    "id": 7561,
-    "problem_id": 7380,
-    "problem": "line A C, line B A, \\odot A lieson C B, line A C, line B A, \\odot A lieson C B\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7380.jpg"
-  },
-  {
-    "id": 7562,
-    "problem_id": 7381,
-    "problem": "line A C, line B A, \\odot A lieson C B, line A C, line B A, \\odot A lieson C B\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7381.jpg"
-  },
-  {
-    "id": 7563,
-    "problem_id": 7382,
-    "problem": "line A C, line B A, \\odot A lieson C B, line A C, line B A, \\odot A lieson C B\nFind the circumference of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7382.jpg"
-  },
-  {
-    "id": 7564,
-    "problem_id": 7383,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nWhat is the length of \\widehat PR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7383.jpg"
-  },
-  {
-    "id": 7565,
-    "problem_id": 7384,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nWhat is the length of \\widehat PR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7384.jpg"
-  },
-  {
-    "id": 7566,
-    "problem_id": 7385,
-    "problem": "line P R, line Q R, line Q P, \\odot Q lieson R P, line P R, line Q R, line Q P, \\odot Q lieson R P\nWhat is the length of \\widehat PR?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7385.jpg"
-  },
-  {
-    "id": 7567,
-    "problem_id": 7386,
-    "problem": "line F A E D H, line G C E B I, \\odot J lieson A B D C, line F A E D H, line G C E B I, \\odot J lieson A B D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7386.jpg"
-  },
-  {
-    "id": 7568,
-    "problem_id": 7387,
-    "problem": "line F A E D H, line G C E B I, \\odot J lieson A B D C, line F A E D H, line G C E B I, \\odot J lieson A B D C\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7387.jpg"
-  },
-  {
-    "id": 7569,
-    "problem_id": 7388,
-    "problem": "line C B, line C A, \\odot C lieson B A, line C B, line C A, \\odot C lieson B A\nDetermine the length of CB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7388.jpg"
-  },
-  {
-    "id": 7570,
-    "problem_id": 7389,
-    "problem": "line Y Z, line X Y, line X Z, line J K, line K L, line J L, line Y Z, line X Y, line X Z, line J K, line K L, line J L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7389.jpg"
-  },
-  {
-    "id": 7571,
-    "problem_id": 7390,
-    "problem": "line Y Z, line X Y, line X Z, line J K, line K L, line J L, line Y Z, line X Y, line X Z, line J K, line K L, line J L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7390.jpg"
-  },
-  {
-    "id": 7572,
-    "problem_id": 7391,
-    "problem": "line Y Z, line X Y, line X Z, line J K, line K L, line J L, line Y Z, line X Y, line X Z, line J K, line K L, line J L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7391.jpg"
-  },
-  {
-    "id": 7573,
-    "problem_id": 7392,
-    "problem": "line Y Z, line X Y, line X Z, line J K, line K L, line J L, line Y Z, line X Y, line X Z, line J K, line K L, line J L\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7392.jpg"
-  },
-  {
-    "id": 7574,
-    "problem_id": 7393,
-    "problem": "line E D H A, line m lieson F D C, line l lieson G H B, line E D H A, line m lieson F D C, line l lieson G H B\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7393.jpg"
-  },
-  {
-    "id": 7575,
-    "problem_id": 7394,
-    "problem": "line E D H A, line m lieson F D C, line l lieson G H B, line E D H A, line m lieson F D C, line l lieson G H B\nFind x so that line m \\parallel line n.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7394.jpg"
-  },
-  {
-    "id": 7576,
-    "problem_id": 7395,
-    "problem": "line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E, line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E\nDCHG \\sim EFAB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7395.jpg"
-  },
-  {
-    "id": 7577,
-    "problem_id": 7396,
-    "problem": "line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E, line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E\nDCHG \\sim EFAB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7396.jpg"
-  },
-  {
-    "id": 7578,
-    "problem_id": 7397,
-    "problem": "line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E, line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E\nDCHG \\sim EFAB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7397.jpg"
-  },
-  {
-    "id": 7579,
-    "problem_id": 7398,
-    "problem": "line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E, line G H, line A B, line D C, line C H, line D G, line F E, line A F, line B E\nDCHG \\sim EFAB. Find the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7398.jpg"
-  },
-  {
-    "id": 7580,
-    "problem_id": 7399,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7399.jpg"
-  },
-  {
-    "id": 7581,
-    "problem_id": 7400,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7400.jpg"
-  },
-  {
-    "id": 7582,
-    "problem_id": 7401,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7401.jpg"
-  },
-  {
-    "id": 7583,
-    "problem_id": 7402,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7402.jpg"
-  },
-  {
-    "id": 7584,
-    "problem_id": 7403,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7403.jpg"
-  },
-  {
-    "id": 7585,
-    "problem_id": 7404,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7404.jpg"
-  },
-  {
-    "id": 7586,
-    "problem_id": 7405,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7405.jpg"
-  },
-  {
-    "id": 7587,
-    "problem_id": 7406,
-    "problem": "line P Q A, line N P, line N Q, line P Q A, line N P, line N Q\nFind m \\angle N.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7406.jpg"
-  },
-  {
-    "id": 7588,
-    "problem_id": 7407,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7407.jpg"
-  },
-  {
-    "id": 7589,
-    "problem_id": 7408,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7408.jpg"
-  },
-  {
-    "id": 7590,
-    "problem_id": 7409,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7409.jpg"
-  },
-  {
-    "id": 7591,
-    "problem_id": 7410,
-    "problem": "line A C, line C D, line B D, line B A, line A D, line A C, line C D, line B D, line B A, line A D\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7410.jpg"
-  },
-  {
-    "id": 7592,
-    "problem_id": 7411,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7411.jpg"
-  },
-  {
-    "id": 7593,
-    "problem_id": 7412,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7412.jpg"
-  },
-  {
-    "id": 7594,
-    "problem_id": 7413,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7413.jpg"
-  },
-  {
-    "id": 7595,
-    "problem_id": 7414,
-    "problem": "line A B, line C B, line D C, line D A, line A B, line C B, line D C, line D A\nFind the perimeter of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7414.jpg"
-  },
-  {
-    "id": 7596,
-    "problem_id": 7415,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind the length of CB in the isosceles triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7415.jpg"
-  },
-  {
-    "id": 7597,
-    "problem_id": 7416,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind the length of CB in the isosceles triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7416.jpg"
-  },
-  {
-    "id": 7598,
-    "problem_id": 7417,
-    "problem": "line A C, line C B, line A B, line A C, line C B, line A B\nFind the length of CB in the isosceles triangle ABC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7417.jpg"
-  },
-  {
-    "id": 7599,
-    "problem_id": 7418,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7418.jpg"
-  },
-  {
-    "id": 7600,
-    "problem_id": 7419,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7419.jpg"
-  },
-  {
-    "id": 7601,
-    "problem_id": 7420,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7420.jpg"
-  },
-  {
-    "id": 7602,
-    "problem_id": 7421,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7421.jpg"
-  },
-  {
-    "id": 7603,
-    "problem_id": 7422,
-    "problem": "line E H, line E F G, line G H, line F H, line E H, line E F G, line G H, line F H\nFind GH.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7422.jpg"
-  },
-  {
-    "id": 7604,
-    "problem_id": 7423,
-    "problem": "line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A, line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7423.jpg"
-  },
-  {
-    "id": 7605,
-    "problem_id": 7424,
-    "problem": "line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A, line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7424.jpg"
-  },
-  {
-    "id": 7606,
-    "problem_id": 7425,
-    "problem": "line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A, line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7425.jpg"
-  },
-  {
-    "id": 7607,
-    "problem_id": 7426,
-    "problem": "line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A, line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7426.jpg"
-  },
-  {
-    "id": 7608,
-    "problem_id": 7427,
-    "problem": "line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A, line C F, line B E, line B A, line A C, line D C, line E F, \\odot D lieson B E F C A\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7427.jpg"
-  },
-  {
-    "id": 7609,
-    "problem_id": 7428,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7428.jpg"
-  },
-  {
-    "id": 7610,
-    "problem_id": 7429,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7429.jpg"
-  },
-  {
-    "id": 7611,
-    "problem_id": 7430,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7430.jpg"
-  },
-  {
-    "id": 7612,
-    "problem_id": 7431,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7431.jpg"
-  },
-  {
-    "id": 7613,
-    "problem_id": 7432,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7432.jpg"
-  },
-  {
-    "id": 7614,
-    "problem_id": 7433,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7433.jpg"
-  },
-  {
-    "id": 7615,
-    "problem_id": 7434,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the value of variable y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7434.jpg"
-  },
-  {
-    "id": 7616,
-    "problem_id": 7435,
-    "problem": "line C E, line F E, line B F, line B A, line A C, line D C, \\odot D lieson B F E C A, line C E, line F E, line B F, line B A, line A C, line D C, \\odot D lieson B F E C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7435.jpg"
-  },
-  {
-    "id": 7617,
-    "problem_id": 7436,
-    "problem": "line C E, line F E, line B F, line B A, line A C, line D C, \\odot D lieson B F E C A, line C E, line F E, line B F, line B A, line A C, line D C, \\odot D lieson B F E C A\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7436.jpg"
-  },
-  {
-    "id": 7618,
-    "problem_id": 7437,
-    "problem": "line A B C, line C G F, line E H F, line A D E, \\odot I lieson D H G B, line A B C, line C G F, line E H F, line A D E, \\odot I lieson D H G B\nThe polygon below circumscribes the circle. Find the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7437.jpg"
-  },
-  {
-    "id": 7619,
-    "problem_id": 7438,
-    "problem": "line A D, line A B C, line D C, line D B, line A D, line A B C, line D C, line D B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7438.jpg"
-  },
-  {
-    "id": 7620,
-    "problem_id": 7439,
-    "problem": "line A D, line A B C, line D C, line D B, line A D, line A B C, line D C, line D B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7439.jpg"
-  },
-  {
-    "id": 7621,
-    "problem_id": 7440,
-    "problem": "line A D, line A B C, line D C, line D B, line A D, line A B C, line D C, line D B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7440.jpg"
-  },
-  {
-    "id": 7622,
-    "problem_id": 7441,
-    "problem": "line A D, line A B C, line D C, line D B, line A D, line A B C, line D C, line D B\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7441.jpg"
-  },
-  {
-    "id": 7623,
-    "problem_id": 7442,
-    "problem": "line A B D, line E D C, line I J B, line H G J, line G E F, line A B D, line E D C, line I J B, line H G J, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7442.jpg"
-  },
-  {
-    "id": 7624,
-    "problem_id": 7443,
-    "problem": "line A B D, line E D C, line I J B, line H G J, line G E F, line A B D, line E D C, line I J B, line H G J, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7443.jpg"
-  },
-  {
-    "id": 7625,
-    "problem_id": 7444,
-    "problem": "line A B D, line E D C, line I J B, line H G J, line G E F, line A B D, line E D C, line I J B, line H G J, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7444.jpg"
-  },
-  {
-    "id": 7627,
-    "problem_id": 7445,
-    "problem": "line A B D, line E D C, line I J B, line H G J, line G E F, line A B D, line E D C, line I J B, line H G J, line G E F\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7445.jpg"
-  },
-  {
-    "id": 7628,
-    "problem_id": 7446,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7446.jpg"
-  },
-  {
-    "id": 7629,
-    "problem_id": 7447,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7447.jpg"
-  },
-  {
-    "id": 7630,
-    "problem_id": 7448,
-    "problem": "line E A C F, line A B, line B C D, line A D, line E A C F, line A B, line B C D, line A D\nFind AB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7448.jpg"
-  },
-  {
-    "id": 7631,
-    "problem_id": 7449,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7449.jpg"
-  },
-  {
-    "id": 7633,
-    "problem_id": 7450,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7450.jpg"
-  },
-  {
-    "id": 7634,
-    "problem_id": 7451,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7451.jpg"
-  },
-  {
-    "id": 7635,
-    "problem_id": 7452,
-    "problem": "line B C, line A C, line B A, line B C, line A C, line B A\nFind m \\angle A.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7452.jpg"
-  },
-  {
-    "id": 7636,
-    "problem_id": 7453,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7453.jpg"
-  },
-  {
-    "id": 7637,
-    "problem_id": 7454,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7454.jpg"
-  },
-  {
-    "id": 7638,
-    "problem_id": 7455,
-    "problem": "line D C B, line A C E, line A D, line B E, line D C B, line A C E, line A D, line B E\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7455.jpg"
-  },
-  {
-    "id": 7639,
-    "problem_id": 7456,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7456.jpg"
-  },
-  {
-    "id": 7640,
-    "problem_id": 7457,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7457.jpg"
-  },
-  {
-    "id": 7641,
-    "problem_id": 7458,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7458.jpg"
-  },
-  {
-    "id": 7642,
-    "problem_id": 7459,
-    "problem": "line C A, line A D, line C D, \\odot B lieson C D A, line C A, line A D, line C D, \\odot B lieson C D A\nDetermine d.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7459.jpg"
-  },
-  {
-    "id": 7643,
-    "problem_id": 7460,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable w in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7460.jpg"
-  },
-  {
-    "id": 7644,
-    "problem_id": 7461,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable w in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7461.jpg"
-  },
-  {
-    "id": 7645,
-    "problem_id": 7462,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable w in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7462.jpg"
-  },
-  {
-    "id": 7646,
-    "problem_id": 7463,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable w in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7463.jpg"
-  },
-  {
-    "id": 7647,
-    "problem_id": 7464,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable w in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7464.jpg"
-  },
-  {
-    "id": 7648,
-    "problem_id": 7465,
-    "problem": "line C D, line A B, line B D, line A C, line C D, line A B, line B D, line A C\nFind the value of variable w in the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7465.jpg"
-  },
-  {
-    "id": 7649,
-    "problem_id": 7466,
-    "problem": "line B C D E, line A C G, line D F, line B C D E, line A C G, line D F\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7466.jpg"
-  },
-  {
-    "id": 7650,
-    "problem_id": 7467,
-    "problem": "line B C D E, line A C G, line D F, line B C D E, line A C G, line D F\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7467.jpg"
-  },
-  {
-    "id": 7651,
-    "problem_id": 7468,
-    "problem": "line B C D E, line A C G, line D F, line B C D E, line A C G, line D F\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7468.jpg"
-  },
-  {
-    "id": 7652,
-    "problem_id": 7469,
-    "problem": "line B C D E, line A C G, line D F, line B C D E, line A C G, line D F\nFind the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7469.jpg"
-  },
-  {
-    "id": 7653,
-    "problem_id": 7470,
-    "problem": "line B C D, line A C, \\odot E lieson C A, line B C D, line A C, \\odot E lieson C A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7470.jpg"
-  },
-  {
-    "id": 7654,
-    "problem_id": 7471,
-    "problem": "line B C D, line A C, \\odot E lieson C A, line B C D, line A C, \\odot E lieson C A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7471.jpg"
-  },
-  {
-    "id": 7655,
-    "problem_id": 7472,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind CF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7472.jpg"
-  },
-  {
-    "id": 7656,
-    "problem_id": 7473,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind CF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7473.jpg"
-  },
-  {
-    "id": 7657,
-    "problem_id": 7474,
-    "problem": "line A D C, line A E B, line B F C, line D F, line E D, line A D C, line A E B, line B F C, line D F, line E D\nFind CF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7474.jpg"
-  },
-  {
-    "id": 7658,
-    "problem_id": 7475,
-    "problem": "line R P, line Q P, line Q R, line R P, line Q P, line Q R\nExpress the ratio of \\sin Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7475.jpg"
-  },
-  {
-    "id": 7659,
-    "problem_id": 7476,
-    "problem": "line R P, line Q P, line Q R, line R P, line Q P, line Q R\nExpress the ratio of \\sin Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7476.jpg"
-  },
-  {
-    "id": 7660,
-    "problem_id": 7477,
-    "problem": "line R P, line Q P, line Q R, line R P, line Q P, line Q R\nExpress the ratio of \\sin Q.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7477.jpg"
-  },
-  {
-    "id": 7661,
-    "problem_id": 7478,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7478.jpg"
-  },
-  {
-    "id": 7662,
-    "problem_id": 7479,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7479.jpg"
-  },
-  {
-    "id": 7663,
-    "problem_id": 7480,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7480.jpg"
-  },
-  {
-    "id": 7664,
-    "problem_id": 7481,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7481.jpg"
-  },
-  {
-    "id": 7665,
-    "problem_id": 7482,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nDetermine the perimeter of the polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7482.jpg"
-  },
-  {
-    "id": 7666,
-    "problem_id": 7483,
-    "problem": "line Q R, line P S, line S R, line P Q, line Q R, line P S, line S R, line P Q\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7483.jpg"
-  },
-  {
-    "id": 7667,
-    "problem_id": 7484,
-    "problem": "line Q R, line P S, line S R, line P Q, line Q R, line P S, line S R, line P Q\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7484.jpg"
-  },
-  {
-    "id": 7668,
-    "problem_id": 7485,
-    "problem": "line Q R, line P S, line S R, line P Q, line Q R, line P S, line S R, line P Q\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7485.jpg"
-  },
-  {
-    "id": 7669,
-    "problem_id": 7486,
-    "problem": "line Q R, line P S, line S R, line P Q, line Q R, line P S, line S R, line P Q\nFind c.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7486.jpg"
-  },
-  {
-    "id": 7670,
-    "problem_id": 7487,
-    "problem": "line D E, line E F, \\odot E lieson D F, line D E, line E F, \\odot E lieson D F\nFind the diameter of the circle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7487.jpg"
-  },
-  {
-    "id": 7671,
-    "problem_id": 7488,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7488.jpg"
-  },
-  {
-    "id": 7672,
-    "problem_id": 7489,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7489.jpg"
-  },
-  {
-    "id": 7673,
-    "problem_id": 7490,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7490.jpg"
-  },
-  {
-    "id": 7674,
-    "problem_id": 7491,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7491.jpg"
-  },
-  {
-    "id": 7675,
-    "problem_id": 7492,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7492.jpg"
-  },
-  {
-    "id": 7676,
-    "problem_id": 7493,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7493.jpg"
-  },
-  {
-    "id": 7677,
-    "problem_id": 7494,
-    "problem": "line A B, line D C B, line A D, line A C, line A B, line D C B, line A D, line A C\nWhat is the area of the triangle?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7494.jpg"
-  },
-  {
-    "id": 7678,
-    "problem_id": 7495,
-    "problem": "line M R, line R P, line M P, line M R, line R P, line M P\nFind m \\angle MRP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7495.jpg"
-  },
-  {
-    "id": 7679,
-    "problem_id": 7496,
-    "problem": "line M R, line R P, line M P, line M R, line R P, line M P\nFind m \\angle MRP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7496.jpg"
-  },
-  {
-    "id": 7680,
-    "problem_id": 7497,
-    "problem": "line M R, line R P, line M P, line M R, line R P, line M P\nFind m \\angle MRP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7497.jpg"
-  },
-  {
-    "id": 7681,
-    "problem_id": 7498,
-    "problem": "line M R, line R P, line M P, line M R, line R P, line M P\nFind m \\angle MRP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7498.jpg"
-  },
-  {
-    "id": 7682,
-    "problem_id": 7499,
-    "problem": "line M R, line R P, line M P, line M R, line R P, line M P\nFind m \\angle MRP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7499.jpg"
-  },
-  {
-    "id": 7683,
-    "problem_id": 7500,
-    "problem": "line M R, line R P, line M P, line M R, line R P, line M P\nFind m \\angle MRP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7500.jpg"
-  },
-  {
-    "id": 7684,
-    "problem_id": 7501,
-    "problem": "line A D, line A B C, line C F, line D E F, \\odot G lieson E B, line A D, line A B C, line C F, line D E F, \\odot G lieson E B\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7501.jpg"
-  },
-  {
-    "id": 7685,
-    "problem_id": 7502,
-    "problem": "line A D, line A B C, line C F, line D E F, \\odot G lieson E B, line A D, line A B C, line C F, line D E F, \\odot G lieson E B\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7502.jpg"
-  },
-  {
-    "id": 7686,
-    "problem_id": 7503,
-    "problem": "line A D, line A B C, line C F, line D E F, \\odot G lieson E B, line A D, line A B C, line C F, line D E F, \\odot G lieson E B\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7503.jpg"
-  },
-  {
-    "id": 7687,
-    "problem_id": 7504,
-    "problem": "line A D, line A B C, line C F, line D E F, \\odot G lieson E B, line A D, line A B C, line C F, line D E F, \\odot G lieson E B\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7504.jpg"
-  },
-  {
-    "id": 7688,
-    "problem_id": 7505,
-    "problem": "line R U T, line Q U S, line R S, line Q T, \\odot A lieson R Q T S, line R U T, line Q U S, line R S, line Q T, \\odot A lieson R Q T S\nm \\widehat QR = 40, and m \\widehat TS = 110. What is m \\angle 5?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7505.jpg"
-  },
-  {
-    "id": 7689,
-    "problem_id": 7506,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7506.jpg"
-  },
-  {
-    "id": 7690,
-    "problem_id": 7507,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7507.jpg"
-  },
-  {
-    "id": 7691,
-    "problem_id": 7508,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7508.jpg"
-  },
-  {
-    "id": 7692,
-    "problem_id": 7509,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7509.jpg"
-  },
-  {
-    "id": 7693,
-    "problem_id": 7510,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7510.jpg"
-  },
-  {
-    "id": 7694,
-    "problem_id": 7511,
-    "problem": "line R Q, line P Q, line P R, line R Q, line P Q, line P R\nFind the measure of \\angle P.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7511.jpg"
-  },
-  {
-    "id": 7695,
-    "problem_id": 7512,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind LN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7512.jpg"
-  },
-  {
-    "id": 7696,
-    "problem_id": 7513,
-    "problem": "line L N, line M N, line L M, line L N, line M N, line L M\nFind LN.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7513.jpg"
-  },
-  {
-    "id": 7697,
-    "problem_id": 7514,
-    "problem": "line L M, line M A K, line L K, \\odot A lieson L K M, line L M, line M A K, line L K, \\odot A lieson L K M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7514.jpg"
-  },
-  {
-    "id": 7698,
-    "problem_id": 7515,
-    "problem": "line L M, line M A K, line L K, \\odot A lieson L K M, line L M, line M A K, line L K, \\odot A lieson L K M\nDetermine the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7515.jpg"
-  },
-  {
-    "id": 7699,
-    "problem_id": 7516,
-    "problem": "line t lieson A C F I K, line n lieson J I H, line m lieson E F G, line l lieson B C D, line t lieson A C F I K, line n lieson J I H, line m lieson E F G, line l lieson B C D\nm \\angle 9 = 75. Find the measure of \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7516.jpg"
-  },
-  {
-    "id": 7700,
-    "problem_id": 7517,
-    "problem": "line C U D, line B V D, line C T B, \\odot A lieson T V U, line C U D, line B V D, line C T B, \\odot A lieson T V U\nThe circle is inscribed in \\triangle CBD. Find the perimeter of \\triangle CBD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7517.jpg"
-  },
-  {
-    "id": 7701,
-    "problem_id": 7518,
-    "problem": "line A C, line D C, line A B, line B C, line A D, line A C, line D C, line A B, line B C, line A D\nABCD is a square. Find m \\angle D.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7518.jpg"
-  },
-  {
-    "id": 7702,
-    "problem_id": 7519,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind m \\angle Y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7519.jpg"
-  },
-  {
-    "id": 7703,
-    "problem_id": 7520,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7520.jpg"
-  },
-  {
-    "id": 7704,
-    "problem_id": 7521,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find LP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7521.jpg"
-  },
-  {
-    "id": 7705,
-    "problem_id": 7522,
-    "problem": "line X Y, line Z Y, \\odot Y lieson Z X, line X Y, line Z Y, \\odot Y lieson Z X\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7522.jpg"
-  },
-  {
-    "id": 7706,
-    "problem_id": 7523,
-    "problem": "line X Y, line Z Y, \\odot Y lieson Z X, line X Y, line Z Y, \\odot Y lieson Z X\nFind the area of the shaded sector.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7523.jpg"
-  },
-  {
-    "id": 7707,
-    "problem_id": 7524,
-    "problem": "line B A, line B D, line D C, line A C, line B A, line B D, line D C, line A C\nFind y so that the quadrilateral is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7524.jpg"
-  },
-  {
-    "id": 7708,
-    "problem_id": 7525,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7525.jpg"
-  },
-  {
-    "id": 7709,
-    "problem_id": 7526,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7526.jpg"
-  },
-  {
-    "id": 7710,
-    "problem_id": 7527,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7527.jpg"
-  },
-  {
-    "id": 7711,
-    "problem_id": 7528,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7528.jpg"
-  },
-  {
-    "id": 7712,
-    "problem_id": 7529,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7529.jpg"
-  },
-  {
-    "id": 7713,
-    "problem_id": 7530,
-    "problem": "line L K, line J L, line J K, line L K, line J L, line J K\nFind m \\angle JLK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7530.jpg"
-  },
-  {
-    "id": 7714,
-    "problem_id": 7531,
-    "problem": "line C B, line A C E, line E D, line B D, line A B, line C B, line A C E, line E D, line B D, line A B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7531.jpg"
-  },
-  {
-    "id": 7715,
-    "problem_id": 7532,
-    "problem": "line C B, line A C E, line E D, line B D, line A B, line C B, line A C E, line E D, line B D, line A B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7532.jpg"
-  },
-  {
-    "id": 7716,
-    "problem_id": 7533,
-    "problem": "line C B, line A C E, line E D, line B D, line A B, line C B, line A C E, line E D, line B D, line A B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7533.jpg"
-  },
-  {
-    "id": 7717,
-    "problem_id": 7534,
-    "problem": "line C B, line A C E, line E D, line B D, line A B, line C B, line A C E, line E D, line B D, line A B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7534.jpg"
-  },
-  {
-    "id": 7718,
-    "problem_id": 7535,
-    "problem": "line C B, line A C E, line E D, line B D, line A B, line C B, line A C E, line E D, line B D, line A B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7535.jpg"
-  },
-  {
-    "id": 7719,
-    "problem_id": 7536,
-    "problem": "line C B, line A C E, line E D, line B D, line A B, line C B, line A C E, line E D, line B D, line A B\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7536.jpg"
-  },
-  {
-    "id": 7720,
-    "problem_id": 7537,
-    "problem": "line E D, line A B, \\odot C lieson A E D B, line E D, line A B, \\odot C lieson A E D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7537.jpg"
-  },
-  {
-    "id": 7721,
-    "problem_id": 7538,
-    "problem": "line E D, line A B, \\odot C lieson A E D B, line E D, line A B, \\odot C lieson A E D B\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7538.jpg"
-  },
-  {
-    "id": 7722,
-    "problem_id": 7539,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7539.jpg"
-  },
-  {
-    "id": 7723,
-    "problem_id": 7540,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7540.jpg"
-  },
-  {
-    "id": 7724,
-    "problem_id": 7541,
-    "problem": "line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D, line A B, line B G C, line C D, line A E F D, line B E, line B F, line B D, line G D\nFind m \\angle 3.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7541.jpg"
-  },
-  {
-    "id": 7725,
-    "problem_id": 7542,
-    "problem": "line A D F G, line E F, line E D, line C D B, line C A, line A B, line A D F G, line E F, line E D, line C D B, line C A, line A B\nFind the measure of \\angle 1 if m \\angle 4 = m \\angle 5.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7542.jpg"
-  },
-  {
-    "id": 7726,
-    "problem_id": 7543,
-    "problem": "line C A, line B E, \\odot D lieson C E B A, line C A, line B E, \\odot D lieson C E B A\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7543.jpg"
-  },
-  {
-    "id": 7727,
-    "problem_id": 7544,
-    "problem": "line H J, line G H, \\odot H lieson G J, line H J, line G H, \\odot H lieson G J\nFind the area of sector JHG.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7544.jpg"
-  },
-  {
-    "id": 7728,
-    "problem_id": 7545,
-    "problem": "line l lieson B C D, line m lieson A C E, line l lieson B C D, line m lieson A C E\nm \\angle 9 = 141+x, m \\angle 10 = 25+x, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7545.jpg"
-  },
-  {
-    "id": 7729,
-    "problem_id": 7546,
-    "problem": "line l lieson B C D, line m lieson A C E, line l lieson B C D, line m lieson A C E\nm \\angle 9 = 141+x, m \\angle 10 = 25+x, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7546.jpg"
-  },
-  {
-    "id": 7730,
-    "problem_id": 7547,
-    "problem": "line l lieson B C D, line m lieson A C E, line l lieson B C D, line m lieson A C E\nm \\angle 9 = 141+x, m \\angle 10 = 25+x, find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7547.jpg"
-  },
-  {
-    "id": 7731,
-    "problem_id": 7548,
-    "problem": "line C B A, line G F E, line B D, line D F, \\odot D lieson C G E A, line C B A, line G F E, line B D, line D F, \\odot D lieson C G E A\nWhat is the value of variable x?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7548.jpg"
-  },
-  {
-    "id": 7732,
-    "problem_id": 7549,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find CF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7549.jpg"
-  },
-  {
-    "id": 7733,
-    "problem_id": 7550,
-    "problem": "line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C, line B J, line J F, line C F A, line J A, line C J, line D J, line J E, line B E A, line B D C\nJ is the incenter of \\angle ABC. Find CF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7550.jpg"
-  },
-  {
-    "id": 7734,
-    "problem_id": 7551,
-    "problem": "line A C, line B C, \\odot D lieson A C B, line A C, line B C, \\odot D lieson A C B\nDetermine m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7551.jpg"
-  },
-  {
-    "id": 7735,
-    "problem_id": 7552,
-    "problem": "line A C, line B C, \\odot D lieson A C B, line A C, line B C, \\odot D lieson A C B\nDetermine m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7552.jpg"
-  },
-  {
-    "id": 7736,
-    "problem_id": 7553,
-    "problem": "line A C, line B C, \\odot D lieson A C B, line A C, line B C, \\odot D lieson A C B\nDetermine m \\widehat BA.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7553.jpg"
-  },
-  {
-    "id": 7737,
-    "problem_id": 7554,
-    "problem": "line U W Y, line V W X, line X Y, line U V, line U W Y, line V W X, line X Y, line U V\nFind the length of YW.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7554.jpg"
-  },
-  {
-    "id": 7739,
-    "problem_id": 7555,
-    "problem": "line E A, line A F, \\odot A lieson F E, line E A, line A F, \\odot A lieson F E\nFind the length of \\widehat EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7555.jpg"
-  },
-  {
-    "id": 7740,
-    "problem_id": 7556,
-    "problem": "line E A, line A F, \\odot A lieson F E, line E A, line A F, \\odot A lieson F E\nFind the length of \\widehat EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7556.jpg"
-  },
-  {
-    "id": 7741,
-    "problem_id": 7557,
-    "problem": "line E A, line A F, \\odot A lieson F E, line E A, line A F, \\odot A lieson F E\nFind the length of \\widehat EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7557.jpg"
-  },
-  {
-    "id": 7742,
-    "problem_id": 7558,
-    "problem": "line E A, line A F, \\odot A lieson F E, line E A, line A F, \\odot A lieson F E\nFind the length of \\widehat EF.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7558.jpg"
-  },
-  {
-    "id": 7743,
-    "problem_id": 7559,
-    "problem": "line D H, line G H, line F G, line F D, line D H, line G H, line F G, line F D\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7559.jpg"
-  },
-  {
-    "id": 7744,
-    "problem_id": 7560,
-    "problem": "line D H, line G H, line F G, line F D, line D H, line G H, line F G, line F D\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7560.jpg"
-  },
-  {
-    "id": 7745,
-    "problem_id": 7561,
-    "problem": "line D H, line G H, line F G, line F D, line D H, line G H, line F G, line F D\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7561.jpg"
-  },
-  {
-    "id": 7746,
-    "problem_id": 7562,
-    "problem": "line D H, line G H, line F G, line F D, line D H, line G H, line F G, line F D\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7562.jpg"
-  },
-  {
-    "id": 7747,
-    "problem_id": 7563,
-    "problem": "line D H, line G H, line F G, line F D, line D H, line G H, line F G, line F D\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7563.jpg"
-  },
-  {
-    "id": 7748,
-    "problem_id": 7564,
-    "problem": "line D H, line G H, line F G, line F D, line D H, line G H, line F G, line F D\nUse parallelogram to find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7564.jpg"
-  },
-  {
-    "id": 7749,
-    "problem_id": 7565,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. What is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7565.jpg"
-  },
-  {
-    "id": 7750,
-    "problem_id": 7566,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. What is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7566.jpg"
-  },
-  {
-    "id": 7751,
-    "problem_id": 7567,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. What is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7567.jpg"
-  },
-  {
-    "id": 7752,
-    "problem_id": 7568,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. What is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7568.jpg"
-  },
-  {
-    "id": 7753,
-    "problem_id": 7569,
-    "problem": "line Q R, line P S, line Q P, line R S, line Q R, line P S, line Q P, line R S\nPQRS is a parallelogram. What is a?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7569.jpg"
-  },
-  {
-    "id": 7754,
-    "problem_id": 7570,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7570.jpg"
-  },
-  {
-    "id": 7755,
-    "problem_id": 7571,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7571.jpg"
-  },
-  {
-    "id": 7756,
-    "problem_id": 7572,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7572.jpg"
-  },
-  {
-    "id": 7757,
-    "problem_id": 7573,
-    "problem": "line M L, line K L, line K M, line M L, line K L, line K M\nExpress the ratio of \\sin L.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7573.jpg"
-  },
-  {
-    "id": 7758,
-    "problem_id": 7574,
-    "problem": "line Y X, line P Q, line Y Z, line P R, line Z X, line Q R, line Y X, line P Q, line Y Z, line P R, line Z X, line Q R\nGiven that \\angle PQR \\cong \\angle XYZ. Solve for the length of QR.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7574.jpg"
-  },
-  {
-    "id": 7760,
-    "problem_id": 7575,
-    "problem": "line A B C, line D C, line D B, line A F D, line E A, line E F, line E D, line A B C, line D C, line D B, line A F D, line E A, line E F, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7575.jpg"
-  },
-  {
-    "id": 7761,
-    "problem_id": 7576,
-    "problem": "line A B C, line D C, line D B, line A F D, line E A, line E F, line E D, line A B C, line D C, line D B, line A F D, line E A, line E F, line E D\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7576.jpg"
-  },
-  {
-    "id": 7762,
-    "problem_id": 7577,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7577.jpg"
-  },
-  {
-    "id": 7763,
-    "problem_id": 7578,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7578.jpg"
-  },
-  {
-    "id": 7764,
-    "problem_id": 7579,
-    "problem": "line A D, line B C D, line A B, line A C, line A D, line B C D, line A B, line A C\nWhat is the value of y?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7579.jpg"
-  },
-  {
-    "id": 7765,
-    "problem_id": 7580,
-    "problem": "line B D F, line E D C, line A D G, line C F, line B A, line G F, line B E, line A C, line E G, \\odot D lieson B E G F C A, line B D F, line E D C, line A D G, line C F, line B A, line G F, line B E, line A C, line E G, \\odot D lieson B E G F C A\nFind the area of the shaded region. Assume the inscribed polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7580.jpg"
-  },
-  {
-    "id": 7766,
-    "problem_id": 7581,
-    "problem": "line B D F, line E D C, line A D G, line C F, line B A, line G F, line B E, line A C, line E G, \\odot D lieson B E G F C A, line B D F, line E D C, line A D G, line C F, line B A, line G F, line B E, line A C, line E G, \\odot D lieson B E G F C A\nFind the area of the shaded region. Assume the inscribed polygon is regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7581.jpg"
-  },
-  {
-    "id": 7767,
-    "problem_id": 7582,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7582.jpg"
-  },
-  {
-    "id": 7768,
-    "problem_id": 7583,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7583.jpg"
-  },
-  {
-    "id": 7769,
-    "problem_id": 7584,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7584.jpg"
-  },
-  {
-    "id": 7770,
-    "problem_id": 7585,
-    "problem": "line A B, line C B, line A C, line A B, line C B, line A C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7585.jpg"
-  },
-  {
-    "id": 7771,
-    "problem_id": 7586,
-    "problem": "line A B, line A D, line A C, line B E, line B C D, line D F, line E F, line A B, line A D, line A C, line B E, line B C D, line D F, line E F\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7586.jpg"
-  },
-  {
-    "id": 7772,
-    "problem_id": 7587,
-    "problem": "line A B, line A D, line A C, line B E, line B C D, line D F, line E F, line A B, line A D, line A C, line B E, line B C D, line D F, line E F\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7587.jpg"
-  },
-  {
-    "id": 7773,
-    "problem_id": 7588,
-    "problem": "line A B, line A D, line A C, line B E, line B C D, line D F, line E F, line A B, line A D, line A C, line B E, line B C D, line D F, line E F\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7588.jpg"
-  },
-  {
-    "id": 7774,
-    "problem_id": 7589,
-    "problem": "line A B, line A D, line A C, line B E, line B C D, line D F, line E F, line A B, line A D, line A C, line B E, line B C D, line D F, line E F\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7589.jpg"
-  },
-  {
-    "id": 7775,
-    "problem_id": 7590,
-    "problem": "line A B, line A D, line A C, line B E, line B C D, line D F, line E F, line A B, line A D, line A C, line B E, line B C D, line D F, line E F\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7590.jpg"
-  },
-  {
-    "id": 7776,
-    "problem_id": 7591,
-    "problem": "line A B, line A D, line A C, line B E, line B C D, line D F, line E F, line A B, line A D, line A C, line B E, line B C D, line D F, line E F\nWhat is the area of the figure?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7591.jpg"
-  },
-  {
-    "id": 7777,
-    "problem_id": 7592,
-    "problem": "line A C D E F B, line G D H, line A C D E F B, line G D H\nGH = 4x-1, and DH = 8. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7592.jpg"
-  },
-  {
-    "id": 7778,
-    "problem_id": 7593,
-    "problem": "line J L, line M L, line K M J, line K L, line J L, line M L, line K M J, line K L\nFind z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7593.jpg"
-  },
-  {
-    "id": 7779,
-    "problem_id": 7594,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7594.jpg"
-  },
-  {
-    "id": 7780,
-    "problem_id": 7595,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7595.jpg"
-  },
-  {
-    "id": 7781,
-    "problem_id": 7596,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7596.jpg"
-  },
-  {
-    "id": 7782,
-    "problem_id": 7597,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7597.jpg"
-  },
-  {
-    "id": 7784,
-    "problem_id": 7598,
-    "problem": "line A C, line D C, line B D, line B A, line A C, line D C, line B D, line B A\nFind the measure of \\angle 1.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7598.jpg"
-  },
-  {
-    "id": 7785,
-    "problem_id": 7599,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle FBC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7599.jpg"
-  },
-  {
-    "id": 7786,
-    "problem_id": 7600,
-    "problem": "line G A B C H, line J E B, line I D B, line K F B, line G A B C H, line J E B, line I D B, line K F B\nFind the measure of \\angle FBC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7600.jpg"
-  },
-  {
-    "id": 7787,
-    "problem_id": 7601,
-    "problem": "line A B, line E A C, line C F D, line E G D, \\odot B lieson A F G, line A B, line E A C, line C F D, line E G D, \\odot B lieson A F G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7601.jpg"
-  },
-  {
-    "id": 7788,
-    "problem_id": 7602,
-    "problem": "line A B, line E A C, line C F D, line E G D, \\odot B lieson A F G, line A B, line E A C, line C F D, line E G D, \\odot B lieson A F G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7602.jpg"
-  },
-  {
-    "id": 7789,
-    "problem_id": 7603,
-    "problem": "line A B, line E A C, line C F D, line E G D, \\odot B lieson A F G, line A B, line E A C, line C F D, line E G D, \\odot B lieson A F G\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7603.jpg"
-  },
-  {
-    "id": 7790,
-    "problem_id": 7604,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7604.jpg"
-  },
-  {
-    "id": 7791,
-    "problem_id": 7605,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7605.jpg"
-  },
-  {
-    "id": 7792,
-    "problem_id": 7606,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7606.jpg"
-  },
-  {
-    "id": 7793,
-    "problem_id": 7607,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7607.jpg"
-  },
-  {
-    "id": 7794,
-    "problem_id": 7608,
-    "problem": "line N M, line J K, line K M, line J N, line N M, line J K, line K M, line J N\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7608.jpg"
-  },
-  {
-    "id": 7795,
-    "problem_id": 7609,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7609.jpg"
-  },
-  {
-    "id": 7796,
-    "problem_id": 7610,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7610.jpg"
-  },
-  {
-    "id": 7797,
-    "problem_id": 7611,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7611.jpg"
-  },
-  {
-    "id": 7798,
-    "problem_id": 7612,
-    "problem": "line F K G, line F J H, line H G, line J K, line F K G, line F J H, line H G, line J K\nFind y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7612.jpg"
-  },
-  {
-    "id": 7799,
-    "problem_id": 7613,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7613.jpg"
-  },
-  {
-    "id": 7800,
-    "problem_id": 7614,
-    "problem": "line B A, line B D, \\odot C lieson B D A, line B A, line B D, \\odot C lieson B D A\nFind the value of variable b.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7614.jpg"
-  },
-  {
-    "id": 7801,
-    "problem_id": 7615,
-    "problem": "line J M K, line L K, line J L, line M L, line J M K, line L K, line J L, line M L\nFind the measure of the altitude drawn to the hypotenuse.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7615.jpg"
-  },
-  {
-    "id": 7802,
-    "problem_id": 7616,
-    "problem": "line A C, line A E D, line A B, line D C, line B D, \\odot D lieson B E C, line A C, line A E D, line A B, line D C, line B D, \\odot D lieson B E C\nAB and AC are tangent to D. What is BD?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7616.jpg"
-  },
-  {
-    "id": 7803,
-    "problem_id": 7617,
-    "problem": "line A C E, line B C D, line C F, line A C E, line B C D, line C F\nFind m \\angle 2.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7617.jpg"
-  },
-  {
-    "id": 7804,
-    "problem_id": 7618,
-    "problem": "line U T, line R S, line S T, line R U, line U T, line R S, line S T, line R U\nFind the value of b if RSTU is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7618.jpg"
-  },
-  {
-    "id": 7805,
-    "problem_id": 7619,
-    "problem": "line U T, line R S, line S T, line R U, line U T, line R S, line S T, line R U\nFind the value of b if RSTU is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7619.jpg"
-  },
-  {
-    "id": 7806,
-    "problem_id": 7620,
-    "problem": "line U T, line R S, line S T, line R U, line U T, line R S, line S T, line R U\nFind the value of b if RSTU is a parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7620.jpg"
-  },
-  {
-    "id": 7807,
-    "problem_id": 7621,
-    "problem": "line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E, line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7621.jpg"
-  },
-  {
-    "id": 7808,
-    "problem_id": 7622,
-    "problem": "line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E, line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7622.jpg"
-  },
-  {
-    "id": 7809,
-    "problem_id": 7623,
-    "problem": "line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E, line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7623.jpg"
-  },
-  {
-    "id": 7810,
-    "problem_id": 7624,
-    "problem": "line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E, line A B, line B C, line D C, line E D, line H A, line G H, line F G, line F E\nFind the area of the regular polygon.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7624.jpg"
-  },
-  {
-    "id": 7811,
-    "problem_id": 7625,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind m \\angle V.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7625.jpg"
-  },
-  {
-    "id": 7812,
-    "problem_id": 7626,
-    "problem": "line K J, line J M, line J L, \\odot A lieson K L, \\odot B lieson L M, line K J, line J M, line J L, \\odot A lieson K L, \\odot B lieson L M\nAssume the segments that appear to be tangent are tangent. Find the length of JL.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7626.jpg"
-  },
-  {
-    "id": 7813,
-    "problem_id": 7627,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find QP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7627.jpg"
-  },
-  {
-    "id": 7814,
-    "problem_id": 7628,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find QP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7628.jpg"
-  },
-  {
-    "id": 7815,
-    "problem_id": 7629,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find QP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7629.jpg"
-  },
-  {
-    "id": 7816,
-    "problem_id": 7630,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find QP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7630.jpg"
-  },
-  {
-    "id": 7817,
-    "problem_id": 7631,
-    "problem": "line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K, line J Q, line Q M, line L Q, line Q K, line Q N, line P Q, line L P J, line L M K, line J N K\nQ is the incenter of \\triangle JKL. Find QP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7631.jpg"
-  },
-  {
-    "id": 7818,
-    "problem_id": 7632,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7632.jpg"
-  },
-  {
-    "id": 7819,
-    "problem_id": 7633,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7633.jpg"
-  },
-  {
-    "id": 7820,
-    "problem_id": 7634,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7634.jpg"
-  },
-  {
-    "id": 7821,
-    "problem_id": 7635,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7635.jpg"
-  },
-  {
-    "id": 7822,
-    "problem_id": 7636,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7636.jpg"
-  },
-  {
-    "id": 7823,
-    "problem_id": 7637,
-    "problem": "line B A, line B C, line C A, line B A, line B C, line C A\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7637.jpg"
-  },
-  {
-    "id": 7824,
-    "problem_id": 7638,
-    "problem": "line C D B E, line A D, line A B, line C D B E, line A D, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7638.jpg"
-  },
-  {
-    "id": 7825,
-    "problem_id": 7639,
-    "problem": "line C D B E, line A D, line A B, line C D B E, line A D, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7639.jpg"
-  },
-  {
-    "id": 7826,
-    "problem_id": 7640,
-    "problem": "line C D B E, line A D, line A B, line C D B E, line A D, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7640.jpg"
-  },
-  {
-    "id": 7827,
-    "problem_id": 7641,
-    "problem": "line C D B E, line A D, line A B, line C D B E, line A D, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7641.jpg"
-  },
-  {
-    "id": 7828,
-    "problem_id": 7642,
-    "problem": "line C D B E, line A D, line A B, line C D B E, line A D, line A B\nFind the value of x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7642.jpg"
-  },
-  {
-    "id": 7829,
-    "problem_id": 7643,
-    "problem": "line P O, line Q N, line M Q P, line M N O, line P O, line Q N, line M Q P, line M N O\nFind MP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7643.jpg"
-  },
-  {
-    "id": 7830,
-    "problem_id": 7644,
-    "problem": "line P O, line Q N, line M Q P, line M N O, line P O, line Q N, line M Q P, line M N O\nFind MP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7644.jpg"
-  },
-  {
-    "id": 7831,
-    "problem_id": 7645,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7645.jpg"
-  },
-  {
-    "id": 7832,
-    "problem_id": 7646,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7646.jpg"
-  },
-  {
-    "id": 7833,
-    "problem_id": 7647,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7647.jpg"
-  },
-  {
-    "id": 7834,
-    "problem_id": 7648,
-    "problem": "line B A, line A C, line B C, line B A, line A C, line B C\nUse the Law of Cosines to find the value x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7648.jpg"
-  },
-  {
-    "id": 7835,
-    "problem_id": 7649,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind the measure of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7649.jpg"
-  },
-  {
-    "id": 7836,
-    "problem_id": 7650,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind the measure of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7650.jpg"
-  },
-  {
-    "id": 7837,
-    "problem_id": 7651,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind the measure of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7651.jpg"
-  },
-  {
-    "id": 7838,
-    "problem_id": 7652,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind the measure of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7652.jpg"
-  },
-  {
-    "id": 7839,
-    "problem_id": 7653,
-    "problem": "line K L, line K J, line J L, line K L, line K J, line J L\nFind the measure of JK.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7653.jpg"
-  },
-  {
-    "id": 7840,
-    "problem_id": 7654,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7654.jpg"
-  },
-  {
-    "id": 7841,
-    "problem_id": 7655,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7655.jpg"
-  },
-  {
-    "id": 7842,
-    "problem_id": 7656,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7656.jpg"
-  },
-  {
-    "id": 7843,
-    "problem_id": 7657,
-    "problem": "line B A, line B C, line A C, line B A, line B C, line A C\nFind the area of the figure.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7657.jpg"
-  },
-  {
-    "id": 7844,
-    "problem_id": 7658,
-    "problem": "line A D, line D C, line D E, line B E C, line A B, line A D, line D C, line D E, line B E C, line A B\nFind the perimeter of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7658.jpg"
-  },
-  {
-    "id": 7845,
-    "problem_id": 7659,
-    "problem": "line A D, line D C, line D E, line B E C, line A B, line A D, line D C, line D E, line B E C, line A B\nFind the perimeter of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7659.jpg"
-  },
-  {
-    "id": 7846,
-    "problem_id": 7660,
-    "problem": "line A D, line D C, line D E, line B E C, line A B, line A D, line D C, line D E, line B E C, line A B\nFind the perimeter of \\parallelogram ABCD.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7660.jpg"
-  },
-  {
-    "id": 7847,
-    "problem_id": 7661,
-    "problem": "line E A D F, line A C, line A B, line B D C, line E A D F, line A C, line A B, line B D C\nDetermine the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7661.jpg"
-  },
-  {
-    "id": 7848,
-    "problem_id": 7662,
-    "problem": "line E A D F, line A C, line A B, line B D C, line E A D F, line A C, line A B, line B D C\nDetermine the value of z.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7662.jpg"
-  },
-  {
-    "id": 7849,
-    "problem_id": 7663,
-    "problem": "line A C E, line B C D, \\odot F lieson B A D E, line A C E, line B C D, \\odot F lieson B A D E\nFind x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7663.jpg"
-  },
-  {
-    "id": 7850,
-    "problem_id": 7664,
-    "problem": "line D E, line E C, line D C, line D E, line E C, line D C\nSolve for m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7664.jpg"
-  },
-  {
-    "id": 7851,
-    "problem_id": 7665,
-    "problem": "line D E, line E C, line D C, line D E, line E C, line D C\nSolve for m \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7665.jpg"
-  },
-  {
-    "id": 7852,
-    "problem_id": 7666,
-    "problem": "line B C D, line A D, line A C, line B C D, line A D, line A C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7666.jpg"
-  },
-  {
-    "id": 7853,
-    "problem_id": 7667,
-    "problem": "line B C D, line A D, line A C, line B C D, line A D, line A C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7667.jpg"
-  },
-  {
-    "id": 7854,
-    "problem_id": 7668,
-    "problem": "line B C D, line A D, line A C, line B C D, line A D, line A C\nWhat is the measure of \\angle 1?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7668.jpg"
-  },
-  {
-    "id": 7855,
-    "problem_id": 7669,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the measure of \\angle CAB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7669.jpg"
-  },
-  {
-    "id": 7856,
-    "problem_id": 7670,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the measure of \\angle CAB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7670.jpg"
-  },
-  {
-    "id": 7857,
-    "problem_id": 7671,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the measure of \\angle CAB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7671.jpg"
-  },
-  {
-    "id": 7858,
-    "problem_id": 7672,
-    "problem": "line A C, line B C, line A B, line A C, line B C, line A B\nFind the measure of \\angle CAB.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7672.jpg"
-  },
-  {
-    "id": 7860,
-    "problem_id": 7673,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7673.jpg"
-  },
-  {
-    "id": 7861,
-    "problem_id": 7674,
-    "problem": "line X A Y, line X A Y\nA is the midpoint of XY. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7674.jpg"
-  },
-  {
-    "id": 7862,
-    "problem_id": 7675,
-    "problem": "line A D, line A C B, line D E, line C D, line E B, line A D, line A C B, line D E, line C D, line E B\nFind the area of the trapezoid.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7675.jpg"
-  },
-  {
-    "id": 7863,
-    "problem_id": 7676,
-    "problem": "line A D C, line B C, line B A, \\odot A lieson B D, line A D C, line B C, line B A, \\odot A lieson B D\nIf BC = 8 and DC = 4, what is the radius?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7676.jpg"
-  },
-  {
-    "id": 7864,
-    "problem_id": 7677,
-    "problem": "line E F, line E H, line H G, line F G, line E F, line E H, line H G, line F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7677.jpg"
-  },
-  {
-    "id": 7865,
-    "problem_id": 7678,
-    "problem": "line E F, line E H, line H G, line F G, line E F, line E H, line H G, line F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7678.jpg"
-  },
-  {
-    "id": 7866,
-    "problem_id": 7679,
-    "problem": "line E F, line E H, line H G, line F G, line E F, line E H, line H G, line F G\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7679.jpg"
-  },
-  {
-    "id": 7867,
-    "problem_id": 7680,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7680.jpg"
-  },
-  {
-    "id": 7869,
-    "problem_id": 7681,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7681.jpg"
-  },
-  {
-    "id": 7870,
-    "problem_id": 7682,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7682.jpg"
-  },
-  {
-    "id": 7871,
-    "problem_id": 7683,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7683.jpg"
-  },
-  {
-    "id": 7872,
-    "problem_id": 7684,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7684.jpg"
-  },
-  {
-    "id": 7873,
-    "problem_id": 7685,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 10.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7685.jpg"
-  },
-  {
-    "id": 7874,
-    "problem_id": 7686,
-    "problem": "line T S V, line U S R, \\odot R lieson T U V, line T S V, line U S R, \\odot R lieson T U V\nIn \\odot R, find m \\widehat TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7686.jpg"
-  },
-  {
-    "id": 7875,
-    "problem_id": 7687,
-    "problem": "line T S V, line U S R, \\odot R lieson T U V, line T S V, line U S R, \\odot R lieson T U V\nIn \\odot R, find m \\widehat TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7687.jpg"
-  },
-  {
-    "id": 7876,
-    "problem_id": 7688,
-    "problem": "line T S V, line U S R, \\odot R lieson T U V, line T S V, line U S R, \\odot R lieson T U V\nIn \\odot R, find m \\widehat TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7688.jpg"
-  },
-  {
-    "id": 7877,
-    "problem_id": 7689,
-    "problem": "line T S V, line U S R, \\odot R lieson T U V, line T S V, line U S R, \\odot R lieson T U V\nIn \\odot R, find m \\widehat TUV.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7689.jpg"
-  },
-  {
-    "id": 7878,
-    "problem_id": 7690,
-    "problem": "line A B C, line A B C\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7690.jpg"
-  },
-  {
-    "id": 7879,
-    "problem_id": 7691,
-    "problem": "line A B C, line A B C\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7691.jpg"
-  },
-  {
-    "id": 7880,
-    "problem_id": 7692,
-    "problem": "line A B C, line A B C\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7692.jpg"
-  },
-  {
-    "id": 7881,
-    "problem_id": 7693,
-    "problem": "line A B C, line A B C\nFind the length of BC.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7693.jpg"
-  },
-  {
-    "id": 7882,
-    "problem_id": 7694,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7694.jpg"
-  },
-  {
-    "id": 7883,
-    "problem_id": 7695,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7695.jpg"
-  },
-  {
-    "id": 7884,
-    "problem_id": 7696,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7696.jpg"
-  },
-  {
-    "id": 7885,
-    "problem_id": 7697,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7697.jpg"
-  },
-  {
-    "id": 7886,
-    "problem_id": 7698,
-    "problem": "line A B D, line C A, line C D, line C B, line A B D, line C A, line C D, line C B\nFind the perimeter of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7698.jpg"
-  },
-  {
-    "id": 7887,
-    "problem_id": 7699,
-    "problem": "line A C D, line B C, \\odot C lieson B D A, line A C D, line B C, \\odot C lieson B D A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7699.jpg"
-  },
-  {
-    "id": 7888,
-    "problem_id": 7700,
-    "problem": "line A C D, line B C, \\odot C lieson B D A, line A C D, line B C, \\odot C lieson B D A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7700.jpg"
-  },
-  {
-    "id": 7889,
-    "problem_id": 7701,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7701.jpg"
-  },
-  {
-    "id": 7890,
-    "problem_id": 7702,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7702.jpg"
-  },
-  {
-    "id": 7891,
-    "problem_id": 7703,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7703.jpg"
-  },
-  {
-    "id": 7892,
-    "problem_id": 7704,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7704.jpg"
-  },
-  {
-    "id": 7893,
-    "problem_id": 7705,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7705.jpg"
-  },
-  {
-    "id": 7894,
-    "problem_id": 7706,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7706.jpg"
-  },
-  {
-    "id": 7895,
-    "problem_id": 7707,
-    "problem": "line E B, line A B, line A C E, line D C B, line D A, line E B, line A B, line A C E, line D C B, line D A\nFind the measure of \\angle 8.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7707.jpg"
-  },
-  {
-    "id": 7896,
-    "problem_id": 7708,
-    "problem": "line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A, line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7708.jpg"
-  },
-  {
-    "id": 7897,
-    "problem_id": 7709,
-    "problem": "line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A, line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7709.jpg"
-  },
-  {
-    "id": 7898,
-    "problem_id": 7710,
-    "problem": "line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A, line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7710.jpg"
-  },
-  {
-    "id": 7899,
-    "problem_id": 7711,
-    "problem": "line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A, line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7711.jpg"
-  },
-  {
-    "id": 7900,
-    "problem_id": 7712,
-    "problem": "line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A, line B A, line A E F, line G F, line B D G, \\odot D lieson G C B, \\odot E lieson C F A\nFind the area of the shaded region.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7712.jpg"
-  },
-  {
-    "id": 7901,
-    "problem_id": 7713,
-    "problem": "line A B, line B C, line A C, line R P, line R Q, line Q P, line A B, line B C, line A C, line R P, line R Q, line Q P\n\\triangle ABC \\cong \\triangle PQR, find the measure of \\angle C.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7713.jpg"
-  },
-  {
-    "id": 7902,
-    "problem_id": 7714,
-    "problem": "line D C, line A B D, line A C, line B C, line D C, line A B D, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7714.jpg"
-  },
-  {
-    "id": 7903,
-    "problem_id": 7715,
-    "problem": "line D C, line A B D, line A C, line B C, line D C, line A B D, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7715.jpg"
-  },
-  {
-    "id": 7904,
-    "problem_id": 7716,
-    "problem": "line D C, line A B D, line A C, line B C, line D C, line A B D, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7716.jpg"
-  },
-  {
-    "id": 7905,
-    "problem_id": 7717,
-    "problem": "line D C, line A B D, line A C, line B C, line D C, line A B D, line A C, line B C\nFind the value of y.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7717.jpg"
-  },
-  {
-    "id": 7906,
-    "problem_id": 7718,
-    "problem": "line Q T, line Q R, line R S, line T S, line T P R, line Q P S, line Q T, line Q R, line R S, line T S, line T P R, line Q P S\nQuadrilateral QRST is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7718.jpg"
-  },
-  {
-    "id": 7907,
-    "problem_id": 7719,
-    "problem": "line Q T, line Q R, line R S, line T S, line T P R, line Q P S, line Q T, line Q R, line R S, line T S, line T P R, line Q P S\nQuadrilateral QRST is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7719.jpg"
-  },
-  {
-    "id": 7908,
-    "problem_id": 7720,
-    "problem": "line Q T, line Q R, line R S, line T S, line T P R, line Q P S, line Q T, line Q R, line R S, line T S, line T P R, line Q P S\nQuadrilateral QRST is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7720.jpg"
-  },
-  {
-    "id": 7909,
-    "problem_id": 7721,
-    "problem": "line Q T, line Q R, line R S, line T S, line T P R, line Q P S, line Q T, line Q R, line R S, line T S, line T P R, line Q P S\nQuadrilateral QRST is a rectangle. Find x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7721.jpg"
-  },
-  {
-    "id": 7911,
-    "problem_id": 7722,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7722.jpg"
-  },
-  {
-    "id": 7912,
-    "problem_id": 7723,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7723.jpg"
-  },
-  {
-    "id": 7913,
-    "problem_id": 7724,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7724.jpg"
-  },
-  {
-    "id": 7915,
-    "problem_id": 7725,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7725.jpg"
-  },
-  {
-    "id": 7916,
-    "problem_id": 7726,
-    "problem": "line A B, line C D B, line C A, line A D, line A B, line C D B, line C A, line A D\nFind the area of the triangle.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7726.jpg"
-  },
-  {
-    "id": 7917,
-    "problem_id": 7727,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7727.jpg"
-  },
-  {
-    "id": 7918,
-    "problem_id": 7728,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7728.jpg"
-  },
-  {
-    "id": 7919,
-    "problem_id": 7729,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7729.jpg"
-  },
-  {
-    "id": 7920,
-    "problem_id": 7730,
-    "problem": "line U V, line U Z, line Z Y, line W Y, line V W, line U V, line U Z, line Z Y, line W Y, line V W\nFind m \\angle U.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7730.jpg"
-  },
-  {
-    "id": 7921,
-    "problem_id": 7731,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7731.jpg"
-  },
-  {
-    "id": 7922,
-    "problem_id": 7732,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7732.jpg"
-  },
-  {
-    "id": 7923,
-    "problem_id": 7733,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7733.jpg"
-  },
-  {
-    "id": 7924,
-    "problem_id": 7734,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7734.jpg"
-  },
-  {
-    "id": 7925,
-    "problem_id": 7735,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7735.jpg"
-  },
-  {
-    "id": 7926,
-    "problem_id": 7736,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7736.jpg"
-  },
-  {
-    "id": 7927,
-    "problem_id": 7737,
-    "problem": "line A B, line C D E, line E B, line A C, line A D, line A B, line C D E, line E B, line A C, line A D\nFind the perimeter of the parallelogram.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7737.jpg"
-  },
-  {
-    "id": 7928,
-    "problem_id": 7738,
-    "problem": "line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E, line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7738.jpg"
-  },
-  {
-    "id": 7929,
-    "problem_id": 7739,
-    "problem": "line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E, line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7739.jpg"
-  },
-  {
-    "id": 7930,
-    "problem_id": 7740,
-    "problem": "line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E, line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7740.jpg"
-  },
-  {
-    "id": 7931,
-    "problem_id": 7741,
-    "problem": "line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E, line E D F, line A B, line A D, line B F, line D B, line C D, line A C, line C E\nDetermine x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7741.jpg"
-  },
-  {
-    "id": 7932,
-    "problem_id": 7742,
-    "problem": "line M P, line N P, line N M, line N Q, line Q P, line M P, line N P, line N M, line N Q, line Q P\nGiven that m \\angle NMP = 46 and m \\angle PNQ = 27. Find m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7742.jpg"
-  },
-  {
-    "id": 7933,
-    "problem_id": 7743,
-    "problem": "line M P, line N P, line N M, line N Q, line Q P, line M P, line N P, line N M, line N Q, line Q P\nGiven that m \\angle NMP = 46 and m \\angle PNQ = 27. Find m \\angle MNP.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7743.jpg"
-  },
-  {
-    "id": 7934,
-    "problem_id": 7744,
-    "problem": "line B L M N, line A R N, line C Q P N, line M R, line R P, line B L M N, line A R N, line C Q P N, line M R, line R P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7744.jpg"
-  },
-  {
-    "id": 7935,
-    "problem_id": 7745,
-    "problem": "line B L M N, line A R N, line C Q P N, line M R, line R P, line B L M N, line A R N, line C Q P N, line M R, line R P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7745.jpg"
-  },
-  {
-    "id": 7936,
-    "problem_id": 7746,
-    "problem": "line B L M N, line A R N, line C Q P N, line M R, line R P, line B L M N, line A R N, line C Q P N, line M R, line R P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7746.jpg"
-  },
-  {
-    "id": 7937,
-    "problem_id": 7747,
-    "problem": "line B L M N, line A R N, line C Q P N, line M R, line R P, line B L M N, line A R N, line C Q P N, line M R, line R P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7747.jpg"
-  },
-  {
-    "id": 7938,
-    "problem_id": 7748,
-    "problem": "line B L M N, line A R N, line C Q P N, line M R, line R P, line B L M N, line A R N, line C Q P N, line M R, line R P\nSolve for x.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7748.jpg"
-  },
-  {
-    "id": 7939,
-    "problem_id": 7749,
-    "problem": "line W X, line X Y, \\odot X lieson Y W, line W X, line X Y, \\odot X lieson Y W\nWhat is the area of \\odot X?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7749.jpg"
-  },
-  {
-    "id": 7940,
-    "problem_id": 7750,
-    "problem": "line W X, line X Y, \\odot X lieson Y W, line W X, line X Y, \\odot X lieson Y W\nWhat is the area of \\odot X?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7750.jpg"
-  },
-  {
-    "id": 7941,
-    "problem_id": 7751,
-    "problem": "line W X, line X Y, \\odot X lieson Y W, line W X, line X Y, \\odot X lieson Y W\nWhat is the area of \\odot X?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7751.jpg"
-  },
-  {
-    "id": 7942,
-    "problem_id": 7752,
-    "problem": "line W X, line X Y, \\odot X lieson Y W, line W X, line X Y, \\odot X lieson Y W\nWhat is the area of \\odot X?\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7752.jpg"
-  },
-  {
-    "id": 7943,
-    "problem_id": 7753,
-    "problem": "line B C, line C A, line B E A, line E C, line B C, line C A, line B E A, line E C\nIf a = 10\\sqrt{3}, find CE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7753.jpg"
-  },
-  {
-    "id": 7944,
-    "problem_id": 7754,
-    "problem": "line B C, line C A, line B E A, line E C, line B C, line C A, line B E A, line E C\nIf a = 10\\sqrt{3}, find CE.\nchoices are A. 56.0, B. 82.2, C. 164.3, D. 328.6\nPlease give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7754.jpg"
-  },
-  {
-    "id": 7945,
-    "problem_id": 7755,
-    "problem": "<image>As shown in the figure, diagonal AC of square ABCD intersects with diagonal BD at point O. Point M lies on side AD, and OM is connected. Line ON perpendicular to OM is drawn passing through point O, intersecting with CD at point N. If the area of quadrilateral MOND is 2, then the length of BD is ().. A, B, C, D choices are ['\u221a{2}', '2', '2\u221a{2}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7755.jpg"
-  },
-  {
-    "id": 7946,
-    "problem_id": 7756,
-    "problem": "<image>As shown in the figure, diagonal AC of square ABCD intersects with diagonal BD at point O. Point M lies on side AD, and OM is connected. Line ON perpendicular to OM is drawn passing through point O, intersecting with CD at point N. If the area of quadrilateral MOND is 2, then the length of BD is ().. A, B, C, D choices are ['\u221a{2}', '2', '2\u221a{2}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7756.jpg"
-  },
-  {
-    "id": 7947,
-    "problem_id": 7757,
-    "problem": "<image>As shown in the figure, if a ruler is overlaid with a 30\u00b0 protractor, and \u22201 = 55\u00b0, what is the size of \u22202?. A, B, C, D choices are ['65\u00b0', '70\u00b0', '75\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7757.jpg"
-  },
-  {
-    "id": 7948,
-    "problem_id": 7758,
-    "problem": "<image>As shown in the figure, if a ruler is overlaid with a 30\u00b0 protractor, and \u22201 = 55\u00b0, what is the size of \u22202?. A, B, C, D choices are ['65\u00b0', '70\u00b0', '75\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7758.jpg"
-  },
-  {
-    "id": 7949,
-    "problem_id": 7759,
-    "problem": "<image>In triangle ABC, AB = AC, AD is the altitude on BC, point E is the midpoint of AC, and DE is connected. If the perimeter of triangle ABC is 20, then the perimeter of triangle CDE is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7759.jpg"
-  },
-  {
-    "id": 7950,
-    "problem_id": 7760,
-    "problem": "<image>In triangle ABC, AB = AC, AD is the altitude on BC, point E is the midpoint of AC, and DE is connected. If the perimeter of triangle ABC is 20, then the perimeter of triangle CDE is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7760.jpg"
-  },
-  {
-    "id": 7951,
-    "problem_id": 7761,
-    "problem": "<image>In triangle ABC, AB = AC, AD is the altitude on BC, point E is the midpoint of AC, and DE is connected. If the perimeter of triangle ABC is 20, then the perimeter of triangle CDE is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7761.jpg"
-  },
-  {
-    "id": 7952,
-    "problem_id": 7762,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7762.jpg"
-  },
-  {
-    "id": 7953,
-    "problem_id": 7763,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7763.jpg"
-  },
-  {
-    "id": 7954,
-    "problem_id": 7764,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7764.jpg"
-  },
-  {
-    "id": 7955,
-    "problem_id": 7765,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7765.jpg"
-  },
-  {
-    "id": 7956,
-    "problem_id": 7766,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7766.jpg"
-  },
-  {
-    "id": 7957,
-    "problem_id": 7767,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7767.jpg"
-  },
-  {
-    "id": 7958,
-    "problem_id": 7768,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7768.jpg"
-  },
-  {
-    "id": 7959,
-    "problem_id": 7769,
-    "problem": "<image>In parallelogram ABCD as shown, if \u2220A = 60\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['120\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7769.jpg"
-  },
-  {
-    "id": 7960,
-    "problem_id": 7770,
-    "problem": "<image>In triangle ABC, angle BAC is 90 degrees, AD is perpendicular to BC, AE bisects angle BAC, angle B is twice angle C. What is the degree measure of angle DAE? (). A, B, C, D choices are ['45\u00b0', '20\u00b0', '30\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7770.jpg"
-  },
-  {
-    "id": 7961,
-    "problem_id": 7771,
-    "problem": "<image>In triangle ABC, angle BAC is 90 degrees, AD is perpendicular to BC, AE bisects angle BAC, angle B is twice angle C. What is the degree measure of angle DAE? (). A, B, C, D choices are ['45\u00b0', '20\u00b0', '30\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7771.jpg"
-  },
-  {
-    "id": 7962,
-    "problem_id": 7772,
-    "problem": "<image>In triangle ABC, angle BAC is 90 degrees, AD is perpendicular to BC, AE bisects angle BAC, angle B is twice angle C. What is the degree measure of angle DAE? (). A, B, C, D choices are ['45\u00b0', '20\u00b0', '30\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7772.jpg"
-  },
-  {
-    "id": 7967,
-    "problem_id": 7773,
-    "problem": "<image>As shown in the figure, it is known that line a is parallel to line b and the vertex of the triangle is placed on line b. If \u22201 = 42\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['138\u00b0', '132\u00b0', '128\u00b0', '122\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7773.jpg"
-  },
-  {
-    "id": 7968,
-    "problem_id": 7774,
-    "problem": "<image>As shown in the figure, it is known that line a is parallel to line b and the vertex of the triangle is placed on line b. If \u22201 = 42\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['138\u00b0', '132\u00b0', '128\u00b0', '122\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7774.jpg"
-  },
-  {
-    "id": 7969,
-    "problem_id": 7775,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7775.jpg"
-  },
-  {
-    "id": 7970,
-    "problem_id": 7776,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7776.jpg"
-  },
-  {
-    "id": 7971,
-    "problem_id": 7777,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7777.jpg"
-  },
-  {
-    "id": 7972,
-    "problem_id": 7778,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7778.jpg"
-  },
-  {
-    "id": 7973,
-    "problem_id": 7779,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7779.jpg"
-  },
-  {
-    "id": 7974,
-    "problem_id": 7780,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7780.jpg"
-  },
-  {
-    "id": 7975,
-    "problem_id": 7781,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7781.jpg"
-  },
-  {
-    "id": 7976,
-    "problem_id": 7782,
-    "problem": "<image>Given a rhombus ABCD, AC = 6 and the area is 24, what is the perimeter of rhombus ABCD?. A, B, C, D choices are ['20', '25', '20\u221a{2}', '1530'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7782.jpg"
-  },
-  {
-    "id": 7978,
-    "problem_id": 7783,
-    "problem": "<image>As shown in the figure, if lines a and b are intersected by line c and \u22201 = 55\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['35\u00b0', '45\u00b0', '125\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7783.jpg"
-  },
-  {
-    "id": 7979,
-    "problem_id": 7784,
-    "problem": "<image>As shown in the figure, if lines a and b are intersected by line c and \u22201 = 55\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['35\u00b0', '45\u00b0', '125\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7784.jpg"
-  },
-  {
-    "id": 7980,
-    "problem_id": 7785,
-    "problem": "<image>As shown in the figure, if lines a and b are intersected by line c and \u22201 = 55\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['35\u00b0', '45\u00b0', '125\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7785.jpg"
-  },
-  {
-    "id": 7981,
-    "problem_id": 7786,
-    "problem": "<image>As shown in the figure, if lines a and b are intersected by line c and \u22201 = 55\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['35\u00b0', '45\u00b0', '125\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7786.jpg"
-  },
-  {
-    "id": 7982,
-    "problem_id": 7787,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 130\u00b0, then \u22202 is equal to ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7787.jpg"
-  },
-  {
-    "id": 7983,
-    "problem_id": 7788,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 130\u00b0, then \u22202 is equal to ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7788.jpg"
-  },
-  {
-    "id": 7984,
-    "problem_id": 7789,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 130\u00b0, then \u22202 is equal to ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7789.jpg"
-  },
-  {
-    "id": 7985,
-    "problem_id": 7790,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 130\u00b0, then \u22202 is equal to ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7790.jpg"
-  },
-  {
-    "id": 7987,
-    "problem_id": 7791,
-    "problem": "<image>As shown in the figure, if point O is a point inside triangle ABC and \u2220BOC = 140\u00b0, \u22201 = 20\u00b0, \u22202 = 40\u00b0, then the size of \u2220A is (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '120\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7791.jpg"
-  },
-  {
-    "id": 7988,
-    "problem_id": 7792,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7792.jpg"
-  },
-  {
-    "id": 7989,
-    "problem_id": 7793,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7793.jpg"
-  },
-  {
-    "id": 7990,
-    "problem_id": 7794,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7794.jpg"
-  },
-  {
-    "id": 7991,
-    "problem_id": 7795,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7795.jpg"
-  },
-  {
-    "id": 7992,
-    "problem_id": 7796,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7796.jpg"
-  },
-  {
-    "id": 7993,
-    "problem_id": 7797,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7797.jpg"
-  },
-  {
-    "id": 7994,
-    "problem_id": 7798,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7798.jpg"
-  },
-  {
-    "id": 7995,
-    "problem_id": 7799,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF with point O as the center of similarity. It is known that AB:DE = 0.3333333 and the perimeter of \u25b3ABC is 4. The perimeter of \u25b3DEF is () .. A, B, C, D choices are ['8', '12', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7799.jpg"
-  },
-  {
-    "id": 7996,
-    "problem_id": 7800,
-    "problem": "<image>In the figure, if AC = 8 in ABCD, then the length of AO is (). A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7800.jpg"
-  },
-  {
-    "id": 7997,
-    "problem_id": 7801,
-    "problem": "<image>In the figure, if AC = 8 in ABCD, then the length of AO is (). A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7801.jpg"
-  },
-  {
-    "id": 7998,
-    "problem_id": 7802,
-    "problem": "<image>In the figure, if AC = 8 in ABCD, then the length of AO is (). A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7802.jpg"
-  },
-  {
-    "id": 7999,
-    "problem_id": 7803,
-    "problem": "<image>In the figure, if AC = 8 in ABCD, then the length of AO is (). A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7803.jpg"
-  },
-  {
-    "id": 8000,
-    "problem_id": 7804,
-    "problem": "<image>In right triangle \u25b3ABC as shown in the figure, \u2220ACB = 90\u00b0, G, E, and D are the midpoints of sides AB, BC, and CA, respectively. If DE + CG = 7, then the length of CG is (). A, B, C, D choices are ['3', '3.5', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7804.jpg"
-  },
-  {
-    "id": 8001,
-    "problem_id": 7805,
-    "problem": "<image>In right triangle \u25b3ABC as shown in the figure, \u2220ACB = 90\u00b0, G, E, and D are the midpoints of sides AB, BC, and CA, respectively. If DE + CG = 7, then the length of CG is (). A, B, C, D choices are ['3', '3.5', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7805.jpg"
-  },
-  {
-    "id": 8002,
-    "problem_id": 7806,
-    "problem": "<image>In right triangle \u25b3ABC as shown in the figure, \u2220ACB = 90\u00b0, G, E, and D are the midpoints of sides AB, BC, and CA, respectively. If DE + CG = 7, then the length of CG is (). A, B, C, D choices are ['3', '3.5', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7806.jpg"
-  },
-  {
-    "id": 8003,
-    "problem_id": 7807,
-    "problem": "<image>In right triangle \u25b3ABC as shown in the figure, \u2220ACB = 90\u00b0, G, E, and D are the midpoints of sides AB, BC, and CA, respectively. If DE + CG = 7, then the length of CG is (). A, B, C, D choices are ['3', '3.5', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7807.jpg"
-  },
-  {
-    "id": 8004,
-    "problem_id": 7808,
-    "problem": "<image>In right triangle \u25b3ABC as shown in the figure, \u2220ACB = 90\u00b0, G, E, and D are the midpoints of sides AB, BC, and CA, respectively. If DE + CG = 7, then the length of CG is (). A, B, C, D choices are ['3', '3.5', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7808.jpg"
-  },
-  {
-    "id": 8005,
-    "problem_id": 7809,
-    "problem": "<image>In rectangle ABCD, AB = 24 and BC = 25. A circular arc with BC as the radius and B as the center intersects side AD at point E. What is the length of EC?. A, B, C, D choices are ['26', '28', '30', '32'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7809.jpg"
-  },
-  {
-    "id": 8006,
-    "problem_id": 7810,
-    "problem": "<image>In rectangle ABCD, AB = 24 and BC = 25. A circular arc with BC as the radius and B as the center intersects side AD at point E. What is the length of EC?. A, B, C, D choices are ['26', '28', '30', '32'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7810.jpg"
-  },
-  {
-    "id": 8007,
-    "problem_id": 7811,
-    "problem": "<image>In rectangle ABCD, AB = 24 and BC = 25. A circular arc with BC as the radius and B as the center intersects side AD at point E. What is the length of EC?. A, B, C, D choices are ['26', '28', '30', '32'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7811.jpg"
-  },
-  {
-    "id": 8008,
-    "problem_id": 7812,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7812.jpg"
-  },
-  {
-    "id": 8009,
-    "problem_id": 7813,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7813.jpg"
-  },
-  {
-    "id": 8010,
-    "problem_id": 7814,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7814.jpg"
-  },
-  {
-    "id": 8011,
-    "problem_id": 7815,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7815.jpg"
-  },
-  {
-    "id": 8012,
-    "problem_id": 7816,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7816.jpg"
-  },
-  {
-    "id": 8013,
-    "problem_id": 7817,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7817.jpg"
-  },
-  {
-    "id": 8014,
-    "problem_id": 7818,
-    "problem": "<image>A steel pipe is placed in a V-shaped frame, and its cross section is shown in the figure. The radius of the steel pipe is 24cm. If \u2220ACB\uff1d60\u00b0, the length of the minor arc AB is (). A, B, C, D choices are ['8\u03c0cm', '16\u03c0cm', '32\u03c0cm', '192\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7818.jpg"
-  },
-  {
-    "id": 8015,
-    "problem_id": 7819,
-    "problem": "<image>As shown in the figure, the shape is composed of two right-angled triangles and three squares. The hypotenuse and one of the legs of the larger right-angled triangle are 13 and 12 respectively. What is the area of the shaded region in the figure?. A, B, C, D choices are ['16', '25', '144', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7819.jpg"
-  },
-  {
-    "id": 8016,
-    "problem_id": 7820,
-    "problem": "<image>As shown in the figure, the shape is composed of two right-angled triangles and three squares. The hypotenuse and one of the legs of the larger right-angled triangle are 13 and 12 respectively. What is the area of the shaded region in the figure?. A, B, C, D choices are ['16', '25', '144', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7820.jpg"
-  },
-  {
-    "id": 8017,
-    "problem_id": 7821,
-    "problem": "<image>As shown in the figure, the shape is composed of two right-angled triangles and three squares. The hypotenuse and one of the legs of the larger right-angled triangle are 13 and 12 respectively. What is the area of the shaded region in the figure?. A, B, C, D choices are ['16', '25', '144', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7821.jpg"
-  },
-  {
-    "id": 8018,
-    "problem_id": 7822,
-    "problem": "<image>As shown in the figure, the shape is composed of two right-angled triangles and three squares. The hypotenuse and one of the legs of the larger right-angled triangle are 13 and 12 respectively. What is the area of the shaded region in the figure?. A, B, C, D choices are ['16', '25', '144', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7822.jpg"
-  },
-  {
-    "id": 8019,
-    "problem_id": 7823,
-    "problem": "<image>As shown in the figure, the shape is composed of two right-angled triangles and three squares. The hypotenuse and one of the legs of the larger right-angled triangle are 13 and 12 respectively. What is the area of the shaded region in the figure?. A, B, C, D choices are ['16', '25', '144', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7823.jpg"
-  },
-  {
-    "id": 8020,
-    "problem_id": 7824,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, G is a point on the line CD, E is a point between the line AB and CD, F is a point above the line AB, \u2220F = 40\u00b0, \u2220EGF = 65\u00b0, then \u22201 + \u22202 = ().. A, B, C, D choices are ['40\u00b0', '55\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7824.jpg"
-  },
-  {
-    "id": 8021,
-    "problem_id": 7825,
-    "problem": "<image>As shown in the figure, line a || b || c, the distance between line a and line b is 2, and the distance between line b and line c is 4. Square ABCD's diagonal AC intersects diagonal BD at point O. If vertices A, D, and C are respectively on lines a, b, and c, then the area of triangle AOD is ().. A, B, C, D choices are ['5', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7825.jpg"
-  },
-  {
-    "id": 8022,
-    "problem_id": 7826,
-    "problem": "<image>As shown in the figure, line a || b || c, the distance between line a and line b is 2, and the distance between line b and line c is 4. Square ABCD's diagonal AC intersects diagonal BD at point O. If vertices A, D, and C are respectively on lines a, b, and c, then the area of triangle AOD is ().. A, B, C, D choices are ['5', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7826.jpg"
-  },
-  {
-    "id": 8023,
-    "problem_id": 7827,
-    "problem": "<image>As shown in the figure, line a || b || c, the distance between line a and line b is 2, and the distance between line b and line c is 4. Square ABCD's diagonal AC intersects diagonal BD at point O. If vertices A, D, and C are respectively on lines a, b, and c, then the area of triangle AOD is ().. A, B, C, D choices are ['5', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7827.jpg"
-  },
-  {
-    "id": 8024,
-    "problem_id": 7828,
-    "problem": "<image>As shown in the figure, line a || b || c, the distance between line a and line b is 2, and the distance between line b and line c is 4. Square ABCD's diagonal AC intersects diagonal BD at point O. If vertices A, D, and C are respectively on lines a, b, and c, then the area of triangle AOD is ().. A, B, C, D choices are ['5', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7828.jpg"
-  },
-  {
-    "id": 8025,
-    "problem_id": 7829,
-    "problem": "<image>As shown in the figure, line a || b || c, the distance between line a and line b is 2, and the distance between line b and line c is 4. Square ABCD's diagonal AC intersects diagonal BD at point O. If vertices A, D, and C are respectively on lines a, b, and c, then the area of triangle AOD is ().. A, B, C, D choices are ['5', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7829.jpg"
-  },
-  {
-    "id": 8026,
-    "problem_id": 7830,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 4, what is the area of rectangle ABCD? (). A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7830.jpg"
-  },
-  {
-    "id": 8027,
-    "problem_id": 7831,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 4, what is the area of rectangle ABCD? (). A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7831.jpg"
-  },
-  {
-    "id": 8028,
-    "problem_id": 7832,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 4, what is the area of rectangle ABCD? (). A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7832.jpg"
-  },
-  {
-    "id": 8029,
-    "problem_id": 7833,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 4, what is the area of rectangle ABCD? (). A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7833.jpg"
-  },
-  {
-    "id": 8030,
-    "problem_id": 7834,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 4, what is the area of rectangle ABCD? (). A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7834.jpg"
-  },
-  {
-    "id": 8031,
-    "problem_id": 7835,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 4, what is the area of rectangle ABCD? (). A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7835.jpg"
-  },
-  {
-    "id": 8032,
-    "problem_id": 7836,
-    "problem": "<image>As shown in the figure, equilateral triangle DEF is obtained by translating equilateral triangle ABC in the direction of ray BC. If AB = 3 and EC = 1, the length of BF is (). A, B, C, D choices are ['7', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7836.jpg"
-  },
-  {
-    "id": 8033,
-    "problem_id": 7837,
-    "problem": "<image>As shown in the figure, equilateral triangle DEF is obtained by translating equilateral triangle ABC in the direction of ray BC. If AB = 3 and EC = 1, the length of BF is (). A, B, C, D choices are ['7', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7837.jpg"
-  },
-  {
-    "id": 8034,
-    "problem_id": 7838,
-    "problem": "<image>As shown in the figure, this is a \"Zhao Shuangxian diagram\" made up of four identical right-angled triangles \u25b3ABE, \u25b3BCF, \u25b3CDG and \u25b3DAH, each with an area of 24. If AB=10, what is the length of each side of the square EFGH?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7838.jpg"
-  },
-  {
-    "id": 8035,
-    "problem_id": 7839,
-    "problem": "<image>As shown in the figure, this is a \"Zhao Shuangxian diagram\" made up of four identical right-angled triangles \u25b3ABE, \u25b3BCF, \u25b3CDG and \u25b3DAH, each with an area of 24. If AB=10, what is the length of each side of the square EFGH?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7839.jpg"
-  },
-  {
-    "id": 8036,
-    "problem_id": 7840,
-    "problem": "<image>As shown in the figure, this is a \"Zhao Shuangxian diagram\" made up of four identical right-angled triangles \u25b3ABE, \u25b3BCF, \u25b3CDG and \u25b3DAH, each with an area of 24. If AB=10, what is the length of each side of the square EFGH?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7840.jpg"
-  },
-  {
-    "id": 8037,
-    "problem_id": 7841,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7841.jpg"
-  },
-  {
-    "id": 8038,
-    "problem_id": 7842,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7842.jpg"
-  },
-  {
-    "id": 8039,
-    "problem_id": 7843,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7843.jpg"
-  },
-  {
-    "id": 8040,
-    "problem_id": 7844,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7844.jpg"
-  },
-  {
-    "id": 8041,
-    "problem_id": 7845,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7845.jpg"
-  },
-  {
-    "id": 8042,
-    "problem_id": 7846,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7846.jpg"
-  },
-  {
-    "id": 8043,
-    "problem_id": 7847,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220AOB = 60\u00b0. What is the measure of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7847.jpg"
-  },
-  {
-    "id": 8044,
-    "problem_id": 7848,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7848.jpg"
-  },
-  {
-    "id": 8045,
-    "problem_id": 7849,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7849.jpg"
-  },
-  {
-    "id": 8046,
-    "problem_id": 7850,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7850.jpg"
-  },
-  {
-    "id": 8047,
-    "problem_id": 7851,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7851.jpg"
-  },
-  {
-    "id": 8048,
-    "problem_id": 7852,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7852.jpg"
-  },
-  {
-    "id": 8049,
-    "problem_id": 7853,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7853.jpg"
-  },
-  {
-    "id": 8050,
-    "problem_id": 7854,
-    "problem": "<image>As shown in the figure, if the radius of the base of a cone is 6 cm and its height is 8 cm, what is the lateral surface area of the cone? (). A, B, C, D choices are ['30\u03c0cm2', '48\u03c0cm2', '60\u03c0cm2', '80\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7854.jpg"
-  },
-  {
-    "id": 8051,
-    "problem_id": 7855,
-    "problem": "<image>In the figure, the three vertices of equilateral triangle \u25b3ABC all lie on the circle O, and AD is the diameter of circle O. If OA = 3, then the length of arc BD is () .. A, B, C, D choices are ['frac{\u03c0}{2}', '\u03c0', 'frac{3\u03c0}{2}', '2\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7855.jpg"
-  },
-  {
-    "id": 8052,
-    "problem_id": 7856,
-    "problem": "<image>In the figure, the three vertices of equilateral triangle \u25b3ABC all lie on the circle O, and AD is the diameter of circle O. If OA = 3, then the length of arc BD is () .. A, B, C, D choices are ['frac{\u03c0}{2}', '\u03c0', 'frac{3\u03c0}{2}', '2\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7856.jpg"
-  },
-  {
-    "id": 8053,
-    "problem_id": 7857,
-    "problem": "<image>In the figure, the three vertices of equilateral triangle \u25b3ABC all lie on the circle O, and AD is the diameter of circle O. If OA = 3, then the length of arc BD is () .. A, B, C, D choices are ['frac{\u03c0}{2}', '\u03c0', 'frac{3\u03c0}{2}', '2\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7857.jpg"
-  },
-  {
-    "id": 8054,
-    "problem_id": 7858,
-    "problem": "<image>In the figure, the three vertices of equilateral triangle \u25b3ABC all lie on the circle O, and AD is the diameter of circle O. If OA = 3, then the length of arc BD is () .. A, B, C, D choices are ['frac{\u03c0}{2}', '\u03c0', 'frac{3\u03c0}{2}', '2\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7858.jpg"
-  },
-  {
-    "id": 8055,
-    "problem_id": 7859,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7859.jpg"
-  },
-  {
-    "id": 8056,
-    "problem_id": 7860,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7860.jpg"
-  },
-  {
-    "id": 8057,
-    "problem_id": 7861,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7861.jpg"
-  },
-  {
-    "id": 8058,
-    "problem_id": 7862,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7862.jpg"
-  },
-  {
-    "id": 8059,
-    "problem_id": 7863,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7863.jpg"
-  },
-  {
-    "id": 8060,
-    "problem_id": 7864,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7864.jpg"
-  },
-  {
-    "id": 8061,
-    "problem_id": 7865,
-    "problem": "<image>As shown in the figure, if a triangle ruler is placed as shown, then \u2220\u03b1 = ().. A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7865.jpg"
-  },
-  {
-    "id": 8062,
-    "problem_id": 7866,
-    "problem": "<image>If a right-angled triangle ruler is stacked in the way shown in the figure, what is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7866.jpg"
-  },
-  {
-    "id": 8063,
-    "problem_id": 7867,
-    "problem": "<image>If a right-angled triangle ruler is stacked in the way shown in the figure, what is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7867.jpg"
-  },
-  {
-    "id": 8064,
-    "problem_id": 7868,
-    "problem": "<image>If a right-angled triangle ruler is stacked in the way shown in the figure, what is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7868.jpg"
-  },
-  {
-    "id": 8065,
-    "problem_id": 7869,
-    "problem": "<image>If a right-angled triangle ruler is stacked in the way shown in the figure, what is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7869.jpg"
-  },
-  {
-    "id": 8066,
-    "problem_id": 7870,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on the circle such that \u2220AOC = 126\u00b0. What is the measure of \u2220CDB?. A, B, C, D choices are ['54\u00b0', '64\u00b0', '27\u00b0', '37\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7870.jpg"
-  },
-  {
-    "id": 8067,
-    "problem_id": 7871,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on the circle such that \u2220AOC = 126\u00b0. What is the measure of \u2220CDB?. A, B, C, D choices are ['54\u00b0', '64\u00b0', '27\u00b0', '37\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7871.jpg"
-  },
-  {
-    "id": 8068,
-    "problem_id": 7872,
-    "problem": "<image>In triangle ABC, \u2220ACB = 90\u00b0. M and N are the midpoints of AB and AC respectively. Extend BC to point D so that CD = \\frac{1}{3}\u00d7BD. Connect DM, DN, MN, and CM. If AB = 6, what is the value of DN?. A, B, C, D choices are ['6', '3', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7872.jpg"
-  },
-  {
-    "id": 8069,
-    "problem_id": 7873,
-    "problem": "<image>In triangle ABC, \u2220ACB = 90\u00b0. M and N are the midpoints of AB and AC respectively. Extend BC to point D so that CD = \\frac{1}{3}\u00d7BD. Connect DM, DN, MN, and CM. If AB = 6, what is the value of DN?. A, B, C, D choices are ['6', '3', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7873.jpg"
-  },
-  {
-    "id": 8070,
-    "problem_id": 7874,
-    "problem": "<image>In triangle ABC, \u2220ACB = 90\u00b0. M and N are the midpoints of AB and AC respectively. Extend BC to point D so that CD = \\frac{1}{3}\u00d7BD. Connect DM, DN, MN, and CM. If AB = 6, what is the value of DN?. A, B, C, D choices are ['6', '3', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7874.jpg"
-  },
-  {
-    "id": 8071,
-    "problem_id": 7875,
-    "problem": "<image>In triangle ABC, \u2220ACB = 90\u00b0. M and N are the midpoints of AB and AC respectively. Extend BC to point D so that CD = \\frac{1}{3}\u00d7BD. Connect DM, DN, MN, and CM. If AB = 6, what is the value of DN?. A, B, C, D choices are ['6', '3', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7875.jpg"
-  },
-  {
-    "id": 8072,
-    "problem_id": 7876,
-    "problem": "<image>If the areas of the three squares are as shown in the figure, what is the value of S? (). A, B, C, D choices are ['3', '12', '9', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7876.jpg"
-  },
-  {
-    "id": 8073,
-    "problem_id": 7877,
-    "problem": "<image>If the areas of the three squares are as shown in the figure, what is the value of S? (). A, B, C, D choices are ['3', '12', '9', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7877.jpg"
-  },
-  {
-    "id": 8074,
-    "problem_id": 7878,
-    "problem": "<image>If the areas of the three squares are as shown in the figure, what is the value of S? (). A, B, C, D choices are ['3', '12', '9', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7878.jpg"
-  },
-  {
-    "id": 8075,
-    "problem_id": 7879,
-    "problem": "<image>If the areas of the three squares are as shown in the figure, what is the value of S? (). A, B, C, D choices are ['3', '12', '9', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7879.jpg"
-  },
-  {
-    "id": 8076,
-    "problem_id": 7880,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If angle C is 100 degrees, what is the degree measure of angle A? (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7880.jpg"
-  },
-  {
-    "id": 8077,
-    "problem_id": 7881,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If angle C is 100 degrees, what is the degree measure of angle A? (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7881.jpg"
-  },
-  {
-    "id": 8078,
-    "problem_id": 7882,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If angle C is 100 degrees, what is the degree measure of angle A? (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7882.jpg"
-  },
-  {
-    "id": 8079,
-    "problem_id": 7883,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If angle C is 100 degrees, what is the degree measure of angle A? (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7883.jpg"
-  },
-  {
-    "id": 8080,
-    "problem_id": 7884,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If angle C is 100 degrees, what is the degree measure of angle A? (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7884.jpg"
-  },
-  {
-    "id": 8081,
-    "problem_id": 7885,
-    "problem": "<image>In the square ABCD shown in the figure, point E is a point on the diagonal BD, and BE = AB. Connect CE and AE. What is the degree measure of angle DAE? (). A, B, C, D choices are ['22.5\u00b0', '25\u00b0', '30\u00b0', '32.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7885.jpg"
-  },
-  {
-    "id": 8082,
-    "problem_id": 7886,
-    "problem": "<image>In the square ABCD shown in the figure, point E is a point on the diagonal BD, and BE = AB. Connect CE and AE. What is the degree measure of angle DAE? (). A, B, C, D choices are ['22.5\u00b0', '25\u00b0', '30\u00b0', '32.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7886.jpg"
-  },
-  {
-    "id": 8083,
-    "problem_id": 7887,
-    "problem": "<image>In the square ABCD shown in the figure, point E is a point on the diagonal BD, and BE = AB. Connect CE and AE. What is the degree measure of angle DAE? (). A, B, C, D choices are ['22.5\u00b0', '25\u00b0', '30\u00b0', '32.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7887.jpg"
-  },
-  {
-    "id": 8084,
-    "problem_id": 7888,
-    "problem": "<image>In the square ABCD shown in the figure, point E is a point on the diagonal BD, and BE = AB. Connect CE and AE. What is the degree measure of angle DAE? (). A, B, C, D choices are ['22.5\u00b0', '25\u00b0', '30\u00b0', '32.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7888.jpg"
-  },
-  {
-    "id": 8085,
-    "problem_id": 7889,
-    "problem": "<image>In right triangle ABC, as shown in the figure, points D, E, and F are the midpoints of sides AB, AC, and BC, respectively. If AC = 8 and BC = 6, what is the area of quadrilateral CEDF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7889.jpg"
-  },
-  {
-    "id": 8086,
-    "problem_id": 7890,
-    "problem": "<image>In right triangle ABC, as shown in the figure, points D, E, and F are the midpoints of sides AB, AC, and BC, respectively. If AC = 8 and BC = 6, what is the area of quadrilateral CEDF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7890.jpg"
-  },
-  {
-    "id": 8087,
-    "problem_id": 7891,
-    "problem": "<image>In right triangle ABC, as shown in the figure, points D, E, and F are the midpoints of sides AB, AC, and BC, respectively. If AC = 8 and BC = 6, what is the area of quadrilateral CEDF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7891.jpg"
-  },
-  {
-    "id": 8088,
-    "problem_id": 7892,
-    "problem": "<image>In a math activity measuring the height of a flagpole, a student placed a mirror at his feet and stepped back until he could just see the top of the flagpole in the mirror. If the distance from his eyes to the ground AB is 1.5m, and he measured BC to be 2m and CD to be 12m, then the height of the flagpole DE is () meters.. A, B, C, D choices are ['6m', '8m', '9m', '16m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7892.jpg"
-  },
-  {
-    "id": 8089,
-    "problem_id": 7893,
-    "problem": "<image>In a math activity measuring the height of a flagpole, a student placed a mirror at his feet and stepped back until he could just see the top of the flagpole in the mirror. If the distance from his eyes to the ground AB is 1.5m, and he measured BC to be 2m and CD to be 12m, then the height of the flagpole DE is () meters.. A, B, C, D choices are ['6m', '8m', '9m', '16m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7893.jpg"
-  },
-  {
-    "id": 8090,
-    "problem_id": 7894,
-    "problem": "<image>In a math activity measuring the height of a flagpole, a student placed a mirror at his feet and stepped back until he could just see the top of the flagpole in the mirror. If the distance from his eyes to the ground AB is 1.5m, and he measured BC to be 2m and CD to be 12m, then the height of the flagpole DE is () meters.. A, B, C, D choices are ['6m', '8m', '9m', '16m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7894.jpg"
-  },
-  {
-    "id": 8091,
-    "problem_id": 7895,
-    "problem": "<image>In a math activity measuring the height of a flagpole, a student placed a mirror at his feet and stepped back until he could just see the top of the flagpole in the mirror. If the distance from his eyes to the ground AB is 1.5m, and he measured BC to be 2m and CD to be 12m, then the height of the flagpole DE is () meters.. A, B, C, D choices are ['6m', '8m', '9m', '16m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7895.jpg"
-  },
-  {
-    "id": 8092,
-    "problem_id": 7896,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7896.jpg"
-  },
-  {
-    "id": 8093,
-    "problem_id": 7897,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7897.jpg"
-  },
-  {
-    "id": 8094,
-    "problem_id": 7898,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7898.jpg"
-  },
-  {
-    "id": 8095,
-    "problem_id": 7899,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7899.jpg"
-  },
-  {
-    "id": 8096,
-    "problem_id": 7900,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7900.jpg"
-  },
-  {
-    "id": 8097,
-    "problem_id": 7901,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7901.jpg"
-  },
-  {
-    "id": 8098,
-    "problem_id": 7902,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7902.jpg"
-  },
-  {
-    "id": 8099,
-    "problem_id": 7903,
-    "problem": "<image>In rectangle ABCD, AB=12 and AD=5. The length of diagonal AC is ().. A, B, C, D choices are ['12', '6.5', '13', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7903.jpg"
-  },
-  {
-    "id": 8100,
-    "problem_id": 7904,
-    "problem": "<image>As shown in the figure, point D is on the extension of side BC of triangle ABC, and \u2220ACD = 105\u00b0, \u2220A = 70\u00b0. What is the measure of \u2220B?. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7904.jpg"
-  },
-  {
-    "id": 8101,
-    "problem_id": 7905,
-    "problem": "<image>As shown in the figure, point D is on the extension of side BC of triangle ABC, and \u2220ACD = 105\u00b0, \u2220A = 70\u00b0. What is the measure of \u2220B?. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7905.jpg"
-  },
-  {
-    "id": 8102,
-    "problem_id": 7906,
-    "problem": "<image>As shown in the figure, point D is on the extension of side BC of triangle ABC, and \u2220ACD = 105\u00b0, \u2220A = 70\u00b0. What is the measure of \u2220B?. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7906.jpg"
-  },
-  {
-    "id": 8103,
-    "problem_id": 7907,
-    "problem": "<image>As shown in the figure, point D is on the extension of side BC of triangle ABC, and \u2220ACD = 105\u00b0, \u2220A = 70\u00b0. What is the measure of \u2220B?. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7907.jpg"
-  },
-  {
-    "id": 8104,
-    "problem_id": 7908,
-    "problem": "<image>As shown in the figure, point D is on the extension of side BC of triangle ABC, and \u2220ACD = 105\u00b0, \u2220A = 70\u00b0. What is the measure of \u2220B?. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7908.jpg"
-  },
-  {
-    "id": 8105,
-    "problem_id": 7909,
-    "problem": "<image>As shown in the figure, point D is on the extension of side BC of triangle ABC, and \u2220ACD = 105\u00b0, \u2220A = 70\u00b0. What is the measure of \u2220B?. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7909.jpg"
-  },
-  {
-    "id": 8106,
-    "problem_id": 7910,
-    "problem": "<image>In triangle ABC, D is a point on BC and BD=2, DC=1. If the area of triangle ACD is 12, what is the area of triangle ABC?. A, B, C, D choices are ['30', '36', '72', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7910.jpg"
-  },
-  {
-    "id": 8107,
-    "problem_id": 7911,
-    "problem": "<image>In triangle ABC, D is a point on BC and BD=2, DC=1. If the area of triangle ACD is 12, what is the area of triangle ABC?. A, B, C, D choices are ['30', '36', '72', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7911.jpg"
-  },
-  {
-    "id": 8108,
-    "problem_id": 7912,
-    "problem": "<image>In triangle ABC, D is a point on BC and BD=2, DC=1. If the area of triangle ACD is 12, what is the area of triangle ABC?. A, B, C, D choices are ['30', '36', '72', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7912.jpg"
-  },
-  {
-    "id": 8109,
-    "problem_id": 7913,
-    "problem": "<image>In triangle ABC, D is a point on BC and BD=2, DC=1. If the area of triangle ACD is 12, what is the area of triangle ABC?. A, B, C, D choices are ['30', '36', '72', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7913.jpg"
-  },
-  {
-    "id": 8110,
-    "problem_id": 7914,
-    "problem": "<image>In triangle ABC, D is a point on BC and BD=2, DC=1. If the area of triangle ACD is 12, what is the area of triangle ABC?. A, B, C, D choices are ['30', '36', '72', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7914.jpg"
-  },
-  {
-    "id": 8111,
-    "problem_id": 7915,
-    "problem": "<image>In triangle ABC, D is a point on BC and BD=2, DC=1. If the area of triangle ACD is 12, what is the area of triangle ABC?. A, B, C, D choices are ['30', '36', '72', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7915.jpg"
-  },
-  {
-    "id": 8112,
-    "problem_id": 7916,
-    "problem": "<image>In triangle ABC, with \u2220B = 70\u00b0 and \u2220C = 50\u00b0, if D, E, and F are the midpoints of sides AB, BC, and CA respectively, then what is the measure of \u2220DEF?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7916.jpg"
-  },
-  {
-    "id": 8113,
-    "problem_id": 7917,
-    "problem": "<image>In triangle ABC, with \u2220B = 70\u00b0 and \u2220C = 50\u00b0, if D, E, and F are the midpoints of sides AB, BC, and CA respectively, then what is the measure of \u2220DEF?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7917.jpg"
-  },
-  {
-    "id": 8115,
-    "problem_id": 7918,
-    "problem": "<image>In triangle ABC, with \u2220B = 70\u00b0 and \u2220C = 50\u00b0, if D, E, and F are the midpoints of sides AB, BC, and CA respectively, then what is the measure of \u2220DEF?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7918.jpg"
-  },
-  {
-    "id": 8116,
-    "problem_id": 7919,
-    "problem": "<image>In triangle ABC, with S(\u25b3ABC)=20, AB=AC=10. Point D is on BC, DE\u22a5AB with the foot of the perpendicular being E, and DF\u22a5AC with the foot of the perpendicular being F. What is the value of DE+DF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7919.jpg"
-  },
-  {
-    "id": 8117,
-    "problem_id": 7920,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of sides AB and AC respectively. If DE = 2.5 cm, then what is the length of BC?. A, B, C, D choices are ['2.5', '5', '7.5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7920.jpg"
-  },
-  {
-    "id": 8118,
-    "problem_id": 7921,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of sides AB and AC respectively. If DE = 2.5 cm, then what is the length of BC?. A, B, C, D choices are ['2.5', '5', '7.5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7921.jpg"
-  },
-  {
-    "id": 8119,
-    "problem_id": 7922,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of sides AB and AC respectively. If DE = 2.5 cm, then what is the length of BC?. A, B, C, D choices are ['2.5', '5', '7.5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7922.jpg"
-  },
-  {
-    "id": 8120,
-    "problem_id": 7923,
-    "problem": "<image>As shown in the figure, AB is parallel to DE, GF is perpendicular to BC at F, and \u2220FGA = 140\u00b0. What is the measure of \u2220CDE? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7923.jpg"
-  },
-  {
-    "id": 8121,
-    "problem_id": 7924,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is then connected. If BC = 5 and AC = 4, what is the perimeter of triangle ACE?. A, B, C, D choices are ['9', '10', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7924.jpg"
-  },
-  {
-    "id": 8122,
-    "problem_id": 7925,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is then connected. If BC = 5 and AC = 4, what is the perimeter of triangle ACE?. A, B, C, D choices are ['9', '10', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7925.jpg"
-  },
-  {
-    "id": 8123,
-    "problem_id": 7926,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is then connected. If BC = 5 and AC = 4, what is the perimeter of triangle ACE?. A, B, C, D choices are ['9', '10', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7926.jpg"
-  },
-  {
-    "id": 8124,
-    "problem_id": 7927,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, E is the midpoint of AD, and the area of \u25b3ABE is 2. What is the area of \u25b3ABC?. A, B, C, D choices are ['5', '6', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7927.jpg"
-  },
-  {
-    "id": 8125,
-    "problem_id": 7928,
-    "problem": "<image>There is a flower bed on campus surrounded by two congruent hexagons with a side length of 3.5m. Now the flower bed is expanded into a diamond-shaped area as shown in the figure, and grass is planted in the newly expanded part. What is the perimeter of the expanded diamond-shaped area?. A, B, C, D choices are ['28m', '35m', '42m', '56m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7928.jpg"
-  },
-  {
-    "id": 8126,
-    "problem_id": 7929,
-    "problem": "<image>There is a flower bed on campus surrounded by two congruent hexagons with a side length of 3.5m. Now the flower bed is expanded into a diamond-shaped area as shown in the figure, and grass is planted in the newly expanded part. What is the perimeter of the expanded diamond-shaped area?. A, B, C, D choices are ['28m', '35m', '42m', '56m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7929.jpg"
-  },
-  {
-    "id": 8127,
-    "problem_id": 7930,
-    "problem": "<image>There is a flower bed on campus surrounded by two congruent hexagons with a side length of 3.5m. Now the flower bed is expanded into a diamond-shaped area as shown in the figure, and grass is planted in the newly expanded part. What is the perimeter of the expanded diamond-shaped area?. A, B, C, D choices are ['28m', '35m', '42m', '56m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7930.jpg"
-  },
-  {
-    "id": 8128,
-    "problem_id": 7931,
-    "problem": "<image>Place a set square as shown in the figure so that two right angles coincide. What is the degree measure of \u2220AFE? (). A, B, C, D choices are ['175\u00b0', '165\u00b0', '155\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7931.jpg"
-  },
-  {
-    "id": 8129,
-    "problem_id": 7932,
-    "problem": "<image>Place a set square as shown in the figure so that two right angles coincide. What is the degree measure of \u2220AFE? (). A, B, C, D choices are ['175\u00b0', '165\u00b0', '155\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7932.jpg"
-  },
-  {
-    "id": 8130,
-    "problem_id": 7933,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is an inscribed regular pentagon of circle O. The degree measure of central angle \u2220COD in the regular pentagon is (). A, B, C, D choices are ['60\u00b0', '36\u00b0', '76\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7933.jpg"
-  },
-  {
-    "id": 8131,
-    "problem_id": 7934,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is an inscribed regular pentagon of circle O. The degree measure of central angle \u2220COD in the regular pentagon is (). A, B, C, D choices are ['60\u00b0', '36\u00b0', '76\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7934.jpg"
-  },
-  {
-    "id": 8132,
-    "problem_id": 7935,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is an inscribed regular pentagon of circle O. The degree measure of central angle \u2220COD in the regular pentagon is (). A, B, C, D choices are ['60\u00b0', '36\u00b0', '76\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7935.jpg"
-  },
-  {
-    "id": 8133,
-    "problem_id": 7936,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is an inscribed regular pentagon of circle O. The degree measure of central angle \u2220COD in the regular pentagon is (). A, B, C, D choices are ['60\u00b0', '36\u00b0', '76\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7936.jpg"
-  },
-  {
-    "id": 8134,
-    "problem_id": 7937,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is an inscribed regular pentagon of circle O. The degree measure of central angle \u2220COD in the regular pentagon is (). A, B, C, D choices are ['60\u00b0', '36\u00b0', '76\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7937.jpg"
-  },
-  {
-    "id": 8135,
-    "problem_id": 7938,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is an inscribed regular pentagon of circle O. The degree measure of central angle \u2220COD in the regular pentagon is (). A, B, C, D choices are ['60\u00b0', '36\u00b0', '76\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7938.jpg"
-  },
-  {
-    "id": 8136,
-    "problem_id": 7939,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7939.jpg"
-  },
-  {
-    "id": 8137,
-    "problem_id": 7940,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7940.jpg"
-  },
-  {
-    "id": 8138,
-    "problem_id": 7941,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7941.jpg"
-  },
-  {
-    "id": 8139,
-    "problem_id": 7942,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7942.jpg"
-  },
-  {
-    "id": 8140,
-    "problem_id": 7943,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7943.jpg"
-  },
-  {
-    "id": 8141,
-    "problem_id": 7944,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7944.jpg"
-  },
-  {
-    "id": 8142,
-    "problem_id": 7945,
-    "problem": "<image>As shown in the figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 4.8 km, what is the distance between points M and C? (). A, B, C, D choices are ['1.2km', '2.4km', '3.6km', '4.8km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7945.jpg"
-  },
-  {
-    "id": 8143,
-    "problem_id": 7946,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. What is the length of EF?. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7946.jpg"
-  },
-  {
-    "id": 8144,
-    "problem_id": 7947,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. What is the length of EF?. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7947.jpg"
-  },
-  {
-    "id": 8145,
-    "problem_id": 7948,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. What is the length of EF?. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7948.jpg"
-  },
-  {
-    "id": 8146,
-    "problem_id": 7949,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. What is the length of EF?. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7949.jpg"
-  },
-  {
-    "id": 8147,
-    "problem_id": 7950,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. What is the length of EF?. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7950.jpg"
-  },
-  {
-    "id": 8148,
-    "problem_id": 7951,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. What is the length of EF?. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7951.jpg"
-  },
-  {
-    "id": 8149,
-    "problem_id": 7952,
-    "problem": "<image>In triangle ABC, AB = AC = 10 and BC = 16. Taking points A and B as centers, arcs are drawn with lengths greater than 0.5\u00d7AB. The two arcs intersect at points M and N. A straight line MN is drawn, which intersects AB at D and BC at E. AE is then connected. What is the perimeter of triangle ACE?. A, B, C, D choices are ['21', '36', '26', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7952.jpg"
-  },
-  {
-    "id": 8150,
-    "problem_id": 7953,
-    "problem": "<image>In triangle ABC, AB = AC = 10 and BC = 16. Taking points A and B as centers, arcs are drawn with lengths greater than 0.5\u00d7AB. The two arcs intersect at points M and N. A straight line MN is drawn, which intersects AB at D and BC at E. AE is then connected. What is the perimeter of triangle ACE?. A, B, C, D choices are ['21', '36', '26', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7953.jpg"
-  },
-  {
-    "id": 8151,
-    "problem_id": 7954,
-    "problem": "<image>In triangle ABC, AB = AC = 10 and BC = 16. Taking points A and B as centers, arcs are drawn with lengths greater than 0.5\u00d7AB. The two arcs intersect at points M and N. A straight line MN is drawn, which intersects AB at D and BC at E. AE is then connected. What is the perimeter of triangle ACE?. A, B, C, D choices are ['21', '36', '26', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7954.jpg"
-  },
-  {
-    "id": 8152,
-    "problem_id": 7955,
-    "problem": "<image>In triangle ABC, AB = AC = 10 and BC = 16. Taking points A and B as centers, arcs are drawn with lengths greater than 0.5\u00d7AB. The two arcs intersect at points M and N. A straight line MN is drawn, which intersects AB at D and BC at E. AE is then connected. What is the perimeter of triangle ACE?. A, B, C, D choices are ['21', '36', '26', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7955.jpg"
-  },
-  {
-    "id": 8153,
-    "problem_id": 7956,
-    "problem": "<image>In triangle ABC, AB = AC = 10 and BC = 16. Taking points A and B as centers, arcs are drawn with lengths greater than 0.5\u00d7AB. The two arcs intersect at points M and N. A straight line MN is drawn, which intersects AB at D and BC at E. AE is then connected. What is the perimeter of triangle ACE?. A, B, C, D choices are ['21', '36', '26', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7956.jpg"
-  },
-  {
-    "id": 8154,
-    "problem_id": 7957,
-    "problem": "<image>As shown in the diagram: What is the area of shape A? (). A, B, C, D choices are ['225', '144', '81', '66'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7957.jpg"
-  },
-  {
-    "id": 8156,
-    "problem_id": 7958,
-    "problem": "<image>As shown in the diagram: What is the area of shape A? (). A, B, C, D choices are ['225', '144', '81', '66'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7958.jpg"
-  },
-  {
-    "id": 8157,
-    "problem_id": 7959,
-    "problem": "<image>As shown in the diagram: What is the area of shape A? (). A, B, C, D choices are ['225', '144', '81', '66'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7959.jpg"
-  },
-  {
-    "id": 8158,
-    "problem_id": 7960,
-    "problem": "<image>As shown in the diagram: What is the area of shape A? (). A, B, C, D choices are ['225', '144', '81', '66'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7960.jpg"
-  },
-  {
-    "id": 8159,
-    "problem_id": 7961,
-    "problem": "<image>As shown in the diagram: What is the area of shape A? (). A, B, C, D choices are ['225', '144', '81', '66'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7961.jpg"
-  },
-  {
-    "id": 8160,
-    "problem_id": 7962,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7962.jpg"
-  },
-  {
-    "id": 8161,
-    "problem_id": 7963,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7963.jpg"
-  },
-  {
-    "id": 8162,
-    "problem_id": 7964,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7964.jpg"
-  },
-  {
-    "id": 8163,
-    "problem_id": 7965,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7965.jpg"
-  },
-  {
-    "id": 8164,
-    "problem_id": 7966,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7966.jpg"
-  },
-  {
-    "id": 8165,
-    "problem_id": 7967,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7967.jpg"
-  },
-  {
-    "id": 8166,
-    "problem_id": 7968,
-    "problem": "<image>If a right-angled triangle board and a ruler are placed as shown in the figure, if \u22201 = 35\u00b0, then what is the degree of \u22202? (). A, B, C, D choices are ['55\u00b0', '50\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7968.jpg"
-  },
-  {
-    "id": 8167,
-    "problem_id": 7969,
-    "problem": "<image>A set of triangle rulers, as shown in the figure, are stacked together. What is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['75\u00b0', '60\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7969.jpg"
-  },
-  {
-    "id": 8168,
-    "problem_id": 7970,
-    "problem": "<image>A set of triangle rulers, as shown in the figure, are stacked together. What is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['75\u00b0', '60\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7970.jpg"
-  },
-  {
-    "id": 8169,
-    "problem_id": 7971,
-    "problem": "<image>A set of triangle rulers, as shown in the figure, are stacked together. What is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['75\u00b0', '60\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7971.jpg"
-  },
-  {
-    "id": 8170,
-    "problem_id": 7972,
-    "problem": "<image>A set of triangle rulers, as shown in the figure, are stacked together. What is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['75\u00b0', '60\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7972.jpg"
-  },
-  {
-    "id": 8171,
-    "problem_id": 7973,
-    "problem": "<image>A set of triangle rulers, as shown in the figure, are stacked together. What is the degree of angle \u03b1 in the figure? (). A, B, C, D choices are ['75\u00b0', '60\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7973.jpg"
-  },
-  {
-    "id": 8172,
-    "problem_id": 7974,
-    "problem": "<image>In the figure, an equilateral triangle CDE is constructed outside the square ABCD, and AE is connected. What is the degree measure of \u2220DAE? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '12.5\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7974.jpg"
-  },
-  {
-    "id": 8173,
-    "problem_id": 7975,
-    "problem": "<image>In quadrilateral ABCD, if \u2220A + \u2220C = 140\u00b0, what is the degree measure of \u2220B? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '70\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7975.jpg"
-  },
-  {
-    "id": 8174,
-    "problem_id": 7976,
-    "problem": "<image>In quadrilateral ABCD, if \u2220A + \u2220C = 140\u00b0, what is the degree measure of \u2220B? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '70\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7976.jpg"
-  },
-  {
-    "id": 8175,
-    "problem_id": 7977,
-    "problem": "<image>In quadrilateral ABCD, if \u2220A + \u2220C = 140\u00b0, what is the degree measure of \u2220B? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '70\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7977.jpg"
-  },
-  {
-    "id": 8176,
-    "problem_id": 7978,
-    "problem": "<image>In quadrilateral ABCD, if \u2220A + \u2220C = 140\u00b0, what is the degree measure of \u2220B? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '70\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7978.jpg"
-  },
-  {
-    "id": 8177,
-    "problem_id": 7979,
-    "problem": "<image>As shown in the figure, l1 is parallel to l2, and AE is perpendicular to BE. If \u22201 is 130\u00b0, what is the degree of \u22202?. A, B, C, D choices are ['120\u00b0', '130\u00b0', '140\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7979.jpg"
-  },
-  {
-    "id": 8178,
-    "problem_id": 7980,
-    "problem": "<image>If a regular pentagon and a regular hexagon with equal side lengths are combined as shown in the figure, what is the measure of angle ABO? (). A, B, C, D choices are ['24\u00b0', '48\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7980.jpg"
-  },
-  {
-    "id": 8179,
-    "problem_id": 7981,
-    "problem": "<image>If a regular pentagon and a regular hexagon with equal side lengths are combined as shown in the figure, what is the measure of angle ABO? (). A, B, C, D choices are ['24\u00b0', '48\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7981.jpg"
-  },
-  {
-    "id": 8180,
-    "problem_id": 7982,
-    "problem": "<image>If a regular pentagon and a regular hexagon with equal side lengths are combined as shown in the figure, what is the measure of angle ABO? (). A, B, C, D choices are ['24\u00b0', '48\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7982.jpg"
-  },
-  {
-    "id": 8181,
-    "problem_id": 7983,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, CD is a chord of circle O, and AC, AD, and BD are connected. If \u2220BAC=34\u00b0, then what is the degree measure of \u2220ADC?. A, B, C, D choices are ['34\u00b0', '55\u00b0', '56\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7983.jpg"
-  },
-  {
-    "id": 8183,
-    "problem_id": 7984,
-    "problem": "<image>As shown in the figure, it is known that AB = AC, AB = 10, BC = 6. Using points A and B as centers, arcs with length greater than 0.5 \u00d7 AB are drawn as radii. The two arcs intersect at points M and N. Line MN intersects AC at point D. The perimeter of triangle BDC is () .. A, B, C, D choices are ['16', '20', '22', '26'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7984.jpg"
-  },
-  {
-    "id": 8184,
-    "problem_id": 7985,
-    "problem": "<image>As shown in the figure, line l1 is parallel to line l2, and line l3 intersects l1 at point A and l2 at point B. Line l4 passing through point B intersects l1 at point C. If \u22203 = 50\u00b0 and \u22201 + \u22202 + \u22203 = 240\u00b0, what is the measure of \u22204?. A, B, C, D choices are ['80\u00b0', '70\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7985.jpg"
-  },
-  {
-    "id": 8185,
-    "problem_id": 7986,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ACB = 90\u00b0, AC = 1, AB = 2. An arc with AC as the radius is drawn with point A as the center, intersecting AB at point D. What is the area of sector CAD?. A, B, C, D choices are ['1', '\\\\frac{\u03c0}{3}', '\\\\frac{\u03c0}{6}', '\\\\frac{\u03c0}{12}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7986.jpg"
-  },
-  {
-    "id": 8186,
-    "problem_id": 7987,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ACB = 90\u00b0, AC = 1, AB = 2. An arc with AC as the radius is drawn with point A as the center, intersecting AB at point D. What is the area of sector CAD?. A, B, C, D choices are ['1', '\\\\frac{\u03c0}{3}', '\\\\frac{\u03c0}{6}', '\\\\frac{\u03c0}{12}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7987.jpg"
-  },
-  {
-    "id": 8187,
-    "problem_id": 7988,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ACB = 90\u00b0, AC = 1, AB = 2. An arc with AC as the radius is drawn with point A as the center, intersecting AB at point D. What is the area of sector CAD?. A, B, C, D choices are ['1', '\\\\frac{\u03c0}{3}', '\\\\frac{\u03c0}{6}', '\\\\frac{\u03c0}{12}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7988.jpg"
-  },
-  {
-    "id": 8188,
-    "problem_id": 7989,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ACB = 90\u00b0, AC = 1, AB = 2. An arc with AC as the radius is drawn with point A as the center, intersecting AB at point D. What is the area of sector CAD?. A, B, C, D choices are ['1', '\\\\frac{\u03c0}{3}', '\\\\frac{\u03c0}{6}', '\\\\frac{\u03c0}{12}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7989.jpg"
-  },
-  {
-    "id": 8190,
-    "problem_id": 7990,
-    "problem": "<image>In the parallelogram ABCD as shown, where AB=4 and AD=5, AE bisects angle BAD and intersects side BC at point E. What is the length of CE?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7990.jpg"
-  },
-  {
-    "id": 8192,
-    "problem_id": 7991,
-    "problem": "<image>As shown in the figure, the circumference of the base of a cylinder is 10cm, and the height of the cylinder is 12cm. If a bee wants to fly from point A inside the cylinder to the opposite point B, what is the shortest distance it can fly? (). A, B, C, D choices are ['10\u03c0cm', '13cm', '13\u03c0cm', '15cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7991.jpg"
-  },
-  {
-    "id": 8193,
-    "problem_id": 7992,
-    "problem": "<image>As shown in the figure, PA and PB respectively intersect \u2299O at points A and B, and MN intersects \u2299O at point C. MN also intersects PA and PB at points M and N, respectively. If PA = 7.5cm, what is the perimeter of \u25b3PMN?. A, B, C, D choices are ['7.5cm', '10cm', '12.5cm', '15cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7992.jpg"
-  },
-  {
-    "id": 8195,
-    "problem_id": 7993,
-    "problem": "<image>As shown in the figure, the area of \u25b3PBC is 15cm2, PB is the angle bisector of \u2220ABC, and AP is perpendicular to BP at P. The area of \u25b3ABC is (). A, B, C, D choices are ['25cm2', '30cm2', '32.5cm2', '35cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7993.jpg"
-  },
-  {
-    "id": 8196,
-    "problem_id": 7994,
-    "problem": "<image>As shown in the figure, \u2220CBA = \u2220ACB = 65\u00b0, \u2220ACE = 15\u00b0. What is the degree measure of \u2220AEC?. A, B, C, D choices are ['35\u00b0', '50\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7994.jpg"
-  },
-  {
-    "id": 8197,
-    "problem_id": 7995,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B respectively. CD is tangent to circle O at point E, and intersects PA and PB at points C and D. If the perimeter of triangle PCD is 3, what is the value of PA?. A, B, C, D choices are ['1.5', '\\\\frac{2}{3}', '0.5', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7995.jpg"
-  },
-  {
-    "id": 8198,
-    "problem_id": 7996,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B respectively. CD is tangent to circle O at point E, and intersects PA and PB at points C and D. If the perimeter of triangle PCD is 3, what is the value of PA?. A, B, C, D choices are ['1.5', '\\\\frac{2}{3}', '0.5', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7996.jpg"
-  },
-  {
-    "id": 8201,
-    "problem_id": 7997,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC respectively. If the area of triangle ABC is 8, what is the area of triangle DEC?. A, B, C, D choices are ['6', '4', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7997.jpg"
-  },
-  {
-    "id": 8203,
-    "problem_id": 7998,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC, E is the midpoint of AD, and BE is connected. If the area of triangle ABC is 12, then the area of triangle ABE is ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7998.jpg"
-  },
-  {
-    "id": 8204,
-    "problem_id": 7999,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220DOB = 140\u00b0, then \u2220ACD = ().. A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/7999.jpg"
-  },
-  {
-    "id": 8205,
-    "problem_id": 8000,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, the right-angled vertex of the right triangle ABC lies on line a, point C lies on line b, and line b bisects angle ACB exactly. If angle B is 20\u00b0, then the size of angle 1 is (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8000.jpg"
-  },
-  {
-    "id": 8207,
-    "problem_id": 8001,
-    "problem": "<image>As shown in the figure, in triangle ABC, AB=AC. Point D and E are on BC and AC respectively, and AD=AE. \u2220BAD=\u2220CAD=20\u00b0. What is the measure of \u2220EDC?. A, B, C, D choices are ['30\u00b0', '20\u00b0', '10\u00b0', '5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8001.jpg"
-  },
-  {
-    "id": 8208,
-    "problem_id": 8002,
-    "problem": "<image>As shown in the figure, in triangle ABC, AB=AC. Point D and E are on BC and AC respectively, and AD=AE. \u2220BAD=\u2220CAD=20\u00b0. What is the measure of \u2220EDC?. A, B, C, D choices are ['30\u00b0', '20\u00b0', '10\u00b0', '5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8002.jpg"
-  },
-  {
-    "id": 8209,
-    "problem_id": 8003,
-    "problem": "<image>In triangle ABC, D is a point on side AB, and \u2220ACD = \u2220B. AD = 2 and AC = 4. If the area of triangle ADC is 2, then the area of triangle BCD is ().\n\nNote: No translation is needed for the given problem statement as it is already in Chinese.. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8003.jpg"
-  },
-  {
-    "id": 8210,
-    "problem_id": 8004,
-    "problem": "<image>In triangle ABC, AB = 10, BC = 16. D and E are the midpoints of sides AB and AC, respectively. F is a point on segment DE, and AF and BF are connected. If \u2220AFB = 90\u00b0, what is the length of segment EF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8004.jpg"
-  },
-  {
-    "id": 8211,
-    "problem_id": 8005,
-    "problem": "<image>In triangle ABC, AB = 10, BC = 16. D and E are the midpoints of sides AB and AC, respectively. F is a point on segment DE, and AF and BF are connected. If \u2220AFB = 90\u00b0, what is the length of segment EF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8005.jpg"
-  },
-  {
-    "id": 8212,
-    "problem_id": 8006,
-    "problem": "<image>In triangle ABC, AB = 10, BC = 16. D and E are the midpoints of sides AB and AC, respectively. F is a point on segment DE, and AF and BF are connected. If \u2220AFB = 90\u00b0, what is the length of segment EF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8006.jpg"
-  },
-  {
-    "id": 8213,
-    "problem_id": 8007,
-    "problem": "<image>As shown in the figure, l1\u2225l2\u2225l3, \u22201\uff1d60\u00b0, \u22202\uff1d20\u00b0, what is the degree of \u22203?. A, B, C, D choices are ['120\u00b0', '140\u00b0', '110\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8007.jpg"
-  },
-  {
-    "id": 8214,
-    "problem_id": 8008,
-    "problem": "<image>As shown in the figure, l1\u2225l2\u2225l3, \u22201\uff1d60\u00b0, \u22202\uff1d20\u00b0, what is the degree of \u22203?. A, B, C, D choices are ['120\u00b0', '140\u00b0', '110\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8008.jpg"
-  },
-  {
-    "id": 8216,
-    "problem_id": 8009,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O, BC is the diameter of circle O, \u2220ACB = 18\u00b0, D is the midpoint of AC, then the degree of \u2220DAC is (). A, B, C, D choices are ['36\u00b0', '44\u00b0', '52\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8009.jpg"
-  },
-  {
-    "id": 8217,
-    "problem_id": 8010,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O, BC is the diameter of circle O, \u2220ACB = 18\u00b0, D is the midpoint of AC, then the degree of \u2220DAC is (). A, B, C, D choices are ['36\u00b0', '44\u00b0', '52\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8010.jpg"
-  },
-  {
-    "id": 8218,
-    "problem_id": 8011,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O, BC is the diameter of circle O, \u2220ACB = 18\u00b0, D is the midpoint of AC, then the degree of \u2220DAC is (). A, B, C, D choices are ['36\u00b0', '44\u00b0', '52\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8011.jpg"
-  },
-  {
-    "id": 8219,
-    "problem_id": 8012,
-    "problem": "<image>Line l is parallel to line m as shown in the diagram. The right-angled triangle ABC has its right angle vertex C on line m. If angle B is 45 degrees and angle 1 is 65 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8012.jpg"
-  },
-  {
-    "id": 8220,
-    "problem_id": 8013,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC respectively. AC = 10 and F is a point on DE. DF = 1. Connect AF and CF. If \u2220AFC = 90\u00b0, then the length of BC is (). A, B, C, D choices are ['18', '16', '14', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8013.jpg"
-  },
-  {
-    "id": 8221,
-    "problem_id": 8014,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC respectively. AC = 10 and F is a point on DE. DF = 1. Connect AF and CF. If \u2220AFC = 90\u00b0, then the length of BC is (). A, B, C, D choices are ['18', '16', '14', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8014.jpg"
-  },
-  {
-    "id": 8222,
-    "problem_id": 8015,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B, respectively. If angle P is 72 degrees, what is the degree measure of angle C? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8015.jpg"
-  },
-  {
-    "id": 8223,
-    "problem_id": 8016,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B, respectively. If angle P is 72 degrees, what is the degree measure of angle C? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8016.jpg"
-  },
-  {
-    "id": 8224,
-    "problem_id": 8017,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B, respectively. If angle P is 72 degrees, what is the degree measure of angle C? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8017.jpg"
-  },
-  {
-    "id": 8225,
-    "problem_id": 8018,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B, respectively. If angle P is 72 degrees, what is the degree measure of angle C? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8018.jpg"
-  },
-  {
-    "id": 8226,
-    "problem_id": 8019,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B, respectively. If angle P is 72 degrees, what is the degree measure of angle C? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8019.jpg"
-  },
-  {
-    "id": 8228,
-    "problem_id": 8020,
-    "problem": "<image>As shown in the figure, the radius of the sector is 6cm and the central angle is 120\u00b0. What is the area of the sector? (). A, B, C, D choices are ['6\u03c0cm2', '9\u03c0cm2', '12\u03c0cm2', '18\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8020.jpg"
-  },
-  {
-    "id": 8229,
-    "problem_id": 8021,
-    "problem": "<image>As shown in the figure, the radius of the sector is 6cm and the central angle is 120\u00b0. What is the area of the sector? (). A, B, C, D choices are ['6\u03c0cm2', '9\u03c0cm2', '12\u03c0cm2', '18\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8021.jpg"
-  },
-  {
-    "id": 8230,
-    "problem_id": 8022,
-    "problem": "<image>As shown in the figure, the radius of the sector is 6cm and the central angle is 120\u00b0. What is the area of the sector? (). A, B, C, D choices are ['6\u03c0cm2', '9\u03c0cm2', '12\u03c0cm2', '18\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8022.jpg"
-  },
-  {
-    "id": 8231,
-    "problem_id": 8023,
-    "problem": "<image>As shown in the figure, the radius of the sector is 6cm and the central angle is 120\u00b0. What is the area of the sector? (). A, B, C, D choices are ['6\u03c0cm2', '9\u03c0cm2', '12\u03c0cm2', '18\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8023.jpg"
-  },
-  {
-    "id": 8232,
-    "problem_id": 8024,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The right-angle vertex of the triangle is placed on line b, and the two legs intersect line a. If angle 2 is 27\u00b0, then what is the measure of angle 1?. A, B, C, D choices are ['53\u00b0', '63\u00b0', '27\u00b0', '37\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8024.jpg"
-  },
-  {
-    "id": 8233,
-    "problem_id": 8025,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The right-angle vertex of the triangle is placed on line b, and the two legs intersect line a. If angle 2 is 27\u00b0, then what is the measure of angle 1?. A, B, C, D choices are ['53\u00b0', '63\u00b0', '27\u00b0', '37\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8025.jpg"
-  },
-  {
-    "id": 8234,
-    "problem_id": 8026,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The right-angle vertex of the triangle is placed on line b, and the two legs intersect line a. If angle 2 is 27\u00b0, then what is the measure of angle 1?. A, B, C, D choices are ['53\u00b0', '63\u00b0', '27\u00b0', '37\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8026.jpg"
-  },
-  {
-    "id": 8235,
-    "problem_id": 8027,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The right-angle vertex of the triangle is placed on line b, and the two legs intersect line a. If angle 2 is 27\u00b0, then what is the measure of angle 1?. A, B, C, D choices are ['53\u00b0', '63\u00b0', '27\u00b0', '37\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8027.jpg"
-  },
-  {
-    "id": 8236,
-    "problem_id": 8028,
-    "problem": "<image>In triangle ABC, BC = 10 and AC - AB = 4. A perpendicular line is drawn from point C to the angle bisector of angle BAC, with the foot of the perpendicular at point D. BD and CD are then connected. What is the maximum area of triangle BDC?. A, B, C, D choices are ['10', '15', '12', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8028.jpg"
-  },
-  {
-    "id": 8237,
-    "problem_id": 8029,
-    "problem": "<image>In triangle ABC, BC = 10 and AC - AB = 4. A perpendicular line is drawn from point C to the angle bisector of angle BAC, with the foot of the perpendicular at point D. BD and CD are then connected. What is the maximum area of triangle BDC?. A, B, C, D choices are ['10', '15', '12', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8029.jpg"
-  },
-  {
-    "id": 8238,
-    "problem_id": 8030,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. Ray PA and PB are tangent to the circle O at points A and B, respectively. CD is tangent to the circle O at point E and intersects PA and PB at points D and C, respectively. If PB = 4, then what is the perimeter of triangle PCD?. A, B, C, D choices are ['4', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8030.jpg"
-  },
-  {
-    "id": 8239,
-    "problem_id": 8031,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. Ray PA and PB are tangent to the circle O at points A and B, respectively. CD is tangent to the circle O at point E and intersects PA and PB at points D and C, respectively. If PB = 4, then what is the perimeter of triangle PCD?. A, B, C, D choices are ['4', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8031.jpg"
-  },
-  {
-    "id": 8240,
-    "problem_id": 8032,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. Ray PA and PB are tangent to the circle O at points A and B, respectively. CD is tangent to the circle O at point E and intersects PA and PB at points D and C, respectively. If PB = 4, then what is the perimeter of triangle PCD?. A, B, C, D choices are ['4', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8032.jpg"
-  },
-  {
-    "id": 8241,
-    "problem_id": 8033,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8033.jpg"
-  },
-  {
-    "id": 8242,
-    "problem_id": 8034,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8034.jpg"
-  },
-  {
-    "id": 8243,
-    "problem_id": 8035,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8035.jpg"
-  },
-  {
-    "id": 8244,
-    "problem_id": 8036,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8036.jpg"
-  },
-  {
-    "id": 8245,
-    "problem_id": 8037,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8037.jpg"
-  },
-  {
-    "id": 8246,
-    "problem_id": 8038,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8038.jpg"
-  },
-  {
-    "id": 8247,
-    "problem_id": 8039,
-    "problem": "<image>In triangle ABC, AB=5, BC=3, AC=4. A circle with center C is tangent to AB. What is the radius of circle C?. A, B, C, D choices are ['2.6', '2.5', '2.4', '2.3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8039.jpg"
-  },
-  {
-    "id": 8249,
-    "problem_id": 8040,
-    "problem": "<image>In the rectangle ABCD, diagonal lines AC and BD intersect at point O. Line AE is perpendicular and bisects line BO. If AE = 2\u221a{3}, then OD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8040.jpg"
-  },
-  {
-    "id": 8250,
-    "problem_id": 8041,
-    "problem": "<image>In the rectangle ABCD, diagonal lines AC and BD intersect at point O. Line AE is perpendicular and bisects line BO. If AE = 2\u221a{3}, then OD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8041.jpg"
-  },
-  {
-    "id": 8251,
-    "problem_id": 8042,
-    "problem": "<image>In the rectangle ABCD, diagonal lines AC and BD intersect at point O. Line AE is perpendicular and bisects line BO. If AE = 2\u221a{3}, then OD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8042.jpg"
-  },
-  {
-    "id": 8252,
-    "problem_id": 8043,
-    "problem": "<image>As shown in the figure, points A, B, C, D, and E are on the circle O. AB = CD, \u2220AOB = 42\u00b0. Then, what is the measure of \u2220CED?. A, B, C, D choices are ['48\u00b0', '24\u00b0', '22\u00b0', '21\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8043.jpg"
-  },
-  {
-    "id": 8253,
-    "problem_id": 8044,
-    "problem": "<image>As shown in the figure, points A, B, C, D, and E are on the circle O. AB = CD, \u2220AOB = 42\u00b0. Then, what is the measure of \u2220CED?. A, B, C, D choices are ['48\u00b0', '24\u00b0', '22\u00b0', '21\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8044.jpg"
-  },
-  {
-    "id": 8254,
-    "problem_id": 8045,
-    "problem": "<image>As shown in the figure, points A, B, C, D, and E are on the circle O. AB = CD, \u2220AOB = 42\u00b0. Then, what is the measure of \u2220CED?. A, B, C, D choices are ['48\u00b0', '24\u00b0', '22\u00b0', '21\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8045.jpg"
-  },
-  {
-    "id": 8255,
-    "problem_id": 8046,
-    "problem": "<image>As shown in the figure, points A, B, C, D, and E are on the circle O. AB = CD, \u2220AOB = 42\u00b0. Then, what is the measure of \u2220CED?. A, B, C, D choices are ['48\u00b0', '24\u00b0', '22\u00b0', '21\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8046.jpg"
-  },
-  {
-    "id": 8256,
-    "problem_id": 8047,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle at points A and B, respectively. If PA = 3, then PB = (). A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n\n**Note:** If there was additional information in the diagram that I'm not considering, such as angles or other lengths, I might need to adjust my approach. However, based on the information provided in the problem description, the answer should be B) 3.</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8047.jpg"
-  },
-  {
-    "id": 8257,
-    "problem_id": 8048,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle at points A and B, respectively. If PA = 3, then PB = (). A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8048.jpg"
-  },
-  {
-    "id": 8258,
-    "problem_id": 8049,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle at points A and B, respectively. If PA = 3, then PB = (). A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8049.jpg"
-  },
-  {
-    "id": 8259,
-    "problem_id": 8050,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle at points A and B, respectively. If PA = 3, then PB = (). A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8050.jpg"
-  },
-  {
-    "id": 8260,
-    "problem_id": 8051,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle at points A and B, respectively. If PA = 3, then PB = (). A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8051.jpg"
-  },
-  {
-    "id": 8261,
-    "problem_id": 8052,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8052.jpg"
-  },
-  {
-    "id": 8262,
-    "problem_id": 8053,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8053.jpg"
-  },
-  {
-    "id": 8263,
-    "problem_id": 8054,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8054.jpg"
-  },
-  {
-    "id": 8264,
-    "problem_id": 8055,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8055.jpg"
-  },
-  {
-    "id": 8265,
-    "problem_id": 8056,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8056.jpg"
-  },
-  {
-    "id": 8266,
-    "problem_id": 8057,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8057.jpg"
-  },
-  {
-    "id": 8267,
-    "problem_id": 8058,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8058.jpg"
-  },
-  {
-    "id": 8268,
-    "problem_id": 8059,
-    "problem": "<image>As shown in the figure, Xiaoming made a cone-shaped funnel model with paper. The diameter of the bottom surface is AB=12cm and the height is OC=8cm. What is the lateral area of the cone-shaped funnel? (). A, B, C, D choices are ['30cm2', '36\u03c0cm2', '60\u03c0cm2', '120cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8059.jpg"
-  },
-  {
-    "id": 8269,
-    "problem_id": 8060,
-    "problem": "<image>As shown in the figure, BD is the median of triangle ABC, and E and F are the midpoints of BD and CE, respectively. If the area of triangle AEF is 3cm2, then the area of triangle ABC is (). A, B, C, D choices are ['6cm2', '9cm2', '12cm2', '15cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8060.jpg"
-  },
-  {
-    "id": 8270,
-    "problem_id": 8061,
-    "problem": "<image>As shown in the figure, BD is the median of triangle ABC, and E and F are the midpoints of BD and CE, respectively. If the area of triangle AEF is 3cm2, then the area of triangle ABC is (). A, B, C, D choices are ['6cm2', '9cm2', '12cm2', '15cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8061.jpg"
-  },
-  {
-    "id": 8271,
-    "problem_id": 8062,
-    "problem": "<image>As shown in the figure, BD is the median of triangle ABC, and E and F are the midpoints of BD and CE, respectively. If the area of triangle AEF is 3cm2, then the area of triangle ABC is (). A, B, C, D choices are ['6cm2', '9cm2', '12cm2', '15cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8062.jpg"
-  },
-  {
-    "id": 8272,
-    "problem_id": 8063,
-    "problem": "<image>As shown in the figure, BD is the median of triangle ABC, and E and F are the midpoints of BD and CE, respectively. If the area of triangle AEF is 3cm2, then the area of triangle ABC is (). A, B, C, D choices are ['6cm2', '9cm2', '12cm2', '15cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8063.jpg"
-  },
-  {
-    "id": 8273,
-    "problem_id": 8064,
-    "problem": "<image>In triangle ABC, point D and E are the midpoint of sides AB and AC, respectively. If DE = 3, what is the length of BC?. A, B, C, D choices are ['3', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8064.jpg"
-  },
-  {
-    "id": 8274,
-    "problem_id": 8065,
-    "problem": "<image>In triangle ABC, point D and E are the midpoint of sides AB and AC, respectively. If DE = 3, what is the length of BC?. A, B, C, D choices are ['3', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8065.jpg"
-  },
-  {
-    "id": 8275,
-    "problem_id": 8066,
-    "problem": "<image>In triangle ABC, point D and E are the midpoint of sides AB and AC, respectively. If DE = 3, what is the length of BC?. A, B, C, D choices are ['3', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8066.jpg"
-  },
-  {
-    "id": 8276,
-    "problem_id": 8067,
-    "problem": "<image>In triangle ABC, point D and E are the midpoint of sides AB and AC, respectively. If DE = 3, what is the length of BC?. A, B, C, D choices are ['3', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8067.jpg"
-  },
-  {
-    "id": 8277,
-    "problem_id": 8068,
-    "problem": "<image>In triangle ABC, point D and E are the midpoint of sides AB and AC, respectively. If DE = 3, what is the length of BC?. A, B, C, D choices are ['3', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8068.jpg"
-  },
-  {
-    "id": 8278,
-    "problem_id": 8069,
-    "problem": "<image>As shown in the figure, when Xiaoming folds a rectangular piece of paper into a regular pentagon, what is the degree of angle 1 in the figure? (). A, B, C, D choices are ['72\u00b0', '80\u00b0', '90\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8069.jpg"
-  },
-  {
-    "id": 8279,
-    "problem_id": 8070,
-    "problem": "<image>As shown in the figure, when Xiaoming folds a rectangular piece of paper into a regular pentagon, what is the degree of angle 1 in the figure? (). A, B, C, D choices are ['72\u00b0', '80\u00b0', '90\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8070.jpg"
-  },
-  {
-    "id": 8280,
-    "problem_id": 8071,
-    "problem": "<image>As shown in the figure, when Xiaoming folds a rectangular piece of paper into a regular pentagon, what is the degree of angle 1 in the figure? (). A, B, C, D choices are ['72\u00b0', '80\u00b0', '90\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8071.jpg"
-  },
-  {
-    "id": 8281,
-    "problem_id": 8072,
-    "problem": "<image>As shown in the figure, when Xiaoming folds a rectangular piece of paper into a regular pentagon, what is the degree of angle 1 in the figure? (). A, B, C, D choices are ['72\u00b0', '80\u00b0', '90\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8072.jpg"
-  },
-  {
-    "id": 8282,
-    "problem_id": 8073,
-    "problem": "<image>As shown in the figure, when Xiaoming folds a rectangular piece of paper into a regular pentagon, what is the degree of angle 1 in the figure? (). A, B, C, D choices are ['72\u00b0', '80\u00b0', '90\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8073.jpg"
-  },
-  {
-    "id": 8283,
-    "problem_id": 8074,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB=90\u00b0. Squares are constructed outwardly on the sides AB, BC, and AC. If the areas of the three squares are 225, 400, and S respectively, what is the value of S? (). A, B, C, D choices are ['25', '175', '600', '625'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8074.jpg"
-  },
-  {
-    "id": 8284,
-    "problem_id": 8075,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle O at points A and B respectively. If PA = 5, then PB = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8075.jpg"
-  },
-  {
-    "id": 8285,
-    "problem_id": 8076,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle O at points A and B respectively. If PA = 5, then PB = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8076.jpg"
-  },
-  {
-    "id": 8286,
-    "problem_id": 8077,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle O at points A and B respectively. If PA = 5, then PB = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8077.jpg"
-  },
-  {
-    "id": 8287,
-    "problem_id": 8078,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle O at points A and B respectively. If PA = 5, then PB = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8078.jpg"
-  },
-  {
-    "id": 8288,
-    "problem_id": 8079,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O. PA and PB are tangent to the circle O at points A and B respectively. If PA = 5, then PB = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8079.jpg"
-  },
-  {
-    "id": 8289,
-    "problem_id": 8080,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. Point F is on DE and AF is perpendicular to CF. If AC = 3 and BC = 6, what is the length of DF?. A, B, C, D choices are ['1.5', '1', '0.5', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8080.jpg"
-  },
-  {
-    "id": 8290,
-    "problem_id": 8081,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. Point F is on DE and AF is perpendicular to CF. If AC = 3 and BC = 6, what is the length of DF?. A, B, C, D choices are ['1.5', '1', '0.5', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8081.jpg"
-  },
-  {
-    "id": 8291,
-    "problem_id": 8082,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 28 cm\u00b2, what is the area of the shaded region?. A, B, C, D choices are ['21cm2', '14cm2', '10cm2', '7cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8082.jpg"
-  },
-  {
-    "id": 8292,
-    "problem_id": 8083,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 28 cm\u00b2, what is the area of the shaded region?. A, B, C, D choices are ['21cm2', '14cm2', '10cm2', '7cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8083.jpg"
-  },
-  {
-    "id": 8293,
-    "problem_id": 8084,
-    "problem": "<image>As shown in the diagram, it is known that BC is the diameter of the circle O, and \u2220AOC = 58\u00b0. Then what is the degree measurement of \u2220A? (). A, B, C, D choices are ['28\u00b0', '29\u00b0', '32\u00b0', '42\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8084.jpg"
-  },
-  {
-    "id": 8294,
-    "problem_id": 8085,
-    "problem": "<image>As shown in the diagram, it is known that BC is the diameter of the circle O, and \u2220AOC = 58\u00b0. Then what is the degree measurement of \u2220A? (). A, B, C, D choices are ['28\u00b0', '29\u00b0', '32\u00b0', '42\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8085.jpg"
-  },
-  {
-    "id": 8296,
-    "problem_id": 8086,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8086.jpg"
-  },
-  {
-    "id": 8297,
-    "problem_id": 8087,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8087.jpg"
-  },
-  {
-    "id": 8298,
-    "problem_id": 8088,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8088.jpg"
-  },
-  {
-    "id": 8299,
-    "problem_id": 8089,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8089.jpg"
-  },
-  {
-    "id": 8300,
-    "problem_id": 8090,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8090.jpg"
-  },
-  {
-    "id": 8301,
-    "problem_id": 8091,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8091.jpg"
-  },
-  {
-    "id": 8302,
-    "problem_id": 8092,
-    "problem": "<image>As shown in the figure, AD is the median of triangle ABC. It is known that the perimeter of triangle ABD is 28cm and AB is 6cm longer than AC. Then the perimeter of triangle ACD is (). A, B, C, D choices are ['31cm', '25cm', '22cm', '19cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8092.jpg"
-  },
-  {
-    "id": 8304,
-    "problem_id": 8093,
-    "problem": "<image>In the rectangle ABCD, diagonal AC intersects diagonal BD at point O. If \u2220OAD = 40\u00b0, then \u2220COD = ().. A, B, C, D choices are ['20\u00b0', '40\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8093.jpg"
-  },
-  {
-    "id": 8305,
-    "problem_id": 8094,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8094.jpg"
-  },
-  {
-    "id": 8306,
-    "problem_id": 8095,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8095.jpg"
-  },
-  {
-    "id": 8307,
-    "problem_id": 8096,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8096.jpg"
-  },
-  {
-    "id": 8308,
-    "problem_id": 8097,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8097.jpg"
-  },
-  {
-    "id": 8309,
-    "problem_id": 8098,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8098.jpg"
-  },
-  {
-    "id": 8310,
-    "problem_id": 8099,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8099.jpg"
-  },
-  {
-    "id": 8311,
-    "problem_id": 8100,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8100.jpg"
-  },
-  {
-    "id": 8312,
-    "problem_id": 8101,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of the rhombus ABCD intersect at point O. If the perimeter is 20 and BD = 8, then the length of AC is (). A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8101.jpg"
-  },
-  {
-    "id": 8313,
-    "problem_id": 8102,
-    "problem": "<image>If l1 and l2 are to be parallel as shown in the diagram, what is the minimum degree that l1 needs to rotate around point O? (). A, B, C, D choices are ['38\u00b0', '42\u00b0', '80\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8102.jpg"
-  },
-  {
-    "id": 8314,
-    "problem_id": 8103,
-    "problem": "<image>If l1 and l2 are to be parallel as shown in the diagram, what is the minimum degree that l1 needs to rotate around point O? (). A, B, C, D choices are ['38\u00b0', '42\u00b0', '80\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8103.jpg"
-  },
-  {
-    "id": 8315,
-    "problem_id": 8104,
-    "problem": "<image>If l1 and l2 are to be parallel as shown in the diagram, what is the minimum degree that l1 needs to rotate around point O? (). A, B, C, D choices are ['38\u00b0', '42\u00b0', '80\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8104.jpg"
-  },
-  {
-    "id": 8316,
-    "problem_id": 8105,
-    "problem": "<image>If l1 and l2 are to be parallel as shown in the diagram, what is the minimum degree that l1 needs to rotate around point O? (). A, B, C, D choices are ['38\u00b0', '42\u00b0', '80\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8105.jpg"
-  },
-  {
-    "id": 8317,
-    "problem_id": 8106,
-    "problem": "<image>If l1 and l2 are to be parallel as shown in the diagram, what is the minimum degree that l1 needs to rotate around point O? (). A, B, C, D choices are ['38\u00b0', '42\u00b0', '80\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8106.jpg"
-  },
-  {
-    "id": 8318,
-    "problem_id": 8107,
-    "problem": "<image>If l1 and l2 are to be parallel as shown in the diagram, what is the minimum degree that l1 needs to rotate around point O? (). A, B, C, D choices are ['38\u00b0', '42\u00b0', '80\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8107.jpg"
-  },
-  {
-    "id": 8319,
-    "problem_id": 8108,
-    "problem": "<image>In triangle ABC, points D, E, and F are the midpoints of BC, AD, and BE, respectively. If the area of triangle ABC is 12cm2, then the area of triangle CEF is (). A, B, C, D choices are ['0.75', '1.5', '3', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8108.jpg"
-  },
-  {
-    "id": 8320,
-    "problem_id": 8109,
-    "problem": "<image>In triangle ABC, points D, E, and F are the midpoints of BC, AD, and BE, respectively. If the area of triangle ABC is 12cm2, then the area of triangle CEF is (). A, B, C, D choices are ['0.75', '1.5', '3', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8109.jpg"
-  },
-  {
-    "id": 8321,
-    "problem_id": 8110,
-    "problem": "<image>In triangle ABC, points D, E, and F are the midpoints of BC, AD, and BE, respectively. If the area of triangle ABC is 12cm2, then the area of triangle CEF is (). A, B, C, D choices are ['0.75', '1.5', '3', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8110.jpg"
-  },
-  {
-    "id": 8322,
-    "problem_id": 8111,
-    "problem": "<image>In triangle ABC, points D, E, and F are the midpoints of BC, AD, and BE, respectively. If the area of triangle ABC is 12cm2, then the area of triangle CEF is (). A, B, C, D choices are ['0.75', '1.5', '3', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8111.jpg"
-  },
-  {
-    "id": 8323,
-    "problem_id": 8112,
-    "problem": "<image>In triangle ABC, points D, E, and F are the midpoints of BC, AD, and BE, respectively. If the area of triangle ABC is 12cm2, then the area of triangle CEF is (). A, B, C, D choices are ['0.75', '1.5', '3', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8112.jpg"
-  },
-  {
-    "id": 8324,
-    "problem_id": 8113,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8113.jpg"
-  },
-  {
-    "id": 8325,
-    "problem_id": 8114,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8114.jpg"
-  },
-  {
-    "id": 8326,
-    "problem_id": 8115,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8115.jpg"
-  },
-  {
-    "id": 8327,
-    "problem_id": 8116,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8116.jpg"
-  },
-  {
-    "id": 8328,
-    "problem_id": 8117,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8117.jpg"
-  },
-  {
-    "id": 8329,
-    "problem_id": 8118,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8118.jpg"
-  },
-  {
-    "id": 8330,
-    "problem_id": 8119,
-    "problem": "<image>In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AD and OE = 3. What is the length of CD?. A, B, C, D choices are ['3', '5', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8119.jpg"
-  },
-  {
-    "id": 8331,
-    "problem_id": 8120,
-    "problem": "<image>In triangle ABC, if the external angle \u2220DCA = 110\u00b0 and \u2220A = 75\u00b0, what is the degree measure of \u2220B?. A, B, C, D choices are ['70\u00b0', '40\u00b0', '35\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8120.jpg"
-  },
-  {
-    "id": 8332,
-    "problem_id": 8121,
-    "problem": "<image>In triangle ABC, if the external angle \u2220DCA = 110\u00b0 and \u2220A = 75\u00b0, what is the degree measure of \u2220B?. A, B, C, D choices are ['70\u00b0', '40\u00b0', '35\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8121.jpg"
-  },
-  {
-    "id": 8333,
-    "problem_id": 8122,
-    "problem": "<image>In triangle ABC, if the external angle \u2220DCA = 110\u00b0 and \u2220A = 75\u00b0, what is the degree measure of \u2220B?. A, B, C, D choices are ['70\u00b0', '40\u00b0', '35\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8122.jpg"
-  },
-  {
-    "id": 8334,
-    "problem_id": 8123,
-    "problem": "<image>In triangle ABC, if the external angle \u2220DCA = 110\u00b0 and \u2220A = 75\u00b0, what is the degree measure of \u2220B?. A, B, C, D choices are ['70\u00b0', '40\u00b0', '35\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8123.jpg"
-  },
-  {
-    "id": 8335,
-    "problem_id": 8124,
-    "problem": "<image>In triangle ABC, if the external angle \u2220DCA = 110\u00b0 and \u2220A = 75\u00b0, what is the degree measure of \u2220B?. A, B, C, D choices are ['70\u00b0', '40\u00b0', '35\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8124.jpg"
-  },
-  {
-    "id": 8336,
-    "problem_id": 8125,
-    "problem": "<image>In triangle ABC, if the external angle \u2220DCA = 110\u00b0 and \u2220A = 75\u00b0, what is the degree measure of \u2220B?. A, B, C, D choices are ['70\u00b0', '40\u00b0', '35\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8125.jpg"
-  },
-  {
-    "id": 8337,
-    "problem_id": 8126,
-    "problem": "<image>In circle O as shown, AB = AC, if \u2220B = 70\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['70\u00b0', '40\u00b0', '20\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8126.jpg"
-  },
-  {
-    "id": 8338,
-    "problem_id": 8127,
-    "problem": "<image>In circle O as shown, AB = AC, if \u2220B = 70\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['70\u00b0', '40\u00b0', '20\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8127.jpg"
-  },
-  {
-    "id": 8339,
-    "problem_id": 8128,
-    "problem": "<image>In circle O as shown, AB = AC, if \u2220B = 70\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['70\u00b0', '40\u00b0', '20\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8128.jpg"
-  },
-  {
-    "id": 8340,
-    "problem_id": 8129,
-    "problem": "<image>In circle O as shown, AB = AC, if \u2220B = 70\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['70\u00b0', '40\u00b0', '20\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8129.jpg"
-  },
-  {
-    "id": 8341,
-    "problem_id": 8130,
-    "problem": "<image>In circle O as shown, AB = AC, if \u2220B = 70\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['70\u00b0', '40\u00b0', '20\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8130.jpg"
-  },
-  {
-    "id": 8342,
-    "problem_id": 8131,
-    "problem": "<image>In circle O as shown, AB = AC, if \u2220B = 70\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['70\u00b0', '40\u00b0', '20\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8131.jpg"
-  },
-  {
-    "id": 8343,
-    "problem_id": 8132,
-    "problem": "<image>As shown in the figure, line l1 is parallel to lines l2 and l3. Lines AC and DF are intersected by l1, l2, and l3. If AC = 11, BC = 6, and EF = 4, what is the length of DE?. A, B, C, D choices are ['2', '3', '4', '\\\\frac{10}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8132.jpg"
-  },
-  {
-    "id": 8344,
-    "problem_id": 8133,
-    "problem": "<image>As shown in the figure, line l1 is parallel to lines l2 and l3. Lines AC and DF are intersected by l1, l2, and l3. If AC = 11, BC = 6, and EF = 4, what is the length of DE?. A, B, C, D choices are ['2', '3', '4', '\\\\frac{10}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8133.jpg"
-  },
-  {
-    "id": 8345,
-    "problem_id": 8134,
-    "problem": "<image>As shown in the figure, line l1 is parallel to lines l2 and l3. Lines AC and DF are intersected by l1, l2, and l3. If AC = 11, BC = 6, and EF = 4, what is the length of DE?. A, B, C, D choices are ['2', '3', '4', '\\\\frac{10}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8134.jpg"
-  },
-  {
-    "id": 8346,
-    "problem_id": 8135,
-    "problem": "<image>As shown in the figure, line l1 is parallel to lines l2 and l3. Lines AC and DF are intersected by l1, l2, and l3. If AC = 11, BC = 6, and EF = 4, what is the length of DE?. A, B, C, D choices are ['2', '3', '4', '\\\\frac{10}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8135.jpg"
-  },
-  {
-    "id": 8347,
-    "problem_id": 8136,
-    "problem": "<image>As shown in the figure, line l1 is parallel to lines l2 and l3. Lines AC and DF are intersected by l1, l2, and l3. If AC = 11, BC = 6, and EF = 4, what is the length of DE?. A, B, C, D choices are ['2', '3', '4', '\\\\frac{10}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8136.jpg"
-  },
-  {
-    "id": 8348,
-    "problem_id": 8137,
-    "problem": "<image>As shown in the figure, line l1 is parallel to lines l2 and l3. Lines AC and DF are intersected by l1, l2, and l3. If AC = 11, BC = 6, and EF = 4, what is the length of DE?. A, B, C, D choices are ['2', '3', '4', '\\\\frac{10}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8137.jpg"
-  },
-  {
-    "id": 8351,
-    "problem_id": 8138,
-    "problem": "<image>In triangle ABC, AB = 4, AC = 5, BC = 6. D, E, and F are the midpoints of AB, BC, and CA, respectively. If we connect DE and EF, what is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8138.jpg"
-  },
-  {
-    "id": 8352,
-    "problem_id": 8139,
-    "problem": "<image>As shown in the diagram, a beam of light is shining on the ground at an angle of 60\u00b0 with the horizontal plane. Now a plane mirror CD is placed on the ground AB, so that the beam of light can reflect off the mirror and shoot out as a horizontal beam of light (\u22201 = \u22202). The degree of the angle \u2220DCA between the plane mirror CD and the ground AB is equal to ().. A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8139.jpg"
-  },
-  {
-    "id": 8353,
-    "problem_id": 8140,
-    "problem": "<image>As shown in the figure, AC is parallel to BD, AE bisects angle BAC and intersects BD at point E. If angle 1 is 50\u00b0, then angle 2 is (). A, B, C, D choices are ['110\u00b0', '120\u00b0', '130\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8140.jpg"
-  },
-  {
-    "id": 8354,
-    "problem_id": 8141,
-    "problem": "<image>As shown in the figure, AC is parallel to BD, AE bisects angle BAC and intersects BD at point E. If angle 1 is 50\u00b0, then angle 2 is (). A, B, C, D choices are ['110\u00b0', '120\u00b0', '130\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8141.jpg"
-  },
-  {
-    "id": 8356,
-    "problem_id": 8142,
-    "problem": "<image>In triangle ABC, point D and E are the midpoints of AC and AB, respectively. If the area of triangle ABC is 12, then the area of triangle BDE is ().. A, B, C, D choices are ['12', '6', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8142.jpg"
-  },
-  {
-    "id": 8357,
-    "problem_id": 8143,
-    "problem": "<image>In triangle ABC, point D and E are the midpoints of AC and AB, respectively. If the area of triangle ABC is 12, then the area of triangle BDE is ().. A, B, C, D choices are ['12', '6', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8143.jpg"
-  },
-  {
-    "id": 8358,
-    "problem_id": 8144,
-    "problem": "<image>In the figure, the degree of angle CAD in the regular pentagon ABCDE is ().. A, B, C, D choices are ['72\u00b0', '45\u00b0', '36\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8144.jpg"
-  },
-  {
-    "id": 8359,
-    "problem_id": 8145,
-    "problem": "<image>In the figure, the degree of angle CAD in the regular pentagon ABCDE is ().. A, B, C, D choices are ['72\u00b0', '45\u00b0', '36\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8145.jpg"
-  },
-  {
-    "id": 8360,
-    "problem_id": 8146,
-    "problem": "<image>As shown in the diagram, there is a straight and wide ribbon. When folding according to the diagram, the degree of \u2220\u03b1 is equal to ().. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8146.jpg"
-  },
-  {
-    "id": 8361,
-    "problem_id": 8147,
-    "problem": "<image>In triangle ABC, as shown in the figure, angle B is 40 degrees and angle C is 30 degrees. Point D is on side BC. After folding triangle ADC along the line AD, point C moves to point E. If DE is parallel to AB, what is the degree measure of angle ADE?. A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8147.jpg"
-  },
-  {
-    "id": 8362,
-    "problem_id": 8148,
-    "problem": "<image>In rectangle ABCD as shown, AB = 6 and AD = 8. P is a moving point on AD that does not coincide with A or D. Perpendiculars are drawn from point P to AC and BD, with E and F as the respective feet of the perpendiculars. What is the value of PE + PF?. A, B, C, D choices are ['10', '4.8', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8148.jpg"
-  },
-  {
-    "id": 8363,
-    "problem_id": 8149,
-    "problem": "<image>In rectangle ABCD as shown, AB = 6 and AD = 8. P is a moving point on AD that does not coincide with A or D. Perpendiculars are drawn from point P to AC and BD, with E and F as the respective feet of the perpendiculars. What is the value of PE + PF?. A, B, C, D choices are ['10', '4.8', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8149.jpg"
-  },
-  {
-    "id": 8364,
-    "problem_id": 8150,
-    "problem": "<image>In rectangle ABCD as shown, AB = 6 and AD = 8. P is a moving point on AD that does not coincide with A or D. Perpendiculars are drawn from point P to AC and BD, with E and F as the respective feet of the perpendiculars. What is the value of PE + PF?. A, B, C, D choices are ['10', '4.8', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8150.jpg"
-  },
-  {
-    "id": 8365,
-    "problem_id": 8151,
-    "problem": "<image>In rectangle ABCD as shown, AB = 6 and AD = 8. P is a moving point on AD that does not coincide with A or D. Perpendiculars are drawn from point P to AC and BD, with E and F as the respective feet of the perpendiculars. What is the value of PE + PF?. A, B, C, D choices are ['10', '4.8', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8151.jpg"
-  },
-  {
-    "id": 8366,
-    "problem_id": 8152,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8152.jpg"
-  },
-  {
-    "id": 8367,
-    "problem_id": 8153,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8153.jpg"
-  },
-  {
-    "id": 8368,
-    "problem_id": 8154,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8154.jpg"
-  },
-  {
-    "id": 8369,
-    "problem_id": 8155,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8155.jpg"
-  },
-  {
-    "id": 8370,
-    "problem_id": 8156,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8156.jpg"
-  },
-  {
-    "id": 8371,
-    "problem_id": 8157,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8157.jpg"
-  },
-  {
-    "id": 8372,
-    "problem_id": 8158,
-    "problem": "<image>In parallelogram ABCD shown in the figure, \u2220A = 2\u2220B, and the radius of circle C is 3. The area of the shaded region in the figure is (). A, B, C, D choices are ['\u03c0', '2\u03c0', '3\u03c0', '6\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8158.jpg"
-  },
-  {
-    "id": 8373,
-    "problem_id": 8159,
-    "problem": "<image>In the quadrilateral ABCD, AB = 2, BC = 2, CD = 4, DA = 2\u221a6, and \u2220ABC = 90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['4', '1+2\u221a{2}', '2+4\u221a{2}', '1+\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8159.jpg"
-  },
-  {
-    "id": 8374,
-    "problem_id": 8160,
-    "problem": "<image>In the quadrilateral ABCD, AB = 2, BC = 2, CD = 4, DA = 2\u221a6, and \u2220ABC = 90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['4', '1+2\u221a{2}', '2+4\u221a{2}', '1+\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8160.jpg"
-  },
-  {
-    "id": 8375,
-    "problem_id": 8161,
-    "problem": "<image>In the quadrilateral ABCD, AB = 2, BC = 2, CD = 4, DA = 2\u221a6, and \u2220ABC = 90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['4', '1+2\u221a{2}', '2+4\u221a{2}', '1+\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8161.jpg"
-  },
-  {
-    "id": 8376,
-    "problem_id": 8162,
-    "problem": "<image>In the quadrilateral ABCD, AB = 2, BC = 2, CD = 4, DA = 2\u221a6, and \u2220ABC = 90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['4', '1+2\u221a{2}', '2+4\u221a{2}', '1+\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8162.jpg"
-  },
-  {
-    "id": 8377,
-    "problem_id": 8163,
-    "problem": "<image>In the quadrilateral ABCD, AB = 2, BC = 2, CD = 4, DA = 2\u221a6, and \u2220ABC = 90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['4', '1+2\u221a{2}', '2+4\u221a{2}', '1+\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8163.jpg"
-  },
-  {
-    "id": 8378,
-    "problem_id": 8164,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8164.jpg"
-  },
-  {
-    "id": 8379,
-    "problem_id": 8165,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8165.jpg"
-  },
-  {
-    "id": 8380,
-    "problem_id": 8166,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8166.jpg"
-  },
-  {
-    "id": 8381,
-    "problem_id": 8167,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8167.jpg"
-  },
-  {
-    "id": 8382,
-    "problem_id": 8168,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8168.jpg"
-  },
-  {
-    "id": 8383,
-    "problem_id": 8169,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8169.jpg"
-  },
-  {
-    "id": 8384,
-    "problem_id": 8170,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8170.jpg"
-  },
-  {
-    "id": 8385,
-    "problem_id": 8171,
-    "problem": "<image>Given that triangle ABC is congruent to triangle DEF, and angle A is 80 degrees and angle B is 60 degrees, what is the degree measure of angle F? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8171.jpg"
-  },
-  {
-    "id": 8386,
-    "problem_id": 8172,
-    "problem": "<image>As shown in the figure, D and E are points on sides AB and BC of triangle ABC, respectively. AD=2BD and BE=CE. Let S1 be the area of triangle ADF and S2 be the area of triangle CEF. If the area of triangle ABC is 12, then S1-S2 is equal to ().. A, B, C, D choices are ['1.5', '2', '3', '0.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8172.jpg"
-  },
-  {
-    "id": 8388,
-    "problem_id": 8173,
-    "problem": "<image>In triangle ABC, where AB=AC, AD is the median of side BC. If angle B is 70 degrees, then what is the measure of angle BAD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8173.jpg"
-  },
-  {
-    "id": 8389,
-    "problem_id": 8174,
-    "problem": "<image>In triangle ABC, where AB=AC, AD is the median of side BC. If angle B is 70 degrees, then what is the measure of angle BAD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8174.jpg"
-  },
-  {
-    "id": 8390,
-    "problem_id": 8175,
-    "problem": "<image>In triangle ABC, where AB=AC, AD is the median of side BC. If angle B is 70 degrees, then what is the measure of angle BAD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8175.jpg"
-  },
-  {
-    "id": 8391,
-    "problem_id": 8176,
-    "problem": "<image>In triangle ABC, where AB=AC, AD is the median of side BC. If angle B is 70 degrees, then what is the measure of angle BAD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8176.jpg"
-  },
-  {
-    "id": 8392,
-    "problem_id": 8177,
-    "problem": "<image>In triangle ABC, where AB=AC, AD is the median of side BC. If angle B is 70 degrees, then what is the measure of angle BAD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8177.jpg"
-  },
-  {
-    "id": 8393,
-    "problem_id": 8178,
-    "problem": "<image>In triangle ABC, where AB=AC, AD is the median of side BC. If angle B is 70 degrees, then what is the measure of angle BAD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8178.jpg"
-  },
-  {
-    "id": 8394,
-    "problem_id": 8179,
-    "problem": "<image>In triangle ABC as shown in the figure, AC = 6cm, BC = 8cm, AB = 10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. The area of triangle DEF is (). A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8179.jpg"
-  },
-  {
-    "id": 8395,
-    "problem_id": 8180,
-    "problem": "<image>In triangle ABC as shown in the figure, AC = 6cm, BC = 8cm, AB = 10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. The area of triangle DEF is (). A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8180.jpg"
-  },
-  {
-    "id": 8396,
-    "problem_id": 8181,
-    "problem": "<image>In triangle ABC as shown in the figure, AC = 6cm, BC = 8cm, AB = 10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. The area of triangle DEF is (). A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8181.jpg"
-  },
-  {
-    "id": 8397,
-    "problem_id": 8182,
-    "problem": "<image>In triangle ABC as shown in the figure, AC = 6cm, BC = 8cm, AB = 10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. The area of triangle DEF is (). A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8182.jpg"
-  },
-  {
-    "id": 8398,
-    "problem_id": 8183,
-    "problem": "<image>In triangle ABC as shown in the figure, AC = 6cm, BC = 8cm, AB = 10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. The area of triangle DEF is (). A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8183.jpg"
-  },
-  {
-    "id": 8399,
-    "problem_id": 8184,
-    "problem": "<image>In triangle ABC as shown in the figure, AC = 6cm, BC = 8cm, AB = 10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. The area of triangle DEF is (). A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8184.jpg"
-  },
-  {
-    "id": 8400,
-    "problem_id": 8185,
-    "problem": "<image>In triangle ABC, AD is the median of side BC, and CE is the median of side AD in triangle ACD. If the area of triangle ABC is 20, what is the area of triangle ACE?. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8185.jpg"
-  },
-  {
-    "id": 8401,
-    "problem_id": 8186,
-    "problem": "<image>In triangle ABC, AD is the median of side BC, and CE is the median of side AD in triangle ACD. If the area of triangle ABC is 20, what is the area of triangle ACE?. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8186.jpg"
-  },
-  {
-    "id": 8402,
-    "problem_id": 8187,
-    "problem": "<image>In triangle ABC, AD is the median of side BC, and CE is the median of side AD in triangle ACD. If the area of triangle ABC is 20, what is the area of triangle ACE?. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8187.jpg"
-  },
-  {
-    "id": 8403,
-    "problem_id": 8188,
-    "problem": "<image>In triangle ABC, AD is the median of side BC, and CE is the median of side AD in triangle ACD. If the area of triangle ABC is 20, what is the area of triangle ACE?. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8188.jpg"
-  },
-  {
-    "id": 8404,
-    "problem_id": 8189,
-    "problem": "<image>In triangle ABC, AD is the median of side BC, and CE is the median of side AD in triangle ACD. If the area of triangle ABC is 20, what is the area of triangle ACE?. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8189.jpg"
-  },
-  {
-    "id": 8405,
-    "problem_id": 8190,
-    "problem": "<image>In triangle ABC, AD is the median of side BC, and CE is the median of side AD in triangle ACD. If the area of triangle ABC is 20, what is the area of triangle ACE?. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8190.jpg"
-  },
-  {
-    "id": 8406,
-    "problem_id": 8191,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8191.jpg"
-  },
-  {
-    "id": 8407,
-    "problem_id": 8192,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8192.jpg"
-  },
-  {
-    "id": 8408,
-    "problem_id": 8193,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8193.jpg"
-  },
-  {
-    "id": 8409,
-    "problem_id": 8194,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8194.jpg"
-  },
-  {
-    "id": 8410,
-    "problem_id": 8195,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8195.jpg"
-  },
-  {
-    "id": 8411,
-    "problem_id": 8196,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8196.jpg"
-  },
-  {
-    "id": 8412,
-    "problem_id": 8197,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rectangle ABCD intersect at point O. Point M is the midpoint of AB. If OM = 4 and AB = 6, then the length of BD is (). A, B, C, D choices are ['4', '5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8197.jpg"
-  },
-  {
-    "id": 8413,
-    "problem_id": 8198,
-    "problem": "<image>In triangle ABD, as shown in the figure, \u2220D = 80\u00b0. Point C is a point on side BD, and AC is connected. If \u2220ACB = 115\u00b0, then \u2220CAD = ().. A, B, C, D choices are ['25\u00b0', '35\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8198.jpg"
-  },
-  {
-    "id": 8414,
-    "problem_id": 8199,
-    "problem": "<image>In triangle ABD, as shown in the figure, \u2220D = 80\u00b0. Point C is a point on side BD, and AC is connected. If \u2220ACB = 115\u00b0, then \u2220CAD = ().. A, B, C, D choices are ['25\u00b0', '35\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8199.jpg"
-  },
-  {
-    "id": 8415,
-    "problem_id": 8200,
-    "problem": "<image>In triangle ABD, as shown in the figure, \u2220D = 80\u00b0. Point C is a point on side BD, and AC is connected. If \u2220ACB = 115\u00b0, then \u2220CAD = ().. A, B, C, D choices are ['25\u00b0', '35\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8200.jpg"
-  },
-  {
-    "id": 8416,
-    "problem_id": 8201,
-    "problem": "<image>In triangle ABC, CD is the altitude of side AB, and CM is the angle bisector of \u2220ACB. If \u2220CAB = 45\u00b0 and \u2220CBA = 75\u00b0, what is the degree measure of \u2220MCD?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8201.jpg"
-  },
-  {
-    "id": 8417,
-    "problem_id": 8202,
-    "problem": "<image>In triangle ABC, CD is the altitude of side AB, and CM is the angle bisector of \u2220ACB. If \u2220CAB = 45\u00b0 and \u2220CBA = 75\u00b0, what is the degree measure of \u2220MCD?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8202.jpg"
-  },
-  {
-    "id": 8418,
-    "problem_id": 8203,
-    "problem": "<image>In triangle ABC, CD is the altitude of side AB, and CM is the angle bisector of \u2220ACB. If \u2220CAB = 45\u00b0 and \u2220CBA = 75\u00b0, what is the degree measure of \u2220MCD?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8203.jpg"
-  },
-  {
-    "id": 8419,
-    "problem_id": 8204,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8204.jpg"
-  },
-  {
-    "id": 8420,
-    "problem_id": 8205,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8205.jpg"
-  },
-  {
-    "id": 8421,
-    "problem_id": 8206,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8206.jpg"
-  },
-  {
-    "id": 8422,
-    "problem_id": 8207,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8207.jpg"
-  },
-  {
-    "id": 8423,
-    "problem_id": 8208,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8208.jpg"
-  },
-  {
-    "id": 8424,
-    "problem_id": 8209,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8209.jpg"
-  },
-  {
-    "id": 8425,
-    "problem_id": 8210,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points B and C on an irregular green area, we can select a point A on one side of the green area, and then measure the midpoints D and E of AB and AC, respectively. If the distance between D and E is 8m, then the distance between points B and C on the green area is ().. A, B, C, D choices are ['4m', '8m', '16m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8210.jpg"
-  },
-  {
-    "id": 8426,
-    "problem_id": 8211,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point O is on AB, OE bisects angle BOD, if angle CDO is 100 degrees, then what is the degree of angle BOE? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8211.jpg"
-  },
-  {
-    "id": 8427,
-    "problem_id": 8212,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point O is on AB, OE bisects angle BOD, if angle CDO is 100 degrees, then what is the degree of angle BOE? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8212.jpg"
-  },
-  {
-    "id": 8428,
-    "problem_id": 8213,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point O is on AB, OE bisects angle BOD, if angle CDO is 100 degrees, then what is the degree of angle BOE? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8213.jpg"
-  },
-  {
-    "id": 8429,
-    "problem_id": 8214,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point O is on AB, OE bisects angle BOD, if angle CDO is 100 degrees, then what is the degree of angle BOE? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8214.jpg"
-  },
-  {
-    "id": 8430,
-    "problem_id": 8215,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point O is on AB, OE bisects angle BOD, if angle CDO is 100 degrees, then what is the degree of angle BOE? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8215.jpg"
-  },
-  {
-    "id": 8431,
-    "problem_id": 8216,
-    "problem": "<image>In the figure, in quadrilateral ABCD, AF bisects angle BAD and intersects BC at point F, while BE bisects angle ABC and intersects AD at point E. If AF=6 and BE=8, then what is the length of side AB?. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8216.jpg"
-  },
-  {
-    "id": 8432,
-    "problem_id": 8217,
-    "problem": "<image>As shown in the figure, AD is the diameter of circle O, AD=8cm, and \u2220DAC=\u2220ABC. What is the length of AC? (). A, B, C, D choices are ['4\u221a{2}cm', '2\u221a{2}cm', '4cm', '3\u221a{3}cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8217.jpg"
-  },
-  {
-    "id": 8433,
-    "problem_id": 8218,
-    "problem": "<image>In triangle ABC as shown in the figure, AB = 6, AC = 10, D, E, and F are the midpoints of AB, BC, and AC respectively. What is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8218.jpg"
-  },
-  {
-    "id": 8434,
-    "problem_id": 8219,
-    "problem": "<image>In triangle ABC as shown in the figure, AB = 6, AC = 10, D, E, and F are the midpoints of AB, BC, and AC respectively. What is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8219.jpg"
-  },
-  {
-    "id": 8435,
-    "problem_id": 8220,
-    "problem": "<image>In the rectangle ABCD, point G is the midpoint of AD. GE is perpendicular to BG and intersects CD at point E. CB = CE. Connect CG and BE at point F. What is the degree measure of angle ECF?. A, B, C, D choices are ['30\u00b0', '22.5\u00b0', '25\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8220.jpg"
-  },
-  {
-    "id": 8436,
-    "problem_id": 8221,
-    "problem": "<image>A set square is placed as shown in the figure (the right angle vertex C coincides with each other), and the edges AB and CD intersect at point F. If DE is parallel to BC, what is the degree of \u2220AFC?. A, B, C, D choices are ['60\u00b0', '75\u00b0', '100\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8221.jpg"
-  },
-  {
-    "id": 8437,
-    "problem_id": 8222,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8222.jpg"
-  },
-  {
-    "id": 8438,
-    "problem_id": 8223,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8223.jpg"
-  },
-  {
-    "id": 8439,
-    "problem_id": 8224,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8224.jpg"
-  },
-  {
-    "id": 8440,
-    "problem_id": 8225,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8225.jpg"
-  },
-  {
-    "id": 8441,
-    "problem_id": 8226,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8226.jpg"
-  },
-  {
-    "id": 8442,
-    "problem_id": 8227,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8227.jpg"
-  },
-  {
-    "id": 8443,
-    "problem_id": 8228,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC as shown. \u2220A=40\u00b0, BO and CO are connected. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8228.jpg"
-  },
-  {
-    "id": 8444,
-    "problem_id": 8229,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Given that \u2220OAB = 25\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['55\u00b0', '65\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8229.jpg"
-  },
-  {
-    "id": 8445,
-    "problem_id": 8230,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Given that \u2220OAB = 25\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['55\u00b0', '65\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8230.jpg"
-  },
-  {
-    "id": 8446,
-    "problem_id": 8231,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Given that \u2220OAB = 25\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['55\u00b0', '65\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8231.jpg"
-  },
-  {
-    "id": 8447,
-    "problem_id": 8232,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Given that \u2220OAB = 25\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['55\u00b0', '65\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8232.jpg"
-  },
-  {
-    "id": 8448,
-    "problem_id": 8233,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Given that \u2220OAB = 25\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['55\u00b0', '65\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8233.jpg"
-  },
-  {
-    "id": 8449,
-    "problem_id": 8234,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Given that \u2220OAB = 25\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['55\u00b0', '65\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8234.jpg"
-  },
-  {
-    "id": 8450,
-    "problem_id": 8235,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8 cm2, then the area of the shaded triangle BEF is ().. A, B, C, D choices are ['4cm2', '2cm2', '0.5cm2', '1cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8235.jpg"
-  },
-  {
-    "id": 8451,
-    "problem_id": 8236,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. AD = \u221a{3} and AB = 1. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '60\u00b0', '120\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8236.jpg"
-  },
-  {
-    "id": 8452,
-    "problem_id": 8237,
-    "problem": "<image>In rectangle ABCD, diagonal AC intersects diagonal BD at point O. AD = \u221a{3} and AB = 1. What is the degree measure of \u2220BOC?. A, B, C, D choices are ['60\u00b0', '60\u00b0', '120\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8237.jpg"
-  },
-  {
-    "id": 8453,
-    "problem_id": 8238,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8238.jpg"
-  },
-  {
-    "id": 8454,
-    "problem_id": 8239,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8239.jpg"
-  },
-  {
-    "id": 8455,
-    "problem_id": 8240,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8240.jpg"
-  },
-  {
-    "id": 8456,
-    "problem_id": 8241,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8241.jpg"
-  },
-  {
-    "id": 8457,
-    "problem_id": 8242,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8242.jpg"
-  },
-  {
-    "id": 8458,
-    "problem_id": 8243,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8243.jpg"
-  },
-  {
-    "id": 8459,
-    "problem_id": 8244,
-    "problem": "<image>As shown in the diagram, a ladder with a length of 25m is leaning against a vertical wall, and the bottom of the ladder is 7m away from the bottom of the wall. If the top of the ladder slides down 4m, the bottom of the ladder will slide to the right ().. A, B, C, D choices are ['15m', '9m', '7m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8244.jpg"
-  },
-  {
-    "id": 8460,
-    "problem_id": 8245,
-    "problem": "<image>In right triangle ABC as shown in the diagram, CD is the altitude on hypotenuse AB, \u2220BCD = 35\u00b0, and the degree measure of \u2220A is ().. A, B, C, D choices are ['55\u00b0', '45\u00b0', '35\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8245.jpg"
-  },
-  {
-    "id": 8461,
-    "problem_id": 8246,
-    "problem": "<image>In right triangle ABC as shown in the diagram, CD is the altitude on hypotenuse AB, \u2220BCD = 35\u00b0, and the degree measure of \u2220A is ().. A, B, C, D choices are ['55\u00b0', '45\u00b0', '35\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8246.jpg"
-  },
-  {
-    "id": 8462,
-    "problem_id": 8247,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8247.jpg"
-  },
-  {
-    "id": 8463,
-    "problem_id": 8248,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8248.jpg"
-  },
-  {
-    "id": 8464,
-    "problem_id": 8249,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8249.jpg"
-  },
-  {
-    "id": 8465,
-    "problem_id": 8250,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8250.jpg"
-  },
-  {
-    "id": 8466,
-    "problem_id": 8251,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8251.jpg"
-  },
-  {
-    "id": 8467,
-    "problem_id": 8252,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8252.jpg"
-  },
-  {
-    "id": 8468,
-    "problem_id": 8253,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8253.jpg"
-  },
-  {
-    "id": 8469,
-    "problem_id": 8254,
-    "problem": "<image>Given AB\u2225CD and \u2220ABC\uff1d115\u00b0, \u2220CDE\uff1d35\u00b0. Find the degree measure of \u2220CED.. A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8254.jpg"
-  },
-  {
-    "id": 8470,
-    "problem_id": 8255,
-    "problem": "<image>In this lesson, we learned how to prove the Pythagorean theorem using Zhao Shuangxian's diagram. In the Zhao Shuangxian diagram shown below, point M is taken on DH such that DM = GH, and AM and CM are connected. If the area of square EFGH is 6, then the difference between the areas of \u25b3ADM and \u25b3CDM is ().. A, B, C, D choices are ['3', '2', '\u221a{3}', '0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8255.jpg"
-  },
-  {
-    "id": 8471,
-    "problem_id": 8256,
-    "problem": "<image>In this lesson, we learned how to prove the Pythagorean theorem using Zhao Shuangxian's diagram. In the Zhao Shuangxian diagram shown below, point M is taken on DH such that DM = GH, and AM and CM are connected. If the area of square EFGH is 6, then the difference between the areas of \u25b3ADM and \u25b3CDM is ().. A, B, C, D choices are ['3', '2', '\u221a{3}', '0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8256.jpg"
-  },
-  {
-    "id": 8472,
-    "problem_id": 8257,
-    "problem": "<image>In this lesson, we learned how to prove the Pythagorean theorem using Zhao Shuangxian's diagram. In the Zhao Shuangxian diagram shown below, point M is taken on DH such that DM = GH, and AM and CM are connected. If the area of square EFGH is 6, then the difference between the areas of \u25b3ADM and \u25b3CDM is ().. A, B, C, D choices are ['3', '2', '\u221a{3}', '0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8257.jpg"
-  },
-  {
-    "id": 8473,
-    "problem_id": 8258,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8258.jpg"
-  },
-  {
-    "id": 8474,
-    "problem_id": 8259,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8259.jpg"
-  },
-  {
-    "id": 8475,
-    "problem_id": 8260,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8260.jpg"
-  },
-  {
-    "id": 8476,
-    "problem_id": 8261,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8261.jpg"
-  },
-  {
-    "id": 8477,
-    "problem_id": 8262,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8262.jpg"
-  },
-  {
-    "id": 8478,
-    "problem_id": 8263,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8263.jpg"
-  },
-  {
-    "id": 8479,
-    "problem_id": 8264,
-    "problem": "<image>As shown in the diagram, a\u2225b\u2225c, AB = 9, BC = 3, DE = 12, what is the length of EF? (). A, B, C, D choices are ['4', '6', '16', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8264.jpg"
-  },
-  {
-    "id": 8480,
-    "problem_id": 8265,
-    "problem": "<image>As shown in the figure, \u2220DAB = 90\u00b0, \u2220DBA = 30\u00b0, AB = BC = \u221a3, DC = \u221a7, then \u2220ACB = ().. A, B, C, D choices are ['45\u00b0', '35\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8265.jpg"
-  },
-  {
-    "id": 8481,
-    "problem_id": 8266,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220CDB = 20\u00b0, then what is the degree of \u2220ABC?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8266.jpg"
-  },
-  {
-    "id": 8482,
-    "problem_id": 8267,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8267.jpg"
-  },
-  {
-    "id": 8483,
-    "problem_id": 8268,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8268.jpg"
-  },
-  {
-    "id": 8484,
-    "problem_id": 8269,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8269.jpg"
-  },
-  {
-    "id": 8485,
-    "problem_id": 8270,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8270.jpg"
-  },
-  {
-    "id": 8486,
-    "problem_id": 8271,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8271.jpg"
-  },
-  {
-    "id": 8487,
-    "problem_id": 8272,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8272.jpg"
-  },
-  {
-    "id": 8488,
-    "problem_id": 8273,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8273.jpg"
-  },
-  {
-    "id": 8489,
-    "problem_id": 8274,
-    "problem": "<image>In the figure, Rt \u25b3ABC, \u2220ACB = 90\u00b0, H, E, and F are the midpoints of sides AB, BC, and CA, respectively. If EF + CH = 4, then the value of CH is ().. A, B, C, D choices are ['1.5', '2', '2.5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8274.jpg"
-  },
-  {
-    "id": 8490,
-    "problem_id": 8275,
-    "problem": "<image>As shown in the figure, if \u22201 = 105\u00b0, \u22202 = 75\u00b0, and \u22204 = 110\u00b0, what is the degree measurement of \u22203? (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8275.jpg"
-  },
-  {
-    "id": 8491,
-    "problem_id": 8276,
-    "problem": "<image>As shown in the figure, if \u22201 = 105\u00b0, \u22202 = 75\u00b0, and \u22204 = 110\u00b0, what is the degree measurement of \u22203? (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8276.jpg"
-  },
-  {
-    "id": 8492,
-    "problem_id": 8277,
-    "problem": "<image>As shown in the figure, if \u22201 = 105\u00b0, \u22202 = 75\u00b0, and \u22204 = 110\u00b0, what is the degree measurement of \u22203? (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{B}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8277.jpg"
-  },
-  {
-    "id": 8493,
-    "problem_id": 8278,
-    "problem": "<image>As shown in the figure, if \u22201 = 105\u00b0, \u22202 = 75\u00b0, and \u22204 = 110\u00b0, what is the degree measurement of \u22203? (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8278.jpg"
-  },
-  {
-    "id": 8494,
-    "problem_id": 8279,
-    "problem": "<image>As shown in the figure, if \u22201 = 105\u00b0, \u22202 = 75\u00b0, and \u22204 = 110\u00b0, what is the degree measurement of \u22203? (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8279.jpg"
-  },
-  {
-    "id": 8495,
-    "problem_id": 8280,
-    "problem": "<image>As shown in the figure, point D is an arbitrary point on the side BC of triangle ABC, and points E and F are the midpoints of segments AD and CE, respectively. If the area of triangle ABC is 24, then the area of triangle BEF is ().. A, B, C, D choices are ['12', '8', '6', '9.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8280.jpg"
-  },
-  {
-    "id": 8496,
-    "problem_id": 8281,
-    "problem": "<image>As shown in the figure, point D is an arbitrary point on the side BC of triangle ABC, and points E and F are the midpoints of segments AD and CE, respectively. If the area of triangle ABC is 24, then the area of triangle BEF is ().. A, B, C, D choices are ['12', '8', '6', '9.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8281.jpg"
-  },
-  {
-    "id": 8497,
-    "problem_id": 8282,
-    "problem": "<image>As shown in the figure, point D is an arbitrary point on the side BC of triangle ABC, and points E and F are the midpoints of segments AD and CE, respectively. If the area of triangle ABC is 24, then the area of triangle BEF is ().. A, B, C, D choices are ['12', '8', '6', '9.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8282.jpg"
-  },
-  {
-    "id": 8498,
-    "problem_id": 8283,
-    "problem": "<image>As shown in the figure, point D is an arbitrary point on the side BC of triangle ABC, and points E and F are the midpoints of segments AD and CE, respectively. If the area of triangle ABC is 24, then the area of triangle BEF is ().. A, B, C, D choices are ['12', '8', '6', '9.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8283.jpg"
-  },
-  {
-    "id": 8499,
-    "problem_id": 8284,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. The area of the shaded triangle AEF is (). A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8284.jpg"
-  },
-  {
-    "id": 8500,
-    "problem_id": 8285,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. The area of the shaded triangle AEF is (). A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8285.jpg"
-  },
-  {
-    "id": 8501,
-    "problem_id": 8286,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. The area of the shaded triangle AEF is (). A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8286.jpg"
-  },
-  {
-    "id": 8502,
-    "problem_id": 8287,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. The area of the shaded triangle AEF is (). A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8287.jpg"
-  },
-  {
-    "id": 8503,
-    "problem_id": 8288,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. The area of the shaded triangle AEF is (). A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8288.jpg"
-  },
-  {
-    "id": 8504,
-    "problem_id": 8289,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. The area of the shaded triangle AEF is (). A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8289.jpg"
-  },
-  {
-    "id": 8506,
-    "problem_id": 8290,
-    "problem": "<image>If the ruler is stacked together with the 45-degree triangle ruler as shown in the figure, and \u03b1 = 20\u00b0, what is the degree of \u03b2? (). A, B, C, D choices are ['65\u00b0', '70\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8290.jpg"
-  },
-  {
-    "id": 8507,
-    "problem_id": 8291,
-    "problem": "<image>If the ruler is stacked together with the 45-degree triangle ruler as shown in the figure, and \u03b1 = 20\u00b0, what is the degree of \u03b2? (). A, B, C, D choices are ['65\u00b0', '70\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8291.jpg"
-  },
-  {
-    "id": 8509,
-    "problem_id": 8292,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and E and F are the midpoints of AC and BD, respectively. If AB = 5 and CD = 3, what is the length of EF? (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8292.jpg"
-  },
-  {
-    "id": 8510,
-    "problem_id": 8293,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and E and F are the midpoints of AC and BD, respectively. If AB = 5 and CD = 3, what is the length of EF? (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8293.jpg"
-  },
-  {
-    "id": 8511,
-    "problem_id": 8294,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and E and F are the midpoints of AC and BD, respectively. If AB = 5 and CD = 3, what is the length of EF? (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8294.jpg"
-  },
-  {
-    "id": 8512,
-    "problem_id": 8295,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8295.jpg"
-  },
-  {
-    "id": 8513,
-    "problem_id": 8296,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8296.jpg"
-  },
-  {
-    "id": 8514,
-    "problem_id": 8297,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8297.jpg"
-  },
-  {
-    "id": 8515,
-    "problem_id": 8298,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8298.jpg"
-  },
-  {
-    "id": 8516,
-    "problem_id": 8299,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8299.jpg"
-  },
-  {
-    "id": 8517,
-    "problem_id": 8300,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8300.jpg"
-  },
-  {
-    "id": 8518,
-    "problem_id": 8301,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of diamond ABCD intersect at point O. Through point A, draw perpendicular AH to BC at point H and connect OH. If OB = 4 and the area of diamond ABCD is 24, then the length of OH is ().. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8301.jpg"
-  },
-  {
-    "id": 8521,
-    "problem_id": 8302,
-    "problem": "<image>In triangle ABC, AB=AD=CD, \u2220C=38.5\u00b0, then \u2220BAD=().. A, B, C, D choices are ['26\u00b0', '28\u00b0', '36\u00b0', '38.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8302.jpg"
-  },
-  {
-    "id": 8522,
-    "problem_id": 8303,
-    "problem": "<image>In triangle ABC, AB=AD=CD, \u2220C=38.5\u00b0, then \u2220BAD=().. A, B, C, D choices are ['26\u00b0', '28\u00b0', '36\u00b0', '38.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8303.jpg"
-  },
-  {
-    "id": 8523,
-    "problem_id": 8304,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8304.jpg"
-  },
-  {
-    "id": 8524,
-    "problem_id": 8305,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8305.jpg"
-  },
-  {
-    "id": 8525,
-    "problem_id": 8306,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8306.jpg"
-  },
-  {
-    "id": 8526,
-    "problem_id": 8307,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8307.jpg"
-  },
-  {
-    "id": 8527,
-    "problem_id": 8308,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8308.jpg"
-  },
-  {
-    "id": 8528,
-    "problem_id": 8309,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8309.jpg"
-  },
-  {
-    "id": 8529,
-    "problem_id": 8310,
-    "problem": "<image>As shown in the figure, if the length of the generatrix AB of a cone is 13cm and the height OB is 12cm, then the lateral area of this cone is ().. A, B, C, D choices are ['25cm2', '60\u03c0cm2', '65\u03c0cm2', '90\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8310.jpg"
-  },
-  {
-    "id": 8530,
-    "problem_id": 8311,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ABO = 36\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['54\u00b0', '27\u00b0', '36\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8311.jpg"
-  },
-  {
-    "id": 8532,
-    "problem_id": 8312,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ABO = 36\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['54\u00b0', '27\u00b0', '36\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8312.jpg"
-  },
-  {
-    "id": 8533,
-    "problem_id": 8313,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ABO = 36\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['54\u00b0', '27\u00b0', '36\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8313.jpg"
-  },
-  {
-    "id": 8534,
-    "problem_id": 8314,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ABO = 36\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['54\u00b0', '27\u00b0', '36\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8314.jpg"
-  },
-  {
-    "id": 8535,
-    "problem_id": 8315,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8315.jpg"
-  },
-  {
-    "id": 8536,
-    "problem_id": 8316,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8316.jpg"
-  },
-  {
-    "id": 8537,
-    "problem_id": 8317,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8317.jpg"
-  },
-  {
-    "id": 8538,
-    "problem_id": 8318,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8318.jpg"
-  },
-  {
-    "id": 8539,
-    "problem_id": 8319,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8319.jpg"
-  },
-  {
-    "id": 8540,
-    "problem_id": 8320,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8320.jpg"
-  },
-  {
-    "id": 8541,
-    "problem_id": 8321,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8321.jpg"
-  },
-  {
-    "id": 8542,
-    "problem_id": 8322,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220BOC = 64\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['64\u00b0', '32\u00b0', '26\u00b0', '23\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8322.jpg"
-  },
-  {
-    "id": 8543,
-    "problem_id": 8323,
-    "problem": "<image>In triangle ABC as shown, AB = 5, BC = 6, AC = 7, D, E, and F are the midpoints of the sides of triangle ABC. The perimeter of triangle DEF is (). A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8323.jpg"
-  },
-  {
-    "id": 8544,
-    "problem_id": 8324,
-    "problem": "<image>In triangle ABC as shown, AB = 5, BC = 6, AC = 7, D, E, and F are the midpoints of the sides of triangle ABC. The perimeter of triangle DEF is (). A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8324.jpg"
-  },
-  {
-    "id": 8545,
-    "problem_id": 8325,
-    "problem": "<image>In triangle ABC as shown, AB = 5, BC = 6, AC = 7, D, E, and F are the midpoints of the sides of triangle ABC. The perimeter of triangle DEF is (). A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8325.jpg"
-  },
-  {
-    "id": 8546,
-    "problem_id": 8326,
-    "problem": "<image>In triangle ABC as shown, AB = 5, BC = 6, AC = 7, D, E, and F are the midpoints of the sides of triangle ABC. The perimeter of triangle DEF is (). A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8326.jpg"
-  },
-  {
-    "id": 8547,
-    "problem_id": 8327,
-    "problem": "<image>In triangle ABC as shown, AB = 5, BC = 6, AC = 7, D, E, and F are the midpoints of the sides of triangle ABC. The perimeter of triangle DEF is (). A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8327.jpg"
-  },
-  {
-    "id": 8548,
-    "problem_id": 8328,
-    "problem": "<image>In triangle ABC as shown, AB = 5, BC = 6, AC = 7, D, E, and F are the midpoints of the sides of triangle ABC. The perimeter of triangle DEF is (). A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8328.jpg"
-  },
-  {
-    "id": 8549,
-    "problem_id": 8329,
-    "problem": "<image>In the figure, in rectangle ABCD, \u2220BOC = 120\u00b0 and AB = 4. What is the length of AC?. A, B, C, D choices are ['2', '2\u221a{3}', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8329.jpg"
-  },
-  {
-    "id": 8550,
-    "problem_id": 8330,
-    "problem": "<image>In the figure, in rectangle ABCD, \u2220BOC = 120\u00b0 and AB = 4. What is the length of AC?. A, B, C, D choices are ['2', '2\u221a{3}', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8330.jpg"
-  },
-  {
-    "id": 8551,
-    "problem_id": 8331,
-    "problem": "<image>In the figure, in rectangle ABCD, \u2220BOC = 120\u00b0 and AB = 4. What is the length of AC?. A, B, C, D choices are ['2', '2\u221a{3}', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8331.jpg"
-  },
-  {
-    "id": 8552,
-    "problem_id": 8332,
-    "problem": "<image>As shown in the diagram, quadrilateral ABCD is a diamond. Diagonals AC and BD intersect at point O. E is the midpoint of side AD. A line perpendicular to BD is drawn through point E, intersecting BD at point F. Similarly, a line perpendicular to AC is drawn through point E, intersecting AC at point G. Points F and G are the foot of the perpendiculars. If AC = 10 and BD = 24, then the length of FG is ().. A, B, C, D choices are ['5', '6.5', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8332.jpg"
-  },
-  {
-    "id": 8553,
-    "problem_id": 8333,
-    "problem": "<image>As shown in the diagram, quadrilateral ABCD is a diamond. Diagonals AC and BD intersect at point O. E is the midpoint of side AD. A line perpendicular to BD is drawn through point E, intersecting BD at point F. Similarly, a line perpendicular to AC is drawn through point E, intersecting AC at point G. Points F and G are the foot of the perpendiculars. If AC = 10 and BD = 24, then the length of FG is ().. A, B, C, D choices are ['5', '6.5', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8333.jpg"
-  },
-  {
-    "id": 8554,
-    "problem_id": 8334,
-    "problem": "<image>As shown in the diagram, quadrilateral ABCD is a diamond. Diagonals AC and BD intersect at point O. E is the midpoint of side AD. A line perpendicular to BD is drawn through point E, intersecting BD at point F. Similarly, a line perpendicular to AC is drawn through point E, intersecting AC at point G. Points F and G are the foot of the perpendiculars. If AC = 10 and BD = 24, then the length of FG is ().. A, B, C, D choices are ['5', '6.5', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8334.jpg"
-  },
-  {
-    "id": 8555,
-    "problem_id": 8335,
-    "problem": "<image>As shown in the diagram, quadrilateral ABCD is a diamond. Diagonals AC and BD intersect at point O. E is the midpoint of side AD. A line perpendicular to BD is drawn through point E, intersecting BD at point F. Similarly, a line perpendicular to AC is drawn through point E, intersecting AC at point G. Points F and G are the foot of the perpendiculars. If AC = 10 and BD = 24, then the length of FG is ().. A, B, C, D choices are ['5', '6.5', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8335.jpg"
-  },
-  {
-    "id": 8556,
-    "problem_id": 8336,
-    "problem": "<image>As shown in the diagram, quadrilateral ABCD is a diamond. Diagonals AC and BD intersect at point O. E is the midpoint of side AD. A line perpendicular to BD is drawn through point E, intersecting BD at point F. Similarly, a line perpendicular to AC is drawn through point E, intersecting AC at point G. Points F and G are the foot of the perpendiculars. If AC = 10 and BD = 24, then the length of FG is ().. A, B, C, D choices are ['5', '6.5', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8336.jpg"
-  },
-  {
-    "id": 8557,
-    "problem_id": 8337,
-    "problem": "<image>In triangle ABC shown in the figure, BC = 20, D and E are the midpoints of AB and AC respectively, F is a point on DE, and DF = 4. Connect AF and CF. If \u2220AFC = 90\u00b0, the length of AC is ().. A, B, C, D choices are ['10', '12', '13', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8337.jpg"
-  },
-  {
-    "id": 8558,
-    "problem_id": 8338,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB=5 and AD=12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['16', '20', '29', '34'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8338.jpg"
-  },
-  {
-    "id": 8559,
-    "problem_id": 8339,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB=5 and AD=12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['16', '20', '29', '34'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8339.jpg"
-  },
-  {
-    "id": 8560,
-    "problem_id": 8340,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB=5 and AD=12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['16', '20', '29', '34'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8340.jpg"
-  },
-  {
-    "id": 8561,
-    "problem_id": 8341,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB=5 and AD=12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['16', '20', '29', '34'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8341.jpg"
-  },
-  {
-    "id": 8562,
-    "problem_id": 8342,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB=5 and AD=12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['16', '20', '29', '34'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8342.jpg"
-  },
-  {
-    "id": 8563,
-    "problem_id": 8343,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB=5 and AD=12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['16', '20', '29', '34'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8343.jpg"
-  },
-  {
-    "id": 8564,
-    "problem_id": 8344,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220ABD = 54\u00b0, then what is the degree measure of \u2220C?. A, B, C, D choices are ['34\u00b0', '36\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8344.jpg"
-  },
-  {
-    "id": 8565,
-    "problem_id": 8345,
-    "problem": "<image>As shown in the figure, the length of segment AB is 6. Point C is a moving point outside segment AB, and \u2220ACB = 45\u00b0. Connect BC, and let M and N be the midpoints of segments AB and BC, respectively. The maximum value of segment MN is () .. A, B, C, D choices are ['3', '4', '3\u221a{2}', '3+\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8345.jpg"
-  },
-  {
-    "id": 8566,
-    "problem_id": 8346,
-    "problem": "<image>As shown in the figure, in triangle ABC, AB=10, AC=8, BC=6. The perpendicular bisector of AC intersects AB at point D, and the foot of the perpendicular is E. Connect CD. The length of CD is () .. A, B, C, D choices are ['3', '4', '4.8', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8346.jpg"
-  },
-  {
-    "id": 8567,
-    "problem_id": 8347,
-    "problem": "<image>As shown in the figure, in triangle ABC, AB=10, AC=8, BC=6. The perpendicular bisector of AC intersects AB at point D, and the foot of the perpendicular is E. Connect CD. The length of CD is () .. A, B, C, D choices are ['3', '4', '4.8', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8347.jpg"
-  },
-  {
-    "id": 8568,
-    "problem_id": 8348,
-    "problem": "<image>As shown in the figure, in triangle ABC, AB=10, AC=8, BC=6. The perpendicular bisector of AC intersects AB at point D, and the foot of the perpendicular is E. Connect CD. The length of CD is () .. A, B, C, D choices are ['3', '4', '4.8', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8348.jpg"
-  },
-  {
-    "id": 8569,
-    "problem_id": 8349,
-    "problem": "<image>As shown in the figure, in triangle ABC, AB=10, AC=8, BC=6. The perpendicular bisector of AC intersects AB at point D, and the foot of the perpendicular is E. Connect CD. The length of CD is () .. A, B, C, D choices are ['3', '4', '4.8', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8349.jpg"
-  },
-  {
-    "id": 8571,
-    "problem_id": 8350,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, EH\u22a5CD at point H, and \u2220HEF\uff1d37\u00b0. Then, \u2220AEG\uff1d(). A, B, C, D choices are ['37', '53', '63', '143'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8350.jpg"
-  },
-  {
-    "id": 8572,
-    "problem_id": 8351,
-    "problem": "<image>As shown in the figure, the diagonals of the parallelogram intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 5cm, then the perimeter of triangle OCD is ().. A, B, C, D choices are ['41', '12', '23', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8351.jpg"
-  },
-  {
-    "id": 8573,
-    "problem_id": 8352,
-    "problem": "<image>As shown in the figure, the diagonals of the parallelogram intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 5cm, then the perimeter of triangle OCD is ().. A, B, C, D choices are ['41', '12', '23', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8352.jpg"
-  },
-  {
-    "id": 8574,
-    "problem_id": 8353,
-    "problem": "<image>As shown in the figure, the diagonals of the parallelogram intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 5cm, then the perimeter of triangle OCD is ().. A, B, C, D choices are ['41', '12', '23', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8353.jpg"
-  },
-  {
-    "id": 8575,
-    "problem_id": 8354,
-    "problem": "<image>As shown in the figure, the diagonals of the parallelogram intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 5cm, then the perimeter of triangle OCD is ().. A, B, C, D choices are ['41', '12', '23', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8354.jpg"
-  },
-  {
-    "id": 8576,
-    "problem_id": 8355,
-    "problem": "<image>As shown in the figure, the diagonals of the parallelogram intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 5cm, then the perimeter of triangle OCD is ().. A, B, C, D choices are ['41', '12', '23', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8355.jpg"
-  },
-  {
-    "id": 8577,
-    "problem_id": 8356,
-    "problem": "<image>As shown in the figure, the diagonals of the parallelogram intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 5cm, then the perimeter of triangle OCD is ().. A, B, C, D choices are ['41', '12', '23', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8356.jpg"
-  },
-  {
-    "id": 8578,
-    "problem_id": 8357,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8357.jpg"
-  },
-  {
-    "id": 8579,
-    "problem_id": 8358,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8358.jpg"
-  },
-  {
-    "id": 8580,
-    "problem_id": 8359,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8359.jpg"
-  },
-  {
-    "id": 8581,
-    "problem_id": 8360,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8360.jpg"
-  },
-  {
-    "id": 8582,
-    "problem_id": 8361,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8361.jpg"
-  },
-  {
-    "id": 8583,
-    "problem_id": 8362,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8362.jpg"
-  },
-  {
-    "id": 8584,
-    "problem_id": 8363,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8363.jpg"
-  },
-  {
-    "id": 8585,
-    "problem_id": 8364,
-    "problem": "<image>When measuring the wall thickness of a small circular container, Xiaoming used the \"x-type rotary pliers\" to measure as shown in the figure. Where OA=OD, OB=OC, AB=5 cm, EF=7 cm, what is the wall thickness of the circular container?. A, B, C, D choices are ['1\u5398\u7c73', '2\u5398\u7c73', '5\u5398\u7c73', '7\u5398\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8364.jpg"
-  },
-  {
-    "id": 8587,
-    "problem_id": 8365,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, OE is perpendicular to CD at point O, and \u2220BOC = 140\u00b0. The degree measure of \u2220AOE is ()?. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8365.jpg"
-  },
-  {
-    "id": 8588,
-    "problem_id": 8366,
-    "problem": "<image>As shown in the figure, AD is the angle bisector of triangle ABC, point E is the midpoint of AC, and DE is connected. If AB = AC = 10 and BC = 8, then the perimeter of triangle CDE is ().. A, B, C, D choices are ['20', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8366.jpg"
-  },
-  {
-    "id": 8589,
-    "problem_id": 8367,
-    "problem": "<image>As shown in the figure, AD is the angle bisector of triangle ABC, point E is the midpoint of AC, and DE is connected. If AB = AC = 10 and BC = 8, then the perimeter of triangle CDE is ().. A, B, C, D choices are ['20', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8367.jpg"
-  },
-  {
-    "id": 8590,
-    "problem_id": 8368,
-    "problem": "<image>As shown in the figure, AD is the angle bisector of triangle ABC, point E is the midpoint of AC, and DE is connected. If AB = AC = 10 and BC = 8, then the perimeter of triangle CDE is ().. A, B, C, D choices are ['20', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8368.jpg"
-  },
-  {
-    "id": 8591,
-    "problem_id": 8369,
-    "problem": "<image>As shown in the figure, AD is the angle bisector of triangle ABC, point E is the midpoint of AC, and DE is connected. If AB = AC = 10 and BC = 8, then the perimeter of triangle CDE is ().. A, B, C, D choices are ['20', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8369.jpg"
-  },
-  {
-    "id": 8592,
-    "problem_id": 8370,
-    "problem": "<image>As shown in the figure, AD is the angle bisector of triangle ABC, point E is the midpoint of AC, and DE is connected. If AB = AC = 10 and BC = 8, then the perimeter of triangle CDE is ().. A, B, C, D choices are ['20', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8370.jpg"
-  },
-  {
-    "id": 8593,
-    "problem_id": 8371,
-    "problem": "<image>As shown in the figure, AD is the angle bisector of triangle ABC, point E is the midpoint of AC, and DE is connected. If AB = AC = 10 and BC = 8, then the perimeter of triangle CDE is ().. A, B, C, D choices are ['20', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8371.jpg"
-  },
-  {
-    "id": 8594,
-    "problem_id": 8372,
-    "problem": "<image>As shown in the figure, in circle O, \u2220ACB = 67\u00b0, point P lies on the minor arc AB, and \u2220AOP = 42\u00b0. What is the degree measure of \u2220BOP? (). A, B, C, D choices are ['25\u00b0', '90\u00b0', '92\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8372.jpg"
-  },
-  {
-    "id": 8595,
-    "problem_id": 8373,
-    "problem": "<image>As shown in the figure, in circle O, \u2220ACB = 67\u00b0, point P lies on the minor arc AB, and \u2220AOP = 42\u00b0. What is the degree measure of \u2220BOP? (). A, B, C, D choices are ['25\u00b0', '90\u00b0', '92\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8373.jpg"
-  },
-  {
-    "id": 8596,
-    "problem_id": 8374,
-    "problem": "<image>As shown in the figure, in circle O, \u2220ACB = 67\u00b0, point P lies on the minor arc AB, and \u2220AOP = 42\u00b0. What is the degree measure of \u2220BOP? (). A, B, C, D choices are ['25\u00b0', '90\u00b0', '92\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8374.jpg"
-  },
-  {
-    "id": 8597,
-    "problem_id": 8375,
-    "problem": "<image>As shown in the figure, in circle O, \u2220ACB = 67\u00b0, point P lies on the minor arc AB, and \u2220AOP = 42\u00b0. What is the degree measure of \u2220BOP? (). A, B, C, D choices are ['25\u00b0', '90\u00b0', '92\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8375.jpg"
-  },
-  {
-    "id": 8598,
-    "problem_id": 8376,
-    "problem": "<image>As shown in the figure, in circle O, \u2220ACB = 67\u00b0, point P lies on the minor arc AB, and \u2220AOP = 42\u00b0. What is the degree measure of \u2220BOP? (). A, B, C, D choices are ['25\u00b0', '90\u00b0', '92\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8376.jpg"
-  },
-  {
-    "id": 8599,
-    "problem_id": 8377,
-    "problem": "<image>In right triangle ABC shown in the figure, \u2220ACB = 90\u00b0. Three squares are constructed outside of triangle ABC with each side being a side of triangle ABC. S1, S2, and S3 represent the area of these three squares respectively. If S1 = 3 and S2 = 11, then S3 = (). A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8377.jpg"
-  },
-  {
-    "id": 8600,
-    "problem_id": 8378,
-    "problem": "<image>In right triangle ABC shown in the figure, \u2220ACB = 90\u00b0. Three squares are constructed outside of triangle ABC with each side being a side of triangle ABC. S1, S2, and S3 represent the area of these three squares respectively. If S1 = 3 and S2 = 11, then S3 = (). A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8378.jpg"
-  },
-  {
-    "id": 8601,
-    "problem_id": 8379,
-    "problem": "<image>In right triangle ABC shown in the figure, \u2220ACB = 90\u00b0. Three squares are constructed outside of triangle ABC with each side being a side of triangle ABC. S1, S2, and S3 represent the area of these three squares respectively. If S1 = 3 and S2 = 11, then S3 = (). A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8379.jpg"
-  },
-  {
-    "id": 8602,
-    "problem_id": 8380,
-    "problem": "<image>In right triangle ABC shown in the figure, \u2220ACB = 90\u00b0. Three squares are constructed outside of triangle ABC with each side being a side of triangle ABC. S1, S2, and S3 represent the area of these three squares respectively. If S1 = 3 and S2 = 11, then S3 = (). A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8380.jpg"
-  },
-  {
-    "id": 8603,
-    "problem_id": 8381,
-    "problem": "<image>In right triangle ABC shown in the figure, \u2220ACB = 90\u00b0. Three squares are constructed outside of triangle ABC with each side being a side of triangle ABC. S1, S2, and S3 represent the area of these three squares respectively. If S1 = 3 and S2 = 11, then S3 = (). A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8381.jpg"
-  },
-  {
-    "id": 8604,
-    "problem_id": 8382,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8382.jpg"
-  },
-  {
-    "id": 8605,
-    "problem_id": 8383,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8383.jpg"
-  },
-  {
-    "id": 8606,
-    "problem_id": 8384,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8384.jpg"
-  },
-  {
-    "id": 8607,
-    "problem_id": 8385,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8385.jpg"
-  },
-  {
-    "id": 8608,
-    "problem_id": 8386,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8386.jpg"
-  },
-  {
-    "id": 8609,
-    "problem_id": 8387,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8387.jpg"
-  },
-  {
-    "id": 8610,
-    "problem_id": 8388,
-    "problem": "<image>As shown in the figure, if the length of the slant height of a cone is 5cm and the length of its height is 4cm, what is the area of the base of the cone? (). A, B, C, D choices are ['3\u03c0cm2', '9\u03c0cm2', '16\u03c0cm2', '25\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8388.jpg"
-  },
-  {
-    "id": 8611,
-    "problem_id": 8389,
-    "problem": "<image>In triangle ABC, with AB = 1, BC = 2, AC = \u221a5, and AD is the median on side BC. What is the length of AD?. A, B, C, D choices are ['1', '2', '\\\\frac{\u221a{5}}{2}', '\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8389.jpg"
-  },
-  {
-    "id": 8612,
-    "problem_id": 8390,
-    "problem": "<image>In triangle ABC, with AB = 1, BC = 2, AC = \u221a5, and AD is the median on side BC. What is the length of AD?. A, B, C, D choices are ['1', '2', '\\\\frac{\u221a{5}}{2}', '\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8390.jpg"
-  },
-  {
-    "id": 8613,
-    "problem_id": 8391,
-    "problem": "<image>In triangle ABC, with AB = 1, BC = 2, AC = \u221a5, and AD is the median on side BC. What is the length of AD?. A, B, C, D choices are ['1', '2', '\\\\frac{\u221a{5}}{2}', '\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8391.jpg"
-  },
-  {
-    "id": 8614,
-    "problem_id": 8392,
-    "problem": "<image>In triangle ABC, with AB = 1, BC = 2, AC = \u221a5, and AD is the median on side BC. What is the length of AD?. A, B, C, D choices are ['1', '2', '\\\\frac{\u221a{5}}{2}', '\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8392.jpg"
-  },
-  {
-    "id": 8615,
-    "problem_id": 8393,
-    "problem": "<image>In triangle ABC, with AB = 1, BC = 2, AC = \u221a5, and AD is the median on side BC. What is the length of AD?. A, B, C, D choices are ['1', '2', '\\\\frac{\u221a{5}}{2}', '\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8393.jpg"
-  },
-  {
-    "id": 8616,
-    "problem_id": 8394,
-    "problem": "<image>In the diamond ABCD shown in the figure, if AB = 13 and AC = 10, what is the length of BD? (). A, B, C, D choices are ['24', '16', '12', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8394.jpg"
-  },
-  {
-    "id": 8617,
-    "problem_id": 8395,
-    "problem": "<image>In the diamond ABCD shown in the figure, if AB = 13 and AC = 10, what is the length of BD? (). A, B, C, D choices are ['24', '16', '12', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8395.jpg"
-  },
-  {
-    "id": 8618,
-    "problem_id": 8396,
-    "problem": "<image>In the diamond ABCD shown in the figure, if AB = 13 and AC = 10, what is the length of BD? (). A, B, C, D choices are ['24', '16', '12', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8396.jpg"
-  },
-  {
-    "id": 8619,
-    "problem_id": 8397,
-    "problem": "<image>In the diamond ABCD shown in the figure, if AB = 13 and AC = 10, what is the length of BD? (). A, B, C, D choices are ['24', '16', '12', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8397.jpg"
-  },
-  {
-    "id": 8620,
-    "problem_id": 8398,
-    "problem": "<image>In the diamond ABCD shown in the figure, if AB = 13 and AC = 10, what is the length of BD? (). A, B, C, D choices are ['24', '16', '12', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8398.jpg"
-  },
-  {
-    "id": 8621,
-    "problem_id": 8399,
-    "problem": "<image>As shown in the figure, a flagpole perpendicular to the ground is torn and broken at point B, which is 5m above the ground. The top of the flagpole falls at point A, which is 12m away from the bottom of the flagpole. What is the height of the broken part AB of the flagpole?. A, B, C, D choices are ['5m', '12m', '13m', '18m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8399.jpg"
-  },
-  {
-    "id": 8622,
-    "problem_id": 8400,
-    "problem": "<image>As shown in the figure, a flagpole perpendicular to the ground is torn and broken at point B, which is 5m above the ground. The top of the flagpole falls at point A, which is 12m away from the bottom of the flagpole. What is the height of the broken part AB of the flagpole?. A, B, C, D choices are ['5m', '12m', '13m', '18m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8400.jpg"
-  },
-  {
-    "id": 8623,
-    "problem_id": 8401,
-    "problem": "<image>As shown in the figure, a flagpole perpendicular to the ground is torn and broken at point B, which is 5m above the ground. The top of the flagpole falls at point A, which is 12m away from the bottom of the flagpole. What is the height of the broken part AB of the flagpole?. A, B, C, D choices are ['5m', '12m', '13m', '18m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8401.jpg"
-  },
-  {
-    "id": 8624,
-    "problem_id": 8402,
-    "problem": "<image>As shown in the figure, a flagpole perpendicular to the ground is torn and broken at point B, which is 5m above the ground. The top of the flagpole falls at point A, which is 12m away from the bottom of the flagpole. What is the height of the broken part AB of the flagpole?. A, B, C, D choices are ['5m', '12m', '13m', '18m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8402.jpg"
-  },
-  {
-    "id": 8625,
-    "problem_id": 8403,
-    "problem": "<image>As shown in the figure, a flagpole perpendicular to the ground is torn and broken at point B, which is 5m above the ground. The top of the flagpole falls at point A, which is 12m away from the bottom of the flagpole. What is the height of the broken part AB of the flagpole?. A, B, C, D choices are ['5m', '12m', '13m', '18m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8403.jpg"
-  },
-  {
-    "id": 8626,
-    "problem_id": 8404,
-    "problem": "<image>As shown in the figure, a tangent line AB is drawn from point A outside of circle O, with point B as the tangent point. Connect AO and extend it to intersect the circle at point C, then connect BC. If angle A is 28\u00b0, what is the degree measurement of angle ACB? (). A, B, C, D choices are ['28\u00b0', '30\u00b0', '31\u00b0', '32\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8404.jpg"
-  },
-  {
-    "id": 8627,
-    "problem_id": 8405,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8405.jpg"
-  },
-  {
-    "id": 8628,
-    "problem_id": 8406,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8406.jpg"
-  },
-  {
-    "id": 8629,
-    "problem_id": 8407,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8407.jpg"
-  },
-  {
-    "id": 8630,
-    "problem_id": 8408,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8408.jpg"
-  },
-  {
-    "id": 8631,
-    "problem_id": 8409,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8409.jpg"
-  },
-  {
-    "id": 8632,
-    "problem_id": 8410,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8410.jpg"
-  },
-  {
-    "id": 8633,
-    "problem_id": 8411,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8411.jpg"
-  },
-  {
-    "id": 8634,
-    "problem_id": 8412,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. If \u2220B = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '68\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8412.jpg"
-  },
-  {
-    "id": 8635,
-    "problem_id": 8413,
-    "problem": "<image>As shown in the diagram, line DE is parallel to BF, and vertex B of the right triangle ABC lies on BF. If \u2220CBF = 20\u00b0, then \u2220ADE = ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '75\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8413.jpg"
-  },
-  {
-    "id": 8636,
-    "problem_id": 8414,
-    "problem": "<image>As shown in the diagram, line DE is parallel to BF, and vertex B of the right triangle ABC lies on BF. If \u2220CBF = 20\u00b0, then \u2220ADE = ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '75\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8414.jpg"
-  },
-  {
-    "id": 8637,
-    "problem_id": 8415,
-    "problem": "<image>As shown in the diagram, it is known that m\u2225n, vertex B of equilateral triangle \u25b3ABC is on line n, and \u22201 = 25\u00b0. The degree of \u22202 is (). A, B, C, D choices are ['25\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8415.jpg"
-  },
-  {
-    "id": 8638,
-    "problem_id": 8416,
-    "problem": "<image>As shown in the diagram, it is known that m\u2225n, vertex B of equilateral triangle \u25b3ABC is on line n, and \u22201 = 25\u00b0. The degree of \u22202 is (). A, B, C, D choices are ['25\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8416.jpg"
-  },
-  {
-    "id": 8639,
-    "problem_id": 8417,
-    "problem": "<image>As shown in the diagram, it is known that m\u2225n, vertex B of equilateral triangle \u25b3ABC is on line n, and \u22201 = 25\u00b0. The degree of \u22202 is (). A, B, C, D choices are ['25\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8417.jpg"
-  },
-  {
-    "id": 8640,
-    "problem_id": 8418,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8418.jpg"
-  },
-  {
-    "id": 8641,
-    "problem_id": 8419,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8419.jpg"
-  },
-  {
-    "id": 8642,
-    "problem_id": 8420,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8420.jpg"
-  },
-  {
-    "id": 8643,
-    "problem_id": 8421,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8421.jpg"
-  },
-  {
-    "id": 8644,
-    "problem_id": 8422,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8422.jpg"
-  },
-  {
-    "id": 8645,
-    "problem_id": 8423,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8423.jpg"
-  },
-  {
-    "id": 8646,
-    "problem_id": 8424,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['18\u00b0', '23\u00b0', '28\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8424.jpg"
-  },
-  {
-    "id": 8647,
-    "problem_id": 8425,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8425.jpg"
-  },
-  {
-    "id": 8648,
-    "problem_id": 8426,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8426.jpg"
-  },
-  {
-    "id": 8649,
-    "problem_id": 8427,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8427.jpg"
-  },
-  {
-    "id": 8650,
-    "problem_id": 8428,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8428.jpg"
-  },
-  {
-    "id": 8651,
-    "problem_id": 8429,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8429.jpg"
-  },
-  {
-    "id": 8652,
-    "problem_id": 8430,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8430.jpg"
-  },
-  {
-    "id": 8653,
-    "problem_id": 8431,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12cm', '14cm', '16cm', '28cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8431.jpg"
-  },
-  {
-    "id": 8654,
-    "problem_id": 8432,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12cm', '14cm', '16cm', '28cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8432.jpg"
-  },
-  {
-    "id": 8655,
-    "problem_id": 8433,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12cm', '14cm', '16cm', '28cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8433.jpg"
-  },
-  {
-    "id": 8656,
-    "problem_id": 8434,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12cm', '14cm', '16cm', '28cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8434.jpg"
-  },
-  {
-    "id": 8657,
-    "problem_id": 8435,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12cm', '14cm', '16cm', '28cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8435.jpg"
-  },
-  {
-    "id": 8658,
-    "problem_id": 8436,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['313', '144', '169', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8436.jpg"
-  },
-  {
-    "id": 8659,
-    "problem_id": 8437,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['313', '144', '169', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8437.jpg"
-  },
-  {
-    "id": 8660,
-    "problem_id": 8438,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['313', '144', '169', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8438.jpg"
-  },
-  {
-    "id": 8661,
-    "problem_id": 8439,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['313', '144', '169', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8439.jpg"
-  },
-  {
-    "id": 8662,
-    "problem_id": 8440,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['313', '144', '169', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8440.jpg"
-  },
-  {
-    "id": 8663,
-    "problem_id": 8441,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8441.jpg"
-  },
-  {
-    "id": 8664,
-    "problem_id": 8442,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8442.jpg"
-  },
-  {
-    "id": 8665,
-    "problem_id": 8443,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8443.jpg"
-  },
-  {
-    "id": 8666,
-    "problem_id": 8444,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8444.jpg"
-  },
-  {
-    "id": 8667,
-    "problem_id": 8445,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8445.jpg"
-  },
-  {
-    "id": 8668,
-    "problem_id": 8446,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8446.jpg"
-  },
-  {
-    "id": 8669,
-    "problem_id": 8447,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['60', '30', '20', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8447.jpg"
-  },
-  {
-    "id": 8671,
-    "problem_id": 8448,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['27\u00b0', '33\u00b0', '54\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8448.jpg"
-  },
-  {
-    "id": 8672,
-    "problem_id": 8449,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['27\u00b0', '33\u00b0', '54\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8449.jpg"
-  },
-  {
-    "id": 8673,
-    "problem_id": 8450,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['27\u00b0', '33\u00b0', '54\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8450.jpg"
-  },
-  {
-    "id": 8674,
-    "problem_id": 8451,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['27\u00b0', '33\u00b0', '54\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8451.jpg"
-  },
-  {
-    "id": 8675,
-    "problem_id": 8452,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['27\u00b0', '33\u00b0', '54\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8452.jpg"
-  },
-  {
-    "id": 8676,
-    "problem_id": 8453,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8453.jpg"
-  },
-  {
-    "id": 8677,
-    "problem_id": 8454,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8454.jpg"
-  },
-  {
-    "id": 8678,
-    "problem_id": 8455,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8455.jpg"
-  },
-  {
-    "id": 8679,
-    "problem_id": 8456,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8456.jpg"
-  },
-  {
-    "id": 8680,
-    "problem_id": 8457,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8457.jpg"
-  },
-  {
-    "id": 8681,
-    "problem_id": 8458,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8458.jpg"
-  },
-  {
-    "id": 8682,
-    "problem_id": 8459,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['130\u00b0', '70\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8459.jpg"
-  },
-  {
-    "id": 8683,
-    "problem_id": 8460,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '\\\\frac{24}{5}', '3\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8460.jpg"
-  },
-  {
-    "id": 8684,
-    "problem_id": 8461,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '\\\\frac{24}{5}', '3\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8461.jpg"
-  },
-  {
-    "id": 8685,
-    "problem_id": 8462,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '\\\\frac{24}{5}', '3\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8462.jpg"
-  },
-  {
-    "id": 8686,
-    "problem_id": 8463,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '\\\\frac{24}{5}', '3\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8463.jpg"
-  },
-  {
-    "id": 8687,
-    "problem_id": 8464,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '\\\\frac{24}{5}', '3\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8464.jpg"
-  },
-  {
-    "id": 8688,
-    "problem_id": 8465,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8465.jpg"
-  },
-  {
-    "id": 8689,
-    "problem_id": 8466,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8466.jpg"
-  },
-  {
-    "id": 8690,
-    "problem_id": 8467,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8467.jpg"
-  },
-  {
-    "id": 8691,
-    "problem_id": 8468,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8468.jpg"
-  },
-  {
-    "id": 8692,
-    "problem_id": 8469,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['52\u00b0', '51\u00b0', '61\u00b0', '64.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8469.jpg"
-  },
-  {
-    "id": 8693,
-    "problem_id": 8470,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['52\u00b0', '51\u00b0', '61\u00b0', '64.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8470.jpg"
-  },
-  {
-    "id": 8694,
-    "problem_id": 8471,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['52\u00b0', '51\u00b0', '61\u00b0', '64.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8471.jpg"
-  },
-  {
-    "id": 8695,
-    "problem_id": 8472,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['52\u00b0', '51\u00b0', '61\u00b0', '64.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8472.jpg"
-  },
-  {
-    "id": 8696,
-    "problem_id": 8473,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['52\u00b0', '51\u00b0', '61\u00b0', '64.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8473.jpg"
-  },
-  {
-    "id": 8697,
-    "problem_id": 8474,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['52\u00b0', '51\u00b0', '61\u00b0', '64.5\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8474.jpg"
-  },
-  {
-    "id": 8698,
-    "problem_id": 8475,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14', '15', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8475.jpg"
-  },
-  {
-    "id": 8699,
-    "problem_id": 8476,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14', '15', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8476.jpg"
-  },
-  {
-    "id": 8700,
-    "problem_id": 8477,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14', '15', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8477.jpg"
-  },
-  {
-    "id": 8701,
-    "problem_id": 8478,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14', '15', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8478.jpg"
-  },
-  {
-    "id": 8702,
-    "problem_id": 8479,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14', '15', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8479.jpg"
-  },
-  {
-    "id": 8703,
-    "problem_id": 8480,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14', '15', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8480.jpg"
-  },
-  {
-    "id": 8704,
-    "problem_id": 8481,
-    "problem": "<image>In the figure, in the quadrilateral ABCD, BD is perpendicular to AD, AB = 10, AD = 6. Rectangle DEBF is constructed. The length of its diagonal EF is ().. A, B, C, D choices are ['8', '9', '10', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8481.jpg"
-  },
-  {
-    "id": 8705,
-    "problem_id": 8482,
-    "problem": "<image>In triangle ABC, cut off angle C along the dotted line in the figure. If angle 1 plus angle 2 equals 260 degrees, what is the degree measure of angle C?. A, B, C, D choices are ['100\u00b0', '90\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8482.jpg"
-  },
-  {
-    "id": 8706,
-    "problem_id": 8483,
-    "problem": "<image>In triangle ABC, cut off angle C along the dotted line in the figure. If angle 1 plus angle 2 equals 260 degrees, what is the degree measure of angle C?. A, B, C, D choices are ['100\u00b0', '90\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8483.jpg"
-  },
-  {
-    "id": 8707,
-    "problem_id": 8484,
-    "problem": "<image>In triangle ABC, cut off angle C along the dotted line in the figure. If angle 1 plus angle 2 equals 260 degrees, what is the degree measure of angle C?. A, B, C, D choices are ['100\u00b0', '90\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8484.jpg"
-  },
-  {
-    "id": 8708,
-    "problem_id": 8485,
-    "problem": "<image>As shown in the diagram, after folding a rectangular piece of paper ABCD along EF, points C and D fall on the positions of C and D respectively. EC intersects AD at point G. Given that \u2220EFG = 57\u00b0, what is the measure of \u2220BEG?. A, B, C, D choices are ['57\u00b0', '114\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8485.jpg"
-  },
-  {
-    "id": 8709,
-    "problem_id": 8486,
-    "problem": "<image>As shown in the diagram, after folding a rectangular piece of paper ABCD along EF, points C and D fall on the positions of C and D respectively. EC intersects AD at point G. Given that \u2220EFG = 57\u00b0, what is the measure of \u2220BEG?. A, B, C, D choices are ['57\u00b0', '114\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8486.jpg"
-  },
-  {
-    "id": 8710,
-    "problem_id": 8487,
-    "problem": "<image>In right triangle ABC as shown, where \u2220BAC=90\u00b0, D, E, and F are the midpoints of the three sides, and DE=4cm, what is the length of AF?. A, B, C, D choices are ['2cm', '3cm', '4cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8487.jpg"
-  },
-  {
-    "id": 8711,
-    "problem_id": 8488,
-    "problem": "<image>In right triangle ABC as shown, where \u2220BAC=90\u00b0, D, E, and F are the midpoints of the three sides, and DE=4cm, what is the length of AF?. A, B, C, D choices are ['2cm', '3cm', '4cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8488.jpg"
-  },
-  {
-    "id": 8712,
-    "problem_id": 8489,
-    "problem": "<image>In right triangle ABC as shown, where \u2220BAC=90\u00b0, D, E, and F are the midpoints of the three sides, and DE=4cm, what is the length of AF?. A, B, C, D choices are ['2cm', '3cm', '4cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8489.jpg"
-  },
-  {
-    "id": 8713,
-    "problem_id": 8490,
-    "problem": "<image>In right triangle ABC as shown, where \u2220BAC=90\u00b0, D, E, and F are the midpoints of the three sides, and DE=4cm, what is the length of AF?. A, B, C, D choices are ['2cm', '3cm', '4cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8490.jpg"
-  },
-  {
-    "id": 8714,
-    "problem_id": 8491,
-    "problem": "<image>In right triangle ABC as shown, where \u2220BAC=90\u00b0, D, E, and F are the midpoints of the three sides, and DE=4cm, what is the length of AF?. A, B, C, D choices are ['2cm', '3cm', '4cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8491.jpg"
-  },
-  {
-    "id": 8715,
-    "problem_id": 8492,
-    "problem": "<image>As shown in the figure, l1 is parallel to l2, and l3 is parallel to l4. If \u22201 = 68\u00b0, then what is the degree measure of \u22202? (). A, B, C, D choices are ['68\u00b0', '132\u00b0', '122\u00b0', '112\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8492.jpg"
-  },
-  {
-    "id": 8716,
-    "problem_id": 8493,
-    "problem": "<image>As shown in the figure, l1 is parallel to l2, and l3 is parallel to l4. If \u22201 = 68\u00b0, then what is the degree measure of \u22202? (). A, B, C, D choices are ['68\u00b0', '132\u00b0', '122\u00b0', '112\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8493.jpg"
-  },
-  {
-    "id": 8718,
-    "problem_id": 8494,
-    "problem": "<image>As shown in the figure, l1 is parallel to l2, and l3 is parallel to l4. If \u22201 = 68\u00b0, then what is the degree measure of \u22202? (). A, B, C, D choices are ['68\u00b0', '132\u00b0', '122\u00b0', '112\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8494.jpg"
-  },
-  {
-    "id": 8719,
-    "problem_id": 8495,
-    "problem": "<image>As shown in the figure, l1 is parallel to l2, and l3 is parallel to l4. If \u22201 = 68\u00b0, then what is the degree measure of \u22202? (). A, B, C, D choices are ['68\u00b0', '132\u00b0', '122\u00b0', '112\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8495.jpg"
-  },
-  {
-    "id": 8720,
-    "problem_id": 8496,
-    "problem": "<image>In the figure, in quadrilateral ABCD, \u2220B + \u2220D = 140\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['140\u00b0', '120\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8496.jpg"
-  },
-  {
-    "id": 8721,
-    "problem_id": 8497,
-    "problem": "<image>As shown in the figure, line AB intersects with line CD at point O. Line OE bisects \u2220AOC and \u2220BOE = 140\u00b0. What is the measure of \u2220BOC?. A, B, C, D choices are ['140\u00b0', '100\u00b0', '80\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8497.jpg"
-  },
-  {
-    "id": 8722,
-    "problem_id": 8498,
-    "problem": "<image>As shown in the figure, line AB intersects with line CD at point O. Line OE bisects \u2220AOC and \u2220BOE = 140\u00b0. What is the measure of \u2220BOC?. A, B, C, D choices are ['140\u00b0', '100\u00b0', '80\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8498.jpg"
-  },
-  {
-    "id": 8723,
-    "problem_id": 8499,
-    "problem": "<image>As shown in the figure, line AB intersects with line CD at point O. Line OE bisects \u2220AOC and \u2220BOE = 140\u00b0. What is the measure of \u2220BOC?. A, B, C, D choices are ['140\u00b0', '100\u00b0', '80\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8499.jpg"
-  },
-  {
-    "id": 8724,
-    "problem_id": 8500,
-    "problem": "<image>In triangle ABC, it is known that points D, E, and F are the midpoints of sides BC, AD, and CE, respectively, and the shaded area of S is 3cm2. What is the area of triangle ABC?. A, B, C, D choices are ['9', '12', '15', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8500.jpg"
-  },
-  {
-    "id": 8725,
-    "problem_id": 8501,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8501.jpg"
-  },
-  {
-    "id": 8726,
-    "problem_id": 8502,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8502.jpg"
-  },
-  {
-    "id": 8727,
-    "problem_id": 8503,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8503.jpg"
-  },
-  {
-    "id": 8728,
-    "problem_id": 8504,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8504.jpg"
-  },
-  {
-    "id": 8729,
-    "problem_id": 8505,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8505.jpg"
-  },
-  {
-    "id": 8730,
-    "problem_id": 8506,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8506.jpg"
-  },
-  {
-    "id": 8731,
-    "problem_id": 8507,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8507.jpg"
-  },
-  {
-    "id": 8732,
-    "problem_id": 8508,
-    "problem": "<image>In the regular pentagon ABCDE shown in the figure, if AD is connected, what is the degree measure of \u2220DAE? (). A, B, C, D choices are ['46\u00b0', '56\u00b0', '36\u00b0', '26\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8508.jpg"
-  },
-  {
-    "id": 8733,
-    "problem_id": 8509,
-    "problem": "<image>In the regular pentagon ABCDE shown in the figure, if AD is connected, what is the degree measure of \u2220DAE? (). A, B, C, D choices are ['46\u00b0', '56\u00b0', '36\u00b0', '26\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8509.jpg"
-  },
-  {
-    "id": 8734,
-    "problem_id": 8510,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8510.jpg"
-  },
-  {
-    "id": 8735,
-    "problem_id": 8511,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8511.jpg"
-  },
-  {
-    "id": 8736,
-    "problem_id": 8512,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8512.jpg"
-  },
-  {
-    "id": 8737,
-    "problem_id": 8513,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8513.jpg"
-  },
-  {
-    "id": 8738,
-    "problem_id": 8514,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8514.jpg"
-  },
-  {
-    "id": 8739,
-    "problem_id": 8515,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8515.jpg"
-  },
-  {
-    "id": 8740,
-    "problem_id": 8516,
-    "problem": "<image>In right triangle ABC shown in the diagram, angle BCA is 90 degrees. In triangle PAB, the height on side AB is equal to the length of AB. In triangle QBC, the height on side BC is equal to the length of BC. In triangle HAC, the height on side AC is equal to the length of AC. The areas of triangles PAB and QBC are 10 and 8, respectively. What is the area of triangle ACH?. A, B, C, D choices are ['2', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8516.jpg"
-  },
-  {
-    "id": 8741,
-    "problem_id": 8517,
-    "problem": "<image>As shown in the figure, the perimeter of ABCD is 22cm. Diagonals AC and BD intersect at point O. A line perpendicular to AC passes through point O and intersects side AD at point E. The perimeter of \u25b3CDE is () cm.. A, B, C, D choices are ['8cm', '9cm', '10cm', '11cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8517.jpg"
-  },
-  {
-    "id": 8742,
-    "problem_id": 8518,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8518.jpg"
-  },
-  {
-    "id": 8743,
-    "problem_id": 8519,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8519.jpg"
-  },
-  {
-    "id": 8744,
-    "problem_id": 8520,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8520.jpg"
-  },
-  {
-    "id": 8745,
-    "problem_id": 8521,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8521.jpg"
-  },
-  {
-    "id": 8746,
-    "problem_id": 8522,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8522.jpg"
-  },
-  {
-    "id": 8747,
-    "problem_id": 8523,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8523.jpg"
-  },
-  {
-    "id": 8748,
-    "problem_id": 8524,
-    "problem": "<image>As shown in the diagram, if \u22201 = 75\u00b0, \u22202 = 75\u00b0, \u22203 = 112\u00b0, then \u22204 = ().. A, B, C, D choices are ['34\u00b0', '44\u00b0', '68\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8524.jpg"
-  },
-  {
-    "id": 8749,
-    "problem_id": 8525,
-    "problem": "<image>In triangle ABC as shown, AB=AC, AD is the altitude, E is the midpoint of AB, and the area of triangle ABC is 8. What is the area of triangle ADE?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8525.jpg"
-  },
-  {
-    "id": 8750,
-    "problem_id": 8526,
-    "problem": "<image>In triangle ABC as shown, AB=AC, AD is the altitude, E is the midpoint of AB, and the area of triangle ABC is 8. What is the area of triangle ADE?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8526.jpg"
-  },
-  {
-    "id": 8751,
-    "problem_id": 8527,
-    "problem": "<image>In triangle ABC as shown, AB=AC, AD is the altitude, E is the midpoint of AB, and the area of triangle ABC is 8. What is the area of triangle ADE?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8527.jpg"
-  },
-  {
-    "id": 8752,
-    "problem_id": 8528,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8528.jpg"
-  },
-  {
-    "id": 8753,
-    "problem_id": 8529,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8529.jpg"
-  },
-  {
-    "id": 8754,
-    "problem_id": 8530,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8530.jpg"
-  },
-  {
-    "id": 8755,
-    "problem_id": 8531,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8531.jpg"
-  },
-  {
-    "id": 8756,
-    "problem_id": 8532,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8532.jpg"
-  },
-  {
-    "id": 8757,
-    "problem_id": 8533,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8533.jpg"
-  },
-  {
-    "id": 8758,
-    "problem_id": 8534,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8534.jpg"
-  },
-  {
-    "id": 8759,
-    "problem_id": 8535,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8535.jpg"
-  },
-  {
-    "id": 8760,
-    "problem_id": 8536,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8536.jpg"
-  },
-  {
-    "id": 8761,
-    "problem_id": 8537,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8537.jpg"
-  },
-  {
-    "id": 8762,
-    "problem_id": 8538,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8538.jpg"
-  },
-  {
-    "id": 8763,
-    "problem_id": 8539,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['23\u00b0', '46\u00b0', '67\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8539.jpg"
-  },
-  {
-    "id": 8764,
-    "problem_id": 8540,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['23\u00b0', '46\u00b0', '67\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8540.jpg"
-  },
-  {
-    "id": 8765,
-    "problem_id": 8541,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['23\u00b0', '46\u00b0', '67\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8541.jpg"
-  },
-  {
-    "id": 8766,
-    "problem_id": 8542,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['23\u00b0', '46\u00b0', '67\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8542.jpg"
-  },
-  {
-    "id": 8767,
-    "problem_id": 8543,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['23\u00b0', '46\u00b0', '67\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8543.jpg"
-  },
-  {
-    "id": 8768,
-    "problem_id": 8544,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['23\u00b0', '46\u00b0', '67\u00b0', '0\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8544.jpg"
-  },
-  {
-    "id": 8769,
-    "problem_id": 8545,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '6.5', '11', '5.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8545.jpg"
-  },
-  {
-    "id": 8770,
-    "problem_id": 8546,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '6.5', '11', '5.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8546.jpg"
-  },
-  {
-    "id": 8771,
-    "problem_id": 8547,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '6.5', '11', '5.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8547.jpg"
-  },
-  {
-    "id": 8772,
-    "problem_id": 8548,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['21', '24', '27', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8548.jpg"
-  },
-  {
-    "id": 8773,
-    "problem_id": 8549,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['21', '24', '27', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8549.jpg"
-  },
-  {
-    "id": 8774,
-    "problem_id": 8550,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['21', '24', '27', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8550.jpg"
-  },
-  {
-    "id": 8775,
-    "problem_id": 8551,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '35\u00b0', '18\u00b0', '17\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8551.jpg"
-  },
-  {
-    "id": 8776,
-    "problem_id": 8552,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '35\u00b0', '18\u00b0', '17\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8552.jpg"
-  },
-  {
-    "id": 8777,
-    "problem_id": 8553,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '35\u00b0', '18\u00b0', '17\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8553.jpg"
-  },
-  {
-    "id": 8778,
-    "problem_id": 8554,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '82\u00b0', '84\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8554.jpg"
-  },
-  {
-    "id": 8779,
-    "problem_id": 8555,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '82\u00b0', '84\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8555.jpg"
-  },
-  {
-    "id": 8780,
-    "problem_id": 8556,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '82\u00b0', '84\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8556.jpg"
-  },
-  {
-    "id": 8781,
-    "problem_id": 8557,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '82\u00b0', '84\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8557.jpg"
-  },
-  {
-    "id": 8782,
-    "problem_id": 8558,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '82\u00b0', '84\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8558.jpg"
-  },
-  {
-    "id": 8783,
-    "problem_id": 8559,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8559.jpg"
-  },
-  {
-    "id": 8784,
-    "problem_id": 8560,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8560.jpg"
-  },
-  {
-    "id": 8785,
-    "problem_id": 8561,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8561.jpg"
-  },
-  {
-    "id": 8786,
-    "problem_id": 8562,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8562.jpg"
-  },
-  {
-    "id": 8787,
-    "problem_id": 8563,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8563.jpg"
-  },
-  {
-    "id": 8788,
-    "problem_id": 8564,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8564.jpg"
-  },
-  {
-    "id": 8789,
-    "problem_id": 8565,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8565.jpg"
-  },
-  {
-    "id": 8790,
-    "problem_id": 8566,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8566.jpg"
-  },
-  {
-    "id": 8791,
-    "problem_id": 8567,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8567.jpg"
-  },
-  {
-    "id": 8792,
-    "problem_id": 8568,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8568.jpg"
-  },
-  {
-    "id": 8793,
-    "problem_id": 8569,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8569.jpg"
-  },
-  {
-    "id": 8794,
-    "problem_id": 8570,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8570.jpg"
-  },
-  {
-    "id": 8795,
-    "problem_id": 8571,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14\u00b0', '28\u00b0', '42\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8571.jpg"
-  },
-  {
-    "id": 8796,
-    "problem_id": 8572,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14\u00b0', '28\u00b0', '42\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8572.jpg"
-  },
-  {
-    "id": 8797,
-    "problem_id": 8573,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14\u00b0', '28\u00b0', '42\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8573.jpg"
-  },
-  {
-    "id": 8798,
-    "problem_id": 8574,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14\u00b0', '28\u00b0', '42\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8574.jpg"
-  },
-  {
-    "id": 8799,
-    "problem_id": 8575,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14\u00b0', '28\u00b0', '42\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8575.jpg"
-  },
-  {
-    "id": 8800,
-    "problem_id": 8576,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14\u00b0', '28\u00b0', '42\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8576.jpg"
-  },
-  {
-    "id": 8801,
-    "problem_id": 8577,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14.5', '15.5', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8577.jpg"
-  },
-  {
-    "id": 8802,
-    "problem_id": 8578,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14.5', '15.5', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8578.jpg"
-  },
-  {
-    "id": 8803,
-    "problem_id": 8579,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14.5', '15.5', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8579.jpg"
-  },
-  {
-    "id": 8804,
-    "problem_id": 8580,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['13', '14.5', '15.5', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8580.jpg"
-  },
-  {
-    "id": 8806,
-    "problem_id": 8581,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, EF intersects AB and CD at points G and H respectively, and \u2220AGE=100\u00b0. What is the degree measure of \u2220DHF?. A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8581.jpg"
-  },
-  {
-    "id": 8807,
-    "problem_id": 8582,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, EF intersects AB and CD at points G and H respectively, and \u2220AGE=100\u00b0. What is the degree measure of \u2220DHF?. A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8582.jpg"
-  },
-  {
-    "id": 8808,
-    "problem_id": 8583,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, EF intersects AB and CD at points G and H respectively, and \u2220AGE=100\u00b0. What is the degree measure of \u2220DHF?. A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8583.jpg"
-  },
-  {
-    "id": 8809,
-    "problem_id": 8584,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8584.jpg"
-  },
-  {
-    "id": 8810,
-    "problem_id": 8585,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8585.jpg"
-  },
-  {
-    "id": 8811,
-    "problem_id": 8586,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8586.jpg"
-  },
-  {
-    "id": 8812,
-    "problem_id": 8587,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8587.jpg"
-  },
-  {
-    "id": 8813,
-    "problem_id": 8588,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8588.jpg"
-  },
-  {
-    "id": 8814,
-    "problem_id": 8589,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8589.jpg"
-  },
-  {
-    "id": 8815,
-    "problem_id": 8590,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8590.jpg"
-  },
-  {
-    "id": 8816,
-    "problem_id": 8591,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8591.jpg"
-  },
-  {
-    "id": 8817,
-    "problem_id": 8592,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8592.jpg"
-  },
-  {
-    "id": 8818,
-    "problem_id": 8593,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8593.jpg"
-  },
-  {
-    "id": 8819,
-    "problem_id": 8594,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8594.jpg"
-  },
-  {
-    "id": 8820,
-    "problem_id": 8595,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8595.jpg"
-  },
-  {
-    "id": 8821,
-    "problem_id": 8596,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8596.jpg"
-  },
-  {
-    "id": 8822,
-    "problem_id": 8597,
-    "problem": "<image>As shown in the diagram, the two diagonals of diamond-shaped ABCD intersect at O. If AC = 8 and BD = 6, what is the perimeter of diamond-shaped ABCD?. A, B, C, D choices are ['32', '24', '40', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8597.jpg"
-  },
-  {
-    "id": 8823,
-    "problem_id": 8598,
-    "problem": "<image>As shown in the figure, a tangent line is drawn from point P to circle O with a radius of 1. The points of tangency are A and B. If \u2220APB = 60\u00b0, then the length of PA is ().. A, B, C, D choices are ['\u221a{2}', '2', '\u221a{3}', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8598.jpg"
-  },
-  {
-    "id": 8824,
-    "problem_id": 8599,
-    "problem": "<image>As shown in the figure, a tangent line is drawn from point P to circle O with a radius of 1. The points of tangency are A and B. If \u2220APB = 60\u00b0, then the length of PA is ().. A, B, C, D choices are ['\u221a{2}', '2', '\u221a{3}', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8599.jpg"
-  },
-  {
-    "id": 8825,
-    "problem_id": 8600,
-    "problem": "<image>In triangle ABC, with \u2220ABC = 60\u00b0, point D is on side AC and the distance from point D to sides AB and BC are both 6. If we connect BD, what is the length of BD?. A, B, C, D choices are ['12', '14', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8600.jpg"
-  },
-  {
-    "id": 8826,
-    "problem_id": 8601,
-    "problem": "<image>In triangle ABC, with \u2220ABC = 60\u00b0, point D is on side AC and the distance from point D to sides AB and BC are both 6. If we connect BD, what is the length of BD?. A, B, C, D choices are ['12', '14', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8601.jpg"
-  },
-  {
-    "id": 8827,
-    "problem_id": 8602,
-    "problem": "<image>In the figure, in ABCD, AC = 3, and the perimeter of triangle ACD is 10. What is the perimeter of ABCD?. A, B, C, D choices are ['10', '12', '13', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8602.jpg"
-  },
-  {
-    "id": 8828,
-    "problem_id": 8603,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8603.jpg"
-  },
-  {
-    "id": 8829,
-    "problem_id": 8604,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8604.jpg"
-  },
-  {
-    "id": 8830,
-    "problem_id": 8605,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8605.jpg"
-  },
-  {
-    "id": 8831,
-    "problem_id": 8606,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8606.jpg"
-  },
-  {
-    "id": 8832,
-    "problem_id": 8607,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8607.jpg"
-  },
-  {
-    "id": 8833,
-    "problem_id": 8608,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8608.jpg"
-  },
-  {
-    "id": 8834,
-    "problem_id": 8609,
-    "problem": "<image>In the diamond ABCD shown in the figure, diagonals AC and BD intersect at point O. If the area of diamond ABCD is 24 and BD = 6, then what is the perimeter of diamond ABCD?. A, B, C, D choices are ['5', '10', '20', '40'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8609.jpg"
-  },
-  {
-    "id": 8835,
-    "problem_id": 8610,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8610.jpg"
-  },
-  {
-    "id": 8836,
-    "problem_id": 8611,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8611.jpg"
-  },
-  {
-    "id": 8837,
-    "problem_id": 8612,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8612.jpg"
-  },
-  {
-    "id": 8838,
-    "problem_id": 8613,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8613.jpg"
-  },
-  {
-    "id": 8839,
-    "problem_id": 8614,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8614.jpg"
-  },
-  {
-    "id": 8840,
-    "problem_id": 8615,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8615.jpg"
-  },
-  {
-    "id": 8841,
-    "problem_id": 8616,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O. It is known that \u2220AOD = 140\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '70\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8616.jpg"
-  },
-  {
-    "id": 8842,
-    "problem_id": 8617,
-    "problem": "<image>In triangle ABC, AB = AC, AD is perpendicular to BC at point D. If angle BAC is 120\u00b0 and AD = 2\u221a{3}, what is the area of triangle ABC?. A, B, C, D choices are ['12', '24', '12\u221a{3}', '24\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8617.jpg"
-  },
-  {
-    "id": 8843,
-    "problem_id": 8618,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8618.jpg"
-  },
-  {
-    "id": 8844,
-    "problem_id": 8619,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8619.jpg"
-  },
-  {
-    "id": 8845,
-    "problem_id": 8620,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8620.jpg"
-  },
-  {
-    "id": 8846,
-    "problem_id": 8621,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8621.jpg"
-  },
-  {
-    "id": 8847,
-    "problem_id": 8622,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8622.jpg"
-  },
-  {
-    "id": 8848,
-    "problem_id": 8623,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8623.jpg"
-  },
-  {
-    "id": 8849,
-    "problem_id": 8624,
-    "problem": "<image>As shown in the figure, if the circumference of the base of a cylinder is 50cm and its height is 120cm, what is the minimum length of a thread that winds around the cylinder from point A at the bottom to point B at the top?. A, B, C, D choices are ['170cm', '70cm', '145cm', '130cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8624.jpg"
-  },
-  {
-    "id": 8850,
-    "problem_id": 8625,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If \u2220D = 110\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['20\u00b0', '35\u00b0', '55\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8625.jpg"
-  },
-  {
-    "id": 8851,
-    "problem_id": 8626,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If \u2220D = 110\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['20\u00b0', '35\u00b0', '55\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8626.jpg"
-  },
-  {
-    "id": 8852,
-    "problem_id": 8627,
-    "problem": "<image>In the figure, if \u2220A + \u2220C = 110\u00b0 in ABCD, then what is the degree measure of \u2220B? (). A, B, C, D choices are ['70\u00b0', '105\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8627.jpg"
-  },
-  {
-    "id": 8853,
-    "problem_id": 8628,
-    "problem": "<image>In the figure, if \u2220A + \u2220C = 110\u00b0 in ABCD, then what is the degree measure of \u2220B? (). A, B, C, D choices are ['70\u00b0', '105\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8628.jpg"
-  },
-  {
-    "id": 8854,
-    "problem_id": 8629,
-    "problem": "<image>In the figure, if \u2220A + \u2220C = 110\u00b0 in ABCD, then what is the degree measure of \u2220B? (). A, B, C, D choices are ['70\u00b0', '105\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8629.jpg"
-  },
-  {
-    "id": 8855,
-    "problem_id": 8630,
-    "problem": "<image>In the figure, if \u2220A + \u2220C = 110\u00b0 in ABCD, then what is the degree measure of \u2220B? (). A, B, C, D choices are ['70\u00b0', '105\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8630.jpg"
-  },
-  {
-    "id": 8856,
-    "problem_id": 8631,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8631.jpg"
-  },
-  {
-    "id": 8857,
-    "problem_id": 8632,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8632.jpg"
-  },
-  {
-    "id": 8859,
-    "problem_id": 8633,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8633.jpg"
-  },
-  {
-    "id": 8860,
-    "problem_id": 8634,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8634.jpg"
-  },
-  {
-    "id": 8861,
-    "problem_id": 8635,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8635.jpg"
-  },
-  {
-    "id": 8862,
-    "problem_id": 8636,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8636.jpg"
-  },
-  {
-    "id": 8863,
-    "problem_id": 8637,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8637.jpg"
-  },
-  {
-    "id": 8864,
-    "problem_id": 8638,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8638.jpg"
-  },
-  {
-    "id": 8865,
-    "problem_id": 8639,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '10', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8639.jpg"
-  },
-  {
-    "id": 8866,
-    "problem_id": 8640,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, \u2220A = 100\u00b0, \u2220BCD = 50\u00b0, what is the degree of \u2220ACB? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8640.jpg"
-  },
-  {
-    "id": 8867,
-    "problem_id": 8641,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '70\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8641.jpg"
-  },
-  {
-    "id": 8869,
-    "problem_id": 8642,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '70\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8642.jpg"
-  },
-  {
-    "id": 8870,
-    "problem_id": 8643,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '70\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8643.jpg"
-  },
-  {
-    "id": 8871,
-    "problem_id": 8644,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '70\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8644.jpg"
-  },
-  {
-    "id": 8872,
-    "problem_id": 8645,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['105\u00b0', '120\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8645.jpg"
-  },
-  {
-    "id": 8873,
-    "problem_id": 8646,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['105\u00b0', '120\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8646.jpg"
-  },
-  {
-    "id": 8874,
-    "problem_id": 8647,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['105\u00b0', '120\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8647.jpg"
-  },
-  {
-    "id": 8875,
-    "problem_id": 8648,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['105\u00b0', '120\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8648.jpg"
-  },
-  {
-    "id": 8876,
-    "problem_id": 8649,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['105\u00b0', '120\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8649.jpg"
-  },
-  {
-    "id": 8877,
-    "problem_id": 8650,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['105\u00b0', '120\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8650.jpg"
-  },
-  {
-    "id": 8878,
-    "problem_id": 8651,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, \u2220B = 75\u00b0, \u2220D = 35\u00b0, then the degree of \u2220E is (). A, B, C, D choices are ['75\u00b0', '35\u00b0', '110\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8651.jpg"
-  },
-  {
-    "id": 8879,
-    "problem_id": 8652,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, \u2220B = 75\u00b0, \u2220D = 35\u00b0, then the degree of \u2220E is (). A, B, C, D choices are ['75\u00b0', '35\u00b0', '110\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8652.jpg"
-  },
-  {
-    "id": 8880,
-    "problem_id": 8653,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, \u2220B = 75\u00b0, \u2220D = 35\u00b0, then the degree of \u2220E is (). A, B, C, D choices are ['75\u00b0', '35\u00b0', '110\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8653.jpg"
-  },
-  {
-    "id": 8881,
-    "problem_id": 8654,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, \u2220B = 75\u00b0, \u2220D = 35\u00b0, then the degree of \u2220E is (). A, B, C, D choices are ['75\u00b0', '35\u00b0', '110\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8654.jpg"
-  },
-  {
-    "id": 8882,
-    "problem_id": 8655,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220DAB\uff1d90\u00b0 and \u2220DCB\uff1d90\u00b0. E and F are the midpoints of BD and AC, respectively. If AC\uff1d6 and BD\uff1d10, then the length of EF is (). A, B, C, D choices are ['3', '4', '5', '\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8655.jpg"
-  },
-  {
-    "id": 8883,
-    "problem_id": 8656,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220DAB\uff1d90\u00b0 and \u2220DCB\uff1d90\u00b0. E and F are the midpoints of BD and AC, respectively. If AC\uff1d6 and BD\uff1d10, then the length of EF is (). A, B, C, D choices are ['3', '4', '5', '\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8656.jpg"
-  },
-  {
-    "id": 8884,
-    "problem_id": 8657,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['19\u00b0', '21\u00b0', '23\u00b0', '26\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8657.jpg"
-  },
-  {
-    "id": 8885,
-    "problem_id": 8658,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['19\u00b0', '21\u00b0', '23\u00b0', '26\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8658.jpg"
-  },
-  {
-    "id": 8886,
-    "problem_id": 8659,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['19\u00b0', '21\u00b0', '23\u00b0', '26\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8659.jpg"
-  },
-  {
-    "id": 8888,
-    "problem_id": 8660,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['19\u00b0', '21\u00b0', '23\u00b0', '26\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8660.jpg"
-  },
-  {
-    "id": 8889,
-    "problem_id": 8661,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8661.jpg"
-  },
-  {
-    "id": 8890,
-    "problem_id": 8662,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8662.jpg"
-  },
-  {
-    "id": 8891,
-    "problem_id": 8663,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8663.jpg"
-  },
-  {
-    "id": 8892,
-    "problem_id": 8664,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8664.jpg"
-  },
-  {
-    "id": 8893,
-    "problem_id": 8665,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8665.jpg"
-  },
-  {
-    "id": 8894,
-    "problem_id": 8666,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8666.jpg"
-  },
-  {
-    "id": 8895,
-    "problem_id": 8667,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8667.jpg"
-  },
-  {
-    "id": 8896,
-    "problem_id": 8668,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8668.jpg"
-  },
-  {
-    "id": 8897,
-    "problem_id": 8669,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8669.jpg"
-  },
-  {
-    "id": 8898,
-    "problem_id": 8670,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8670.jpg"
-  },
-  {
-    "id": 8899,
-    "problem_id": 8671,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8671.jpg"
-  },
-  {
-    "id": 8900,
-    "problem_id": 8672,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['152\u00b0', '124\u00b0', '122\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8672.jpg"
-  },
-  {
-    "id": 8901,
-    "problem_id": 8673,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '8', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8673.jpg"
-  },
-  {
-    "id": 8902,
-    "problem_id": 8674,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '8', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8674.jpg"
-  },
-  {
-    "id": 8903,
-    "problem_id": 8675,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '8', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8675.jpg"
-  },
-  {
-    "id": 8904,
-    "problem_id": 8676,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '8', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8676.jpg"
-  },
-  {
-    "id": 8905,
-    "problem_id": 8677,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '8', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8677.jpg"
-  },
-  {
-    "id": 8906,
-    "problem_id": 8678,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '8', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8678.jpg"
-  },
-  {
-    "id": 8907,
-    "problem_id": 8679,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '6', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8679.jpg"
-  },
-  {
-    "id": 8908,
-    "problem_id": 8680,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '6', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8680.jpg"
-  },
-  {
-    "id": 8909,
-    "problem_id": 8681,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '6', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8681.jpg"
-  },
-  {
-    "id": 8910,
-    "problem_id": 8682,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '6', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8682.jpg"
-  },
-  {
-    "id": 8911,
-    "problem_id": 8683,
-    "problem": "<image>In the square ABCD shown in the figure, BD = 2, \u2220DCE is an external angle of the square ABCD. P is any point on the angle bisector CF of \u2220DCE. The area of triangle PBD is equal to ().. A, B, C, D choices are ['1', '\u221a{2}', '2', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8683.jpg"
-  },
-  {
-    "id": 8912,
-    "problem_id": 8684,
-    "problem": "<image>As shown in the figure, the diagonals of rectangle ABCD intersect at point O. OF is perpendicular to AB and BE is perpendicular to AC. E is the midpoint of OC and OF = 4. What is the length of BD?. A, B, C, D choices are ['16', '8', '4\u221a{3}', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8684.jpg"
-  },
-  {
-    "id": 8913,
-    "problem_id": 8685,
-    "problem": "<image>In triangle ABC shown in the figure, \u2220ACB = 90\u00b0, CD is the median of triangle ABC. If \u2220DCB = 35\u00b0, then what is the degree measure of \u2220A?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8685.jpg"
-  },
-  {
-    "id": 8914,
-    "problem_id": 8686,
-    "problem": "<image>In triangle ABC shown in the figure, AB=6, AC=10, D, E, and F are the midpoints of AB, BC, and AC, respectively. The perimeter of quadrilateral ADEF is ().. A, B, C, D choices are ['16', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8686.jpg"
-  },
-  {
-    "id": 8915,
-    "problem_id": 8687,
-    "problem": "<image>In triangle ABC shown in the figure, AB=6, AC=10, D, E, and F are the midpoints of AB, BC, and AC, respectively. The perimeter of quadrilateral ADEF is ().. A, B, C, D choices are ['16', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8687.jpg"
-  },
-  {
-    "id": 8916,
-    "problem_id": 8688,
-    "problem": "<image>In triangle ABC, the angle bisectors of \u2220ABC and \u2220ACB intersect at point O. If \u2220A = 70\u00b0, what is the degree measure of \u2220BOC?. A, B, C, D choices are ['125\u00b0', '130\u00b0', '135\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8688.jpg"
-  },
-  {
-    "id": 8917,
-    "problem_id": 8689,
-    "problem": "<image>In triangle ABC, the angle bisectors of \u2220ABC and \u2220ACB intersect at point O. If \u2220A = 70\u00b0, what is the degree measure of \u2220BOC?. A, B, C, D choices are ['125\u00b0', '130\u00b0', '135\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8689.jpg"
-  },
-  {
-    "id": 8918,
-    "problem_id": 8690,
-    "problem": "<image>In triangle ABC, the angle bisectors of \u2220ABC and \u2220ACB intersect at point O. If \u2220A = 70\u00b0, what is the degree measure of \u2220BOC?. A, B, C, D choices are ['125\u00b0', '130\u00b0', '135\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8690.jpg"
-  },
-  {
-    "id": 8919,
-    "problem_id": 8691,
-    "problem": "<image>In triangle ABC, the angle bisectors of \u2220ABC and \u2220ACB intersect at point O. If \u2220A = 70\u00b0, what is the degree measure of \u2220BOC?. A, B, C, D choices are ['125\u00b0', '130\u00b0', '135\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8691.jpg"
-  },
-  {
-    "id": 8920,
-    "problem_id": 8692,
-    "problem": "<image>As shown in the figure, if the right angle vertex O of a triangular board is placed on one side CD of a straightedge and \u2220AOC = 37\u00b0, what is the degree of \u2220BOD? (). A, B, C, D choices are ['37\u00b0', '47\u00b0', '53\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8692.jpg"
-  },
-  {
-    "id": 8921,
-    "problem_id": 8693,
-    "problem": "<image>In diamond ABCD as shown in the figure, if \u2220A = 110\u00b0, then what is the degree measure of \u2220CBD? (). A, B, C, D choices are ['90\u00b0', '70\u00b0', '55\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8693.jpg"
-  },
-  {
-    "id": 8923,
-    "problem_id": 8694,
-    "problem": "<image>In diamond ABCD as shown in the figure, if \u2220A = 110\u00b0, then what is the degree measure of \u2220CBD? (). A, B, C, D choices are ['90\u00b0', '70\u00b0', '55\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8694.jpg"
-  },
-  {
-    "id": 8924,
-    "problem_id": 8695,
-    "problem": "<image>In diamond ABCD as shown in the figure, if \u2220A = 110\u00b0, then what is the degree measure of \u2220CBD? (). A, B, C, D choices are ['90\u00b0', '70\u00b0', '55\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8695.jpg"
-  },
-  {
-    "id": 8925,
-    "problem_id": 8696,
-    "problem": "<image>In diamond ABCD as shown in the figure, if \u2220A = 110\u00b0, then what is the degree measure of \u2220CBD? (). A, B, C, D choices are ['90\u00b0', '70\u00b0', '55\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8696.jpg"
-  },
-  {
-    "id": 8926,
-    "problem_id": 8697,
-    "problem": "<image>In diamond ABCD as shown in the figure, if \u2220A = 110\u00b0, then what is the degree measure of \u2220CBD? (). A, B, C, D choices are ['90\u00b0', '70\u00b0', '55\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8697.jpg"
-  },
-  {
-    "id": 8927,
-    "problem_id": 8698,
-    "problem": "<image>In diamond ABCD as shown in the figure, if \u2220A = 110\u00b0, then what is the degree measure of \u2220CBD? (). A, B, C, D choices are ['90\u00b0', '70\u00b0', '55\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8698.jpg"
-  },
-  {
-    "id": 8928,
-    "problem_id": 8699,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220A = 90\u00b0, \u2220C = 30\u00b0, the angle bisector of \u2220ABC intersects segment AC at point D. If CD = 8, what is the length of AD?. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8699.jpg"
-  },
-  {
-    "id": 8929,
-    "problem_id": 8700,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220A = 90\u00b0, \u2220C = 30\u00b0, the angle bisector of \u2220ABC intersects segment AC at point D. If CD = 8, what is the length of AD?. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8700.jpg"
-  },
-  {
-    "id": 8930,
-    "problem_id": 8701,
-    "problem": "<image>In diamond ABCD, diagonal AC intersects diagonal BD at point O, and OE is perpendicular to AB at point E. If \u2220ADC = 110\u00b0, then the size of \u2220AOE is (). A, B, C, D choices are ['20\u00b0', '35\u00b0', '55\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8701.jpg"
-  },
-  {
-    "id": 8931,
-    "problem_id": 8702,
-    "problem": "<image>In diamond ABCD, diagonal AC intersects diagonal BD at point O, and OE is perpendicular to AB at point E. If \u2220ADC = 110\u00b0, then the size of \u2220AOE is (). A, B, C, D choices are ['20\u00b0', '35\u00b0', '55\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8702.jpg"
-  },
-  {
-    "id": 8932,
-    "problem_id": 8703,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8703.jpg"
-  },
-  {
-    "id": 8933,
-    "problem_id": 8704,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8704.jpg"
-  },
-  {
-    "id": 8935,
-    "problem_id": 8705,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8705.jpg"
-  },
-  {
-    "id": 8936,
-    "problem_id": 8706,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8706.jpg"
-  },
-  {
-    "id": 8937,
-    "problem_id": 8707,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8707.jpg"
-  },
-  {
-    "id": 8938,
-    "problem_id": 8708,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40\u00b0', '60\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8708.jpg"
-  },
-  {
-    "id": 8939,
-    "problem_id": 8709,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1', '\u221a{2}', '\u221a{3}', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8709.jpg"
-  },
-  {
-    "id": 8940,
-    "problem_id": 8710,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1cm', '2cm', '3cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8710.jpg"
-  },
-  {
-    "id": 8941,
-    "problem_id": 8711,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1cm', '2cm', '3cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{32 \\text{ cm}^2} \\]\n\n**Problem 30:**\n\nA cube has a surface area of 96 cm\u00b2. Find the length of one edge.\n\n Choices: A) 1 cm B) 2 cm C) 3 cm D) 4 cm\n\n**Solution:**\n\nA cube has six</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8711.jpg"
-  },
-  {
-    "id": 8942,
-    "problem_id": 8712,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1cm', '2cm', '3cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8712.jpg"
-  },
-  {
-    "id": 8943,
-    "problem_id": 8713,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8713.jpg"
-  },
-  {
-    "id": 8944,
-    "problem_id": 8714,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8714.jpg"
-  },
-  {
-    "id": 8945,
-    "problem_id": 8715,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8715.jpg"
-  },
-  {
-    "id": 8946,
-    "problem_id": 8716,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8716.jpg"
-  },
-  {
-    "id": 8948,
-    "problem_id": 8717,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8717.jpg"
-  },
-  {
-    "id": 8949,
-    "problem_id": 8718,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8718.jpg"
-  },
-  {
-    "id": 8950,
-    "problem_id": 8719,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8719.jpg"
-  },
-  {
-    "id": 8951,
-    "problem_id": 8720,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8720.jpg"
-  },
-  {
-    "id": 8952,
-    "problem_id": 8721,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8721.jpg"
-  },
-  {
-    "id": 8953,
-    "problem_id": 8722,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8722.jpg"
-  },
-  {
-    "id": 8954,
-    "problem_id": 8723,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8723.jpg"
-  },
-  {
-    "id": 8955,
-    "problem_id": 8724,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8724.jpg"
-  },
-  {
-    "id": 8956,
-    "problem_id": 8725,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8725.jpg"
-  },
-  {
-    "id": 8957,
-    "problem_id": 8726,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8726.jpg"
-  },
-  {
-    "id": 8958,
-    "problem_id": 8727,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['140\u00b0', '125\u00b0', '110\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8727.jpg"
-  },
-  {
-    "id": 8959,
-    "problem_id": 8728,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\\\\frac{8}{3}', '1', '2', '\\\\frac{7}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8728.jpg"
-  },
-  {
-    "id": 8960,
-    "problem_id": 8729,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\\\\frac{8}{3}', '1', '2', '\\\\frac{7}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8729.jpg"
-  },
-  {
-    "id": 8961,
-    "problem_id": 8730,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\\\\frac{8}{3}', '1', '2', '\\\\frac{7}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8730.jpg"
-  },
-  {
-    "id": 8962,
-    "problem_id": 8731,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\\\\frac{8}{3}', '1', '2', '\\\\frac{7}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8731.jpg"
-  },
-  {
-    "id": 8963,
-    "problem_id": 8732,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\\\\frac{8}{3}', '1', '2', '\\\\frac{7}{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8732.jpg"
-  },
-  {
-    "id": 8964,
-    "problem_id": 8733,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['36\u00b0', '34\u00b0', '27\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8733.jpg"
-  },
-  {
-    "id": 8965,
-    "problem_id": 8734,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['36\u00b0', '34\u00b0', '27\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8734.jpg"
-  },
-  {
-    "id": 8966,
-    "problem_id": 8735,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['36\u00b0', '34\u00b0', '27\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8735.jpg"
-  },
-  {
-    "id": 8967,
-    "problem_id": 8736,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['36\u00b0', '34\u00b0', '27\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8736.jpg"
-  },
-  {
-    "id": 8968,
-    "problem_id": 8737,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['36\u00b0', '34\u00b0', '27\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8737.jpg"
-  },
-  {
-    "id": 8969,
-    "problem_id": 8738,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['36\u00b0', '34\u00b0', '27\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8738.jpg"
-  },
-  {
-    "id": 8970,
-    "problem_id": 8739,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8739.jpg"
-  },
-  {
-    "id": 8971,
-    "problem_id": 8740,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8740.jpg"
-  },
-  {
-    "id": 8972,
-    "problem_id": 8741,
-    "problem": "<image>In the figure, \u25b3ABC is in a grid (where the side length of each small square is 1). What is the value of cos\u2220ABC?. A, B, C, D choices are ['0.75', '\\\\frac{4}{3}', '\\\\frac{3}{5}', '0.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8741.jpg"
-  },
-  {
-    "id": 8973,
-    "problem_id": 8742,
-    "problem": "<image>In the figure, \u25b3ABC is in a grid (where the side length of each small square is 1). What is the value of cos\u2220ABC?. A, B, C, D choices are ['0.75', '\\\\frac{4}{3}', '\\\\frac{3}{5}', '0.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8742.jpg"
-  },
-  {
-    "id": 8974,
-    "problem_id": 8743,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['8m', '4m', '2m', '6m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8743.jpg"
-  },
-  {
-    "id": 8975,
-    "problem_id": 8744,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['8m', '4m', '2m', '6m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8744.jpg"
-  },
-  {
-    "id": 8976,
-    "problem_id": 8745,
-    "problem": "<image>As shown in the figure, OC is the bisector of \u2220AOB. A point D is drawn on OA such that DE is parallel to OB and intersects OC at point E. If \u2220ADE = 55\u00b0, then the degree measure of \u2220DEO is ().. A, B, C, D choices are ['25\u00b0', '27.5\u00b0', '22.5\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8745.jpg"
-  },
-  {
-    "id": 8977,
-    "problem_id": 8746,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '20', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8746.jpg"
-  },
-  {
-    "id": 8978,
-    "problem_id": 8747,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '20', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8747.jpg"
-  },
-  {
-    "id": 8979,
-    "problem_id": 8748,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '20', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8748.jpg"
-  },
-  {
-    "id": 8980,
-    "problem_id": 8749,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '20', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8749.jpg"
-  },
-  {
-    "id": 8981,
-    "problem_id": 8750,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8750.jpg"
-  },
-  {
-    "id": 8982,
-    "problem_id": 8751,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8751.jpg"
-  },
-  {
-    "id": 8983,
-    "problem_id": 8752,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8752.jpg"
-  },
-  {
-    "id": 8984,
-    "problem_id": 8753,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8753.jpg"
-  },
-  {
-    "id": 8985,
-    "problem_id": 8754,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8754.jpg"
-  },
-  {
-    "id": 8986,
-    "problem_id": 8755,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8755.jpg"
-  },
-  {
-    "id": 8987,
-    "problem_id": 8756,
-    "problem": "<image>In right triangle ABC, with \u2220ACB = 90\u00b0 and CD as the median, extend CB to point E such that BE = BC. Connect DE and F is the midpoint of DE. Connect BF. If AC = 8 and BC = 6, what is the length of BF?. A, B, C, D choices are ['2', '2.5', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8756.jpg"
-  },
-  {
-    "id": 8988,
-    "problem_id": 8757,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. From point A, draw a perpendicular line AE to BC at point E, and connect OE. If OB = 6 and the area of rhombus ABCD is 54, then the length of OE is ().. A, B, C, D choices are ['4', '4.5', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8757.jpg"
-  },
-  {
-    "id": 8989,
-    "problem_id": 8758,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. From point A, draw a perpendicular line AE to BC at point E, and connect OE. If OB = 6 and the area of rhombus ABCD is 54, then the length of OE is ().. A, B, C, D choices are ['4', '4.5', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8758.jpg"
-  },
-  {
-    "id": 8990,
-    "problem_id": 8759,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. From point A, draw a perpendicular line AE to BC at point E, and connect OE. If OB = 6 and the area of rhombus ABCD is 54, then the length of OE is ().. A, B, C, D choices are ['4', '4.5', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8759.jpg"
-  },
-  {
-    "id": 8991,
-    "problem_id": 8760,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. From point A, draw a perpendicular line AE to BC at point E, and connect OE. If OB = 6 and the area of rhombus ABCD is 54, then the length of OE is ().. A, B, C, D choices are ['4', '4.5', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8760.jpg"
-  },
-  {
-    "id": 8992,
-    "problem_id": 8761,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. From point A, draw a perpendicular line AE to BC at point E, and connect OE. If OB = 6 and the area of rhombus ABCD is 54, then the length of OE is ().. A, B, C, D choices are ['4', '4.5', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8761.jpg"
-  },
-  {
-    "id": 8993,
-    "problem_id": 8762,
-    "problem": "<image>As shown in the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. From point A, draw a perpendicular line AE to BC at point E, and connect OE. If OB = 6 and the area of rhombus ABCD is 54, then the length of OE is ().. A, B, C, D choices are ['4', '4.5', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8762.jpg"
-  },
-  {
-    "id": 8994,
-    "problem_id": 8763,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of diamond ABCD intersect at point O. Point H is on AB such that DH is perpendicular to AB. OH is then connected. If OA = 4 and the area of diamond ABCD is 24, what is the length of OH?. A, B, C, D choices are ['2', '3', '\u221a{10}', '\u221a{13}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8763.jpg"
-  },
-  {
-    "id": 8995,
-    "problem_id": 8764,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of diamond ABCD intersect at point O. Point H is on AB such that DH is perpendicular to AB. OH is then connected. If OA = 4 and the area of diamond ABCD is 24, what is the length of OH?. A, B, C, D choices are ['2', '3', '\u221a{10}', '\u221a{13}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8764.jpg"
-  },
-  {
-    "id": 8996,
-    "problem_id": 8765,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of diamond ABCD intersect at point O. Point H is on AB such that DH is perpendicular to AB. OH is then connected. If OA = 4 and the area of diamond ABCD is 24, what is the length of OH?. A, B, C, D choices are ['2', '3', '\u221a{10}', '\u221a{13}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8765.jpg"
-  },
-  {
-    "id": 8997,
-    "problem_id": 8766,
-    "problem": "<image>A triangle ABC with a missing angle is shown in the figure. If it is measured that \u2220A = 55\u00b0 and \u2220B = 60\u00b0, what is the degree measure of angle C in the original complete triangle?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8766.jpg"
-  },
-  {
-    "id": 8998,
-    "problem_id": 8767,
-    "problem": "<image>A triangle ABC with a missing angle is shown in the figure. If it is measured that \u2220A = 55\u00b0 and \u2220B = 60\u00b0, what is the degree measure of angle C in the original complete triangle?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8767.jpg"
-  },
-  {
-    "id": 8999,
-    "problem_id": 8768,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O. If AC = 4cm and \u2220AOD = 120\u00b0, what is the length of BC?. A, B, C, D choices are ['4\u221a{3}cm', '4cm', '2\u221a{3}cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8768.jpg"
-  },
-  {
-    "id": 9000,
-    "problem_id": 8769,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O. If AC = 4cm and \u2220AOD = 120\u00b0, what is the length of BC?. A, B, C, D choices are ['4\u221a{3}cm', '4cm', '2\u221a{3}cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8769.jpg"
-  },
-  {
-    "id": 9001,
-    "problem_id": 8770,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O. If AC = 4cm and \u2220AOD = 120\u00b0, what is the length of BC?. A, B, C, D choices are ['4\u221a{3}cm', '4cm', '2\u221a{3}cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8770.jpg"
-  },
-  {
-    "id": 9002,
-    "problem_id": 8771,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O. If AC = 4cm and \u2220AOD = 120\u00b0, what is the length of BC?. A, B, C, D choices are ['4\u221a{3}cm', '4cm', '2\u221a{3}cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8771.jpg"
-  },
-  {
-    "id": 9003,
-    "problem_id": 8772,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of rectangle ABCD intersect at point O. If AC = 4cm and \u2220AOD = 120\u00b0, what is the length of BC?. A, B, C, D choices are ['4\u221a{3}cm', '4cm', '2\u221a{3}cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8772.jpg"
-  },
-  {
-    "id": 9004,
-    "problem_id": 8773,
-    "problem": "<image>As shown in the figure, ray OC is the angle bisector of \u2220AOB. Point D lies on ray OC and DP is perpendicular to OA at point P, with DP = 5. If point Q is a point on ray OB and OQ = 3, then the area of triangle ODQ is ()?. A, B, C, D choices are ['6.5', '7.5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8773.jpg"
-  },
-  {
-    "id": 9005,
-    "problem_id": 8774,
-    "problem": "<image>As shown in the figure, ray OC is the angle bisector of \u2220AOB. Point D lies on ray OC and DP is perpendicular to OA at point P, with DP = 5. If point Q is a point on ray OB and OQ = 3, then the area of triangle ODQ is ()?. A, B, C, D choices are ['6.5', '7.5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8774.jpg"
-  },
-  {
-    "id": 9006,
-    "problem_id": 8775,
-    "problem": "<image>As shown in the figure, ray OC is the angle bisector of \u2220AOB. Point D lies on ray OC and DP is perpendicular to OA at point P, with DP = 5. If point Q is a point on ray OB and OQ = 3, then the area of triangle ODQ is ()?. A, B, C, D choices are ['6.5', '7.5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8775.jpg"
-  },
-  {
-    "id": 9007,
-    "problem_id": 8776,
-    "problem": "<image>As shown in the figure, ray OC is the angle bisector of \u2220AOB. Point D lies on ray OC and DP is perpendicular to OA at point P, with DP = 5. If point Q is a point on ray OB and OQ = 3, then the area of triangle ODQ is ()?. A, B, C, D choices are ['6.5', '7.5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8776.jpg"
-  },
-  {
-    "id": 9008,
-    "problem_id": 8777,
-    "problem": "<image>As shown in the figure, ray OC is the angle bisector of \u2220AOB. Point D lies on ray OC and DP is perpendicular to OA at point P, with DP = 5. If point Q is a point on ray OB and OQ = 3, then the area of triangle ODQ is ()?. A, B, C, D choices are ['6.5', '7.5', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8777.jpg"
-  },
-  {
-    "id": 9009,
-    "problem_id": 8778,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8778.jpg"
-  },
-  {
-    "id": 9010,
-    "problem_id": 8779,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8779.jpg"
-  },
-  {
-    "id": 9011,
-    "problem_id": 8780,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8780.jpg"
-  },
-  {
-    "id": 9012,
-    "problem_id": 8781,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8781.jpg"
-  },
-  {
-    "id": 9013,
-    "problem_id": 8782,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8782.jpg"
-  },
-  {
-    "id": 9014,
-    "problem_id": 8783,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8783.jpg"
-  },
-  {
-    "id": 9015,
-    "problem_id": 8784,
-    "problem": "<image>In quadrilateral ABCD, E and F are the midpoints of AB and AD, respectively. If EF = 6, BC = 13, and CD = 5, what is the area of triangle BCD?. A, B, C, D choices are ['60', '48', '30', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8784.jpg"
-  },
-  {
-    "id": 9016,
-    "problem_id": 8785,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '65\u00b0', '60\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8785.jpg"
-  },
-  {
-    "id": 9017,
-    "problem_id": 8786,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '65\u00b0', '60\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8786.jpg"
-  },
-  {
-    "id": 9018,
-    "problem_id": 8787,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '65\u00b0', '60\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8787.jpg"
-  },
-  {
-    "id": 9019,
-    "problem_id": 8788,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '65\u00b0', '60\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8788.jpg"
-  },
-  {
-    "id": 9020,
-    "problem_id": 8789,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '65\u00b0', '60\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8789.jpg"
-  },
-  {
-    "id": 9021,
-    "problem_id": 8790,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['70\u00b0', '65\u00b0', '60\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8790.jpg"
-  },
-  {
-    "id": 9022,
-    "problem_id": 8791,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '7.5', '\\\\frac{20}{3}', '\\\\frac{15}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8791.jpg"
-  },
-  {
-    "id": 9023,
-    "problem_id": 8792,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '7.5', '\\\\frac{20}{3}', '\\\\frac{15}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8792.jpg"
-  },
-  {
-    "id": 9024,
-    "problem_id": 8793,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '7.5', '\\\\frac{20}{3}', '\\\\frac{15}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8793.jpg"
-  },
-  {
-    "id": 9025,
-    "problem_id": 8794,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '4\u221a{3}', '8', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8794.jpg"
-  },
-  {
-    "id": 9026,
-    "problem_id": 8795,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '4\u221a{3}', '8', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8795.jpg"
-  },
-  {
-    "id": 9027,
-    "problem_id": 8796,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '4\u221a{3}', '8', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8796.jpg"
-  },
-  {
-    "id": 9028,
-    "problem_id": 8797,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '4\u221a{3}', '8', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8797.jpg"
-  },
-  {
-    "id": 9029,
-    "problem_id": 8798,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '4\u221a{3}', '8', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8798.jpg"
-  },
-  {
-    "id": 9030,
-    "problem_id": 8799,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '4\u221a{3}', '8', '8\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8799.jpg"
-  },
-  {
-    "id": 9031,
-    "problem_id": 8800,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8800.jpg"
-  },
-  {
-    "id": 9032,
-    "problem_id": 8801,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8801.jpg"
-  },
-  {
-    "id": 9033,
-    "problem_id": 8802,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8802.jpg"
-  },
-  {
-    "id": 9034,
-    "problem_id": 8803,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8803.jpg"
-  },
-  {
-    "id": 9035,
-    "problem_id": 8804,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8804.jpg"
-  },
-  {
-    "id": 9036,
-    "problem_id": 8805,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8805.jpg"
-  },
-  {
-    "id": 9037,
-    "problem_id": 8806,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['118\u00b0', '34\u00b0', '90\u00b0', '6\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8806.jpg"
-  },
-  {
-    "id": 9038,
-    "problem_id": 8807,
-    "problem": "<image>As shown in the figure, points A, B, C, and D are all on circle O with center O. Connect AB, AC, and then sequentially connect O, B, C, and D to form quadrilateral OBCD. If OD = BC and OB = CD, what is the degree measure of angle A? (). A, B, C, D choices are ['20\u00b0', '25\u00b0', '30\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8807.jpg"
-  },
-  {
-    "id": 9039,
-    "problem_id": 8808,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.8', '0.75', '\\\\frac{4}{3}', '0.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8808.jpg"
-  },
-  {
-    "id": 9040,
-    "problem_id": 8809,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.8', '0.75', '\\\\frac{4}{3}', '0.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8809.jpg"
-  },
-  {
-    "id": 9041,
-    "problem_id": 8810,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.8', '0.75', '\\\\frac{4}{3}', '0.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8810.jpg"
-  },
-  {
-    "id": 9042,
-    "problem_id": 8811,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8811.jpg"
-  },
-  {
-    "id": 9043,
-    "problem_id": 8812,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8812.jpg"
-  },
-  {
-    "id": 9044,
-    "problem_id": 8813,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8813.jpg"
-  },
-  {
-    "id": 9045,
-    "problem_id": 8814,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8814.jpg"
-  },
-  {
-    "id": 9046,
-    "problem_id": 8815,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8815.jpg"
-  },
-  {
-    "id": 9047,
-    "problem_id": 8816,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8816.jpg"
-  },
-  {
-    "id": 9048,
-    "problem_id": 8817,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['20', '24', '28', '32'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8817.jpg"
-  },
-  {
-    "id": 9049,
-    "problem_id": 8818,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['20', '24', '28', '32'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8818.jpg"
-  },
-  {
-    "id": 9050,
-    "problem_id": 8819,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['20', '24', '28', '32'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8819.jpg"
-  },
-  {
-    "id": 9051,
-    "problem_id": 8820,
-    "problem": "<image>As shown in the diagram, the diagonal AC and BD of rectangle ABCD intersect at point O. AB = 6 and BC = 8. A perpendicular line OM is drawn through point O to AC, intersecting BC at point M. Another perpendicular line MN is drawn through point M to BD, intersecting BD at point N. Find the value of OM + MN.. A, B, C, D choices are ['4.8', '3.2', '2.4', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8820.jpg"
-  },
-  {
-    "id": 9052,
-    "problem_id": 8821,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8821.jpg"
-  },
-  {
-    "id": 9053,
-    "problem_id": 8822,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8822.jpg"
-  },
-  {
-    "id": 9054,
-    "problem_id": 8823,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8823.jpg"
-  },
-  {
-    "id": 9055,
-    "problem_id": 8824,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8824.jpg"
-  },
-  {
-    "id": 9056,
-    "problem_id": 8825,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8825.jpg"
-  },
-  {
-    "id": 9057,
-    "problem_id": 8826,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8826.jpg"
-  },
-  {
-    "id": 9058,
-    "problem_id": 8827,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8827.jpg"
-  },
-  {
-    "id": 9059,
-    "problem_id": 8828,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD and \u22201\uff1d56\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['134\u00b0', '128\u00b0', '124\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8828.jpg"
-  },
-  {
-    "id": 9060,
-    "problem_id": 8829,
-    "problem": "<image>In triangle ABC shown in the figure, AB = AC, \u2220B = 65\u00b0. Point D lies on the extension of BA, and AE bisects \u2220DAC. What is the degree measure of \u2220DAE?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8829.jpg"
-  },
-  {
-    "id": 9061,
-    "problem_id": 8830,
-    "problem": "<image>In triangle ABC shown in the figure, AB = AC, \u2220B = 65\u00b0. Point D lies on the extension of BA, and AE bisects \u2220DAC. What is the degree measure of \u2220DAE?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8830.jpg"
-  },
-  {
-    "id": 9062,
-    "problem_id": 8831,
-    "problem": "<image>In triangle ABC shown in the figure, AB = AC, \u2220B = 65\u00b0. Point D lies on the extension of BA, and AE bisects \u2220DAC. What is the degree measure of \u2220DAE?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8831.jpg"
-  },
-  {
-    "id": 9063,
-    "problem_id": 8832,
-    "problem": "<image>In triangle ABC shown in the figure, AB = AC, \u2220B = 65\u00b0. Point D lies on the extension of BA, and AE bisects \u2220DAC. What is the degree measure of \u2220DAE?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8832.jpg"
-  },
-  {
-    "id": 9064,
-    "problem_id": 8833,
-    "problem": "<image>In triangle ABC shown in the figure, AB = AC, \u2220B = 65\u00b0. Point D lies on the extension of BA, and AE bisects \u2220DAC. What is the degree measure of \u2220DAE?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8833.jpg"
-  },
-  {
-    "id": 9065,
-    "problem_id": 8834,
-    "problem": "<image>In triangle ABC shown in the figure, AB = AC, \u2220B = 65\u00b0. Point D lies on the extension of BA, and AE bisects \u2220DAC. What is the degree measure of \u2220DAE?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '75\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8834.jpg"
-  },
-  {
-    "id": 9066,
-    "problem_id": 8835,
-    "problem": "<image>As shown in the figure, the diagonal AC of rectangle ABCD is 8, and \u2220BOC = 120\u00b0. What is the length of AB?. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8835.jpg"
-  },
-  {
-    "id": 9067,
-    "problem_id": 8836,
-    "problem": "<image>As shown in the figure, the diagonal AC of rectangle ABCD is 8, and \u2220BOC = 120\u00b0. What is the length of AB?. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8836.jpg"
-  },
-  {
-    "id": 9068,
-    "problem_id": 8837,
-    "problem": "<image>As shown in the figure, the diagonal AC of rectangle ABCD is 8, and \u2220BOC = 120\u00b0. What is the length of AB?. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8837.jpg"
-  },
-  {
-    "id": 9069,
-    "problem_id": 8838,
-    "problem": "<image>As shown in the figure, the diagonal AC of rectangle ABCD is 8, and \u2220BOC = 120\u00b0. What is the length of AB?. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8838.jpg"
-  },
-  {
-    "id": 9070,
-    "problem_id": 8839,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8839.jpg"
-  },
-  {
-    "id": 9071,
-    "problem_id": 8840,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8840.jpg"
-  },
-  {
-    "id": 9072,
-    "problem_id": 8841,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8841.jpg"
-  },
-  {
-    "id": 9073,
-    "problem_id": 8842,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8842.jpg"
-  },
-  {
-    "id": 9074,
-    "problem_id": 8843,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8843.jpg"
-  },
-  {
-    "id": 9075,
-    "problem_id": 8844,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8844.jpg"
-  },
-  {
-    "id": 9076,
-    "problem_id": 8845,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8845.jpg"
-  },
-  {
-    "id": 9077,
-    "problem_id": 8846,
-    "problem": "<image>As shown in the figure, \u25b3ABC is similar to \u25b3DEF, and point O is their similarity center. If OE = 3OB, what is the ratio of the areas of \u25b3ABC and \u25b3DEF?. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\frac{1}{9}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8846.jpg"
-  },
-  {
-    "id": 9078,
-    "problem_id": 8847,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12\u03c0cm', '15\u03c0cm', '9\u03c0cm', '6\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8847.jpg"
-  },
-  {
-    "id": 9079,
-    "problem_id": 8848,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12\u03c0cm', '15\u03c0cm', '9\u03c0cm', '6\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8848.jpg"
-  },
-  {
-    "id": 9080,
-    "problem_id": 8849,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12\u03c0cm', '15\u03c0cm', '9\u03c0cm', '6\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8849.jpg"
-  },
-  {
-    "id": 9081,
-    "problem_id": 8850,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['12\u03c0cm', '15\u03c0cm', '9\u03c0cm', '6\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8850.jpg"
-  },
-  {
-    "id": 9082,
-    "problem_id": 8851,
-    "problem": "<image>As shown in the figure, a\u2225b, if \u22201 = 100\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8851.jpg"
-  },
-  {
-    "id": 9085,
-    "problem_id": 8852,
-    "problem": "<image>As shown in the figure, a\u2225b, if \u22201 = 100\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8852.jpg"
-  },
-  {
-    "id": 9086,
-    "problem_id": 8853,
-    "problem": "<image>As shown in the figure, if the length of the diagonals AC and BD of rhombus ABCD are 6cm and 8cm respectively, what is the perimeter of this rhombus?. A, B, C, D choices are ['5cm', '10cm', '14cm', '20cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8853.jpg"
-  },
-  {
-    "id": 9087,
-    "problem_id": 8854,
-    "problem": "<image>As shown in the figure, if the length of the diagonals AC and BD of rhombus ABCD are 6cm and 8cm respectively, what is the perimeter of this rhombus?. A, B, C, D choices are ['5cm', '10cm', '14cm', '20cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8854.jpg"
-  },
-  {
-    "id": 9088,
-    "problem_id": 8855,
-    "problem": "<image>As shown in the figure, if the length of the diagonals AC and BD of rhombus ABCD are 6cm and 8cm respectively, what is the perimeter of this rhombus?. A, B, C, D choices are ['5cm', '10cm', '14cm', '20cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8855.jpg"
-  },
-  {
-    "id": 9089,
-    "problem_id": 8856,
-    "problem": "<image>In the rectangle ABCD, diagonal AC and BD intersect at point O, CD = 3. If AE is perpendicular and bisects OB at point E, what is the length of BC?. A, B, C, D choices are ['4', '3\u221a{3}', '6', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8856.jpg"
-  },
-  {
-    "id": 9090,
-    "problem_id": 8857,
-    "problem": "<image>In the rectangle ABCD, diagonal AC and BD intersect at point O, CD = 3. If AE is perpendicular and bisects OB at point E, what is the length of BC?. A, B, C, D choices are ['4', '3\u221a{3}', '6', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8857.jpg"
-  },
-  {
-    "id": 9091,
-    "problem_id": 8858,
-    "problem": "<image>In the rectangle ABCD, diagonal AC and BD intersect at point O, CD = 3. If AE is perpendicular and bisects OB at point E, what is the length of BC?. A, B, C, D choices are ['4', '3\u221a{3}', '6', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8858.jpg"
-  },
-  {
-    "id": 9092,
-    "problem_id": 8859,
-    "problem": "<image>In the rectangle ABCD, diagonal AC and BD intersect at point O, CD = 3. If AE is perpendicular and bisects OB at point E, what is the length of BC?. A, B, C, D choices are ['4', '3\u221a{3}', '6', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8859.jpg"
-  },
-  {
-    "id": 9093,
-    "problem_id": 8860,
-    "problem": "<image>In the rectangle ABCD, diagonal AC and BD intersect at point O, CD = 3. If AE is perpendicular and bisects OB at point E, what is the length of BC?. A, B, C, D choices are ['4', '3\u221a{3}', '6', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8860.jpg"
-  },
-  {
-    "id": 9094,
-    "problem_id": 8861,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8861.jpg"
-  },
-  {
-    "id": 9095,
-    "problem_id": 8862,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8862.jpg"
-  },
-  {
-    "id": 9096,
-    "problem_id": 8863,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8863.jpg"
-  },
-  {
-    "id": 9097,
-    "problem_id": 8864,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8864.jpg"
-  },
-  {
-    "id": 9098,
-    "problem_id": 8865,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8865.jpg"
-  },
-  {
-    "id": 9099,
-    "problem_id": 8866,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8866.jpg"
-  },
-  {
-    "id": 9100,
-    "problem_id": 8867,
-    "problem": "<image>The image shows two congruent triangles. The letters in the image represent the lengths of the sides of the triangles. What is the degree measure of angle 1? (). A, B, C, D choices are ['54\u00b0', '56\u00b0', '60\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8867.jpg"
-  },
-  {
-    "id": 9101,
-    "problem_id": 8868,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 80. If the perimeter of triangle BOC is 20 more than that of triangle AOB, then the length of BC is ().. A, B, C, D choices are ['40', '10', '20', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8868.jpg"
-  },
-  {
-    "id": 9102,
-    "problem_id": 8869,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 80. If the perimeter of triangle BOC is 20 more than that of triangle AOB, then the length of BC is ().. A, B, C, D choices are ['40', '10', '20', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8869.jpg"
-  },
-  {
-    "id": 9103,
-    "problem_id": 8870,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 80. If the perimeter of triangle BOC is 20 more than that of triangle AOB, then the length of BC is ().. A, B, C, D choices are ['40', '10', '20', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8870.jpg"
-  },
-  {
-    "id": 9104,
-    "problem_id": 8871,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 80. If the perimeter of triangle BOC is 20 more than that of triangle AOB, then the length of BC is ().. A, B, C, D choices are ['40', '10', '20', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8871.jpg"
-  },
-  {
-    "id": 9105,
-    "problem_id": 8872,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 80. If the perimeter of triangle BOC is 20 more than that of triangle AOB, then the length of BC is ().. A, B, C, D choices are ['40', '10', '20', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8872.jpg"
-  },
-  {
-    "id": 9106,
-    "problem_id": 8873,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 80. If the perimeter of triangle BOC is 20 more than that of triangle AOB, then the length of BC is ().. A, B, C, D choices are ['40', '10', '20', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8873.jpg"
-  },
-  {
-    "id": 9107,
-    "problem_id": 8874,
-    "problem": "<image>As shown in the diagram, point F is on the line CD, FG bisects angle EFD, AB is parallel to CD, angle 1 is 56\u00b0, and the degree of angle 2 is ().. A, B, C, D choices are ['34\u00b0', '56\u00b0', '62\u00b0', '68\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8874.jpg"
-  },
-  {
-    "id": 9108,
-    "problem_id": 8875,
-    "problem": "<image>As shown in the diagram, point F is on the line CD, FG bisects angle EFD, AB is parallel to CD, angle 1 is 56\u00b0, and the degree of angle 2 is ().. A, B, C, D choices are ['34\u00b0', '56\u00b0', '62\u00b0', '68\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8875.jpg"
-  },
-  {
-    "id": 9109,
-    "problem_id": 8876,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, line c intersects lines a and b at points A and B respectively, AC is perpendicular to AB at point A, and intersects line b at point C. If angle 1 is 52\u00b0, what is the degree measure of angle 2?. A, B, C, D choices are ['52\u00b0', '48\u00b0', '38\u00b0', '32\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8876.jpg"
-  },
-  {
-    "id": 9110,
-    "problem_id": 8877,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, line c intersects lines a and b at points A and B respectively, AC is perpendicular to AB at point A, and intersects line b at point C. If angle 1 is 52\u00b0, what is the degree measure of angle 2?. A, B, C, D choices are ['52\u00b0', '48\u00b0', '38\u00b0', '32\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8877.jpg"
-  },
-  {
-    "id": 9111,
-    "problem_id": 8878,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, line c intersects lines a and b at points A and B respectively, AC is perpendicular to AB at point A, and intersects line b at point C. If angle 1 is 52\u00b0, what is the degree measure of angle 2?. A, B, C, D choices are ['52\u00b0', '48\u00b0', '38\u00b0', '32\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8878.jpg"
-  },
-  {
-    "id": 9112,
-    "problem_id": 8879,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8879.jpg"
-  },
-  {
-    "id": 9113,
-    "problem_id": 8880,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8880.jpg"
-  },
-  {
-    "id": 9114,
-    "problem_id": 8881,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8881.jpg"
-  },
-  {
-    "id": 9115,
-    "problem_id": 8882,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8882.jpg"
-  },
-  {
-    "id": 9116,
-    "problem_id": 8883,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=8. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['20', '12', '16', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8883.jpg"
-  },
-  {
-    "id": 9117,
-    "problem_id": 8884,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=8. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['20', '12', '16', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8884.jpg"
-  },
-  {
-    "id": 9118,
-    "problem_id": 8885,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=8. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['20', '12', '16', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8885.jpg"
-  },
-  {
-    "id": 9119,
-    "problem_id": 8886,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is a regular pentagon. If l1 is parallel to l2, what is the value of angle 1 minus angle 2? (). A, B, C, D choices are ['108\u00b0', '36\u00b0', '72\u00b0', '144\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8886.jpg"
-  },
-  {
-    "id": 9120,
-    "problem_id": 8887,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '1', '3.5', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8887.jpg"
-  },
-  {
-    "id": 9121,
-    "problem_id": 8888,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '1', '3.5', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8888.jpg"
-  },
-  {
-    "id": 9122,
-    "problem_id": 8889,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '1', '3.5', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8889.jpg"
-  },
-  {
-    "id": 9123,
-    "problem_id": 8890,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '1', '3.5', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8890.jpg"
-  },
-  {
-    "id": 9124,
-    "problem_id": 8891,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '1', '3.5', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8891.jpg"
-  },
-  {
-    "id": 9126,
-    "problem_id": 8892,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['115\u00b0', '100\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8892.jpg"
-  },
-  {
-    "id": 9127,
-    "problem_id": 8893,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['115\u00b0', '100\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8893.jpg"
-  },
-  {
-    "id": 9128,
-    "problem_id": 8894,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['115\u00b0', '100\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8894.jpg"
-  },
-  {
-    "id": 9129,
-    "problem_id": 8895,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['115\u00b0', '100\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8895.jpg"
-  },
-  {
-    "id": 9130,
-    "problem_id": 8896,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['115\u00b0', '100\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8896.jpg"
-  },
-  {
-    "id": 9131,
-    "problem_id": 8897,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['115\u00b0', '100\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8897.jpg"
-  },
-  {
-    "id": 9132,
-    "problem_id": 8898,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides BC, AB, and AC, respectively. If the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF?. A, B, C, D choices are ['5', '10', '15', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8898.jpg"
-  },
-  {
-    "id": 9133,
-    "problem_id": 8899,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides BC, AB, and AC, respectively. If the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF?. A, B, C, D choices are ['5', '10', '15', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8899.jpg"
-  },
-  {
-    "id": 9134,
-    "problem_id": 8900,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides BC, AB, and AC, respectively. If the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF?. A, B, C, D choices are ['5', '10', '15', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8900.jpg"
-  },
-  {
-    "id": 9135,
-    "problem_id": 8901,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{2}', '8\u221a{3}', '\u221a{5}', '2\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8901.jpg"
-  },
-  {
-    "id": 9136,
-    "problem_id": 8902,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{2}', '8\u221a{3}', '\u221a{5}', '2\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8902.jpg"
-  },
-  {
-    "id": 9137,
-    "problem_id": 8903,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{2}', '8\u221a{3}', '\u221a{5}', '2\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8903.jpg"
-  },
-  {
-    "id": 9138,
-    "problem_id": 8904,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{2}', '8\u221a{3}', '\u221a{5}', '2\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8904.jpg"
-  },
-  {
-    "id": 9139,
-    "problem_id": 8905,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{2}', '8\u221a{3}', '\u221a{5}', '2\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8905.jpg"
-  },
-  {
-    "id": 9140,
-    "problem_id": 8906,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{2}', '8\u221a{3}', '\u221a{5}', '2\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8906.jpg"
-  },
-  {
-    "id": 9141,
-    "problem_id": 8907,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8907.jpg"
-  },
-  {
-    "id": 9142,
-    "problem_id": 8908,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8908.jpg"
-  },
-  {
-    "id": 9143,
-    "problem_id": 8909,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8909.jpg"
-  },
-  {
-    "id": 9144,
-    "problem_id": 8910,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8910.jpg"
-  },
-  {
-    "id": 9145,
-    "problem_id": 8911,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['14', '12', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8911.jpg"
-  },
-  {
-    "id": 9146,
-    "problem_id": 8912,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['55\u00b0', '70\u00b0', '110\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8912.jpg"
-  },
-  {
-    "id": 9147,
-    "problem_id": 8913,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['55\u00b0', '70\u00b0', '110\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8913.jpg"
-  },
-  {
-    "id": 9148,
-    "problem_id": 8914,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['55\u00b0', '70\u00b0', '110\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8914.jpg"
-  },
-  {
-    "id": 9150,
-    "problem_id": 8915,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25', '20', '15', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8915.jpg"
-  },
-  {
-    "id": 9151,
-    "problem_id": 8916,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25', '20', '15', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8916.jpg"
-  },
-  {
-    "id": 9152,
-    "problem_id": 8917,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['25', '20', '15', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8917.jpg"
-  },
-  {
-    "id": 9153,
-    "problem_id": 8918,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8918.jpg"
-  },
-  {
-    "id": 9154,
-    "problem_id": 8919,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8919.jpg"
-  },
-  {
-    "id": 9155,
-    "problem_id": 8920,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8920.jpg"
-  },
-  {
-    "id": 9156,
-    "problem_id": 8921,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8921.jpg"
-  },
-  {
-    "id": 9157,
-    "problem_id": 8922,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8922.jpg"
-  },
-  {
-    "id": 9158,
-    "problem_id": 8923,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8923.jpg"
-  },
-  {
-    "id": 9159,
-    "problem_id": 8924,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8924.jpg"
-  },
-  {
-    "id": 9160,
-    "problem_id": 8925,
-    "problem": "<image>As shown in the figure, it is known that the diameter of the base circle of a cone is BC=6 and the height OA=4. The area of the unfolded side surface of this cone is (). A, B, C, D choices are ['30\u03c0', '12\u00d7\u221a{3}\u00d7\u03c0', '15\u03c0', '22.5\u00d7\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8925.jpg"
-  },
-  {
-    "id": 9161,
-    "problem_id": 8926,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8926.jpg"
-  },
-  {
-    "id": 9162,
-    "problem_id": 8927,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8927.jpg"
-  },
-  {
-    "id": 9163,
-    "problem_id": 8928,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8928.jpg"
-  },
-  {
-    "id": 9164,
-    "problem_id": 8929,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8929.jpg"
-  },
-  {
-    "id": 9165,
-    "problem_id": 8930,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8930.jpg"
-  },
-  {
-    "id": 9166,
-    "problem_id": 8931,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8931.jpg"
-  },
-  {
-    "id": 9167,
-    "problem_id": 8932,
-    "problem": "<image>As shown in the figure, to measure the distance between points A and B on the edge of a pond, Xiaoming chose a point O on one side of the pond and measured that the midpoints of OA and OB were points C and D, respectively, with CD = 12 meters. What is the distance between A and B?. A, B, C, D choices are ['24\u7c73', '26\u7c73', '28\u7c73', '30\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8932.jpg"
-  },
-  {
-    "id": 9168,
-    "problem_id": 8933,
-    "problem": "<image>In parallelogram ABCD, point E is the midpoint of AB. Connect DE and intersect diagonal AC at point F. If AF = 3, what is the value of AC? (). A, B, C, D choices are ['3', '4', '6', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8933.jpg"
-  },
-  {
-    "id": 9169,
-    "problem_id": 8934,
-    "problem": "<image>In right triangle ABC as shown, \u2220CAB = 90\u00b0, \u2220C = 48\u00b0. An arc is drawn with point B as its center and BA as its radius, intersecting CB at point T. AT is then connected. What is the degree measurement of \u2220CAT?. A, B, C, D choices are ['64\u00b0', '24\u00b0', '21\u00b0', '16\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8934.jpg"
-  },
-  {
-    "id": 9170,
-    "problem_id": 8935,
-    "problem": "<image>In right triangle ABC as shown, \u2220CAB = 90\u00b0, \u2220C = 48\u00b0. An arc is drawn with point B as its center and BA as its radius, intersecting CB at point T. AT is then connected. What is the degree measurement of \u2220CAT?. A, B, C, D choices are ['64\u00b0', '24\u00b0', '21\u00b0', '16\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8935.jpg"
-  },
-  {
-    "id": 9171,
-    "problem_id": 8936,
-    "problem": "<image>In right triangle ABC as shown, \u2220CAB = 90\u00b0, \u2220C = 48\u00b0. An arc is drawn with point B as its center and BA as its radius, intersecting CB at point T. AT is then connected. What is the degree measurement of \u2220CAT?. A, B, C, D choices are ['64\u00b0', '24\u00b0', '21\u00b0', '16\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8936.jpg"
-  },
-  {
-    "id": 9172,
-    "problem_id": 8937,
-    "problem": "<image>In right triangle ABC as shown, \u2220CAB = 90\u00b0, \u2220C = 48\u00b0. An arc is drawn with point B as its center and BA as its radius, intersecting CB at point T. AT is then connected. What is the degree measurement of \u2220CAT?. A, B, C, D choices are ['64\u00b0', '24\u00b0', '21\u00b0', '16\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8937.jpg"
-  },
-  {
-    "id": 9173,
-    "problem_id": 8938,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree measure of arc BC?. A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8938.jpg"
-  },
-  {
-    "id": 9174,
-    "problem_id": 8939,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree measure of arc BC?. A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8939.jpg"
-  },
-  {
-    "id": 9175,
-    "problem_id": 8940,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree measure of arc BC?. A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8940.jpg"
-  },
-  {
-    "id": 9176,
-    "problem_id": 8941,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If \u2220A = 24\u00b0, what is the degree measure of arc BC?. A, B, C, D choices are ['66\u00b0', '48\u00b0', '33\u00b0', '24\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8941.jpg"
-  },
-  {
-    "id": 9177,
-    "problem_id": 8942,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8942.jpg"
-  },
-  {
-    "id": 9178,
-    "problem_id": 8943,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8943.jpg"
-  },
-  {
-    "id": 9179,
-    "problem_id": 8944,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8944.jpg"
-  },
-  {
-    "id": 9180,
-    "problem_id": 8945,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8945.jpg"
-  },
-  {
-    "id": 9181,
-    "problem_id": 8946,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8946.jpg"
-  },
-  {
-    "id": 9182,
-    "problem_id": 8947,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8947.jpg"
-  },
-  {
-    "id": 9183,
-    "problem_id": 8948,
-    "problem": "<image>As shown in the figure, if two triangles are congruent, then \u2220\u03b1 is equal to ().. A, B, C, D choices are ['72\u00b0', '60\u00b0', '58\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8948.jpg"
-  },
-  {
-    "id": 9184,
-    "problem_id": 8949,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, \u2220A = 52\u00b0. With point B as the center, draw an arc with length BC as the radius, which intersects AB at point D. Connect CD. What is the degree measure of \u2220ADC?. A, B, C, D choices are ['142\u00b0', '132\u00b0', '119\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8949.jpg"
-  },
-  {
-    "id": 9185,
-    "problem_id": 8950,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, \u2220A = 52\u00b0. With point B as the center, draw an arc with length BC as the radius, which intersects AB at point D. Connect CD. What is the degree measure of \u2220ADC?. A, B, C, D choices are ['142\u00b0', '132\u00b0', '119\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8950.jpg"
-  },
-  {
-    "id": 9186,
-    "problem_id": 8951,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, \u2220A = 52\u00b0. With point B as the center, draw an arc with length BC as the radius, which intersects AB at point D. Connect CD. What is the degree measure of \u2220ADC?. A, B, C, D choices are ['142\u00b0', '132\u00b0', '119\u00b0', '109\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8951.jpg"
-  },
-  {
-    "id": 9187,
-    "problem_id": 8952,
-    "problem": "<image>As shown in the figure, point B is located in the direction of North-East 45\u00b0 from point A, and in the direction of North-West 30\u00b0 from point C. What is the degree of angle ABC? (). A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '85\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8952.jpg"
-  },
-  {
-    "id": 9188,
-    "problem_id": 8953,
-    "problem": "<image>As shown in the figure, point B is located in the direction of North-East 45\u00b0 from point A, and in the direction of North-West 30\u00b0 from point C. What is the degree of angle ABC? (). A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '85\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8953.jpg"
-  },
-  {
-    "id": 9189,
-    "problem_id": 8954,
-    "problem": "<image>As shown in the figure, point B is located in the direction of North-East 45\u00b0 from point A, and in the direction of North-West 30\u00b0 from point C. What is the degree of angle ABC? (). A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '85\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8954.jpg"
-  },
-  {
-    "id": 9190,
-    "problem_id": 8955,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['7', '9.5', '5\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8955.jpg"
-  },
-  {
-    "id": 9191,
-    "problem_id": 8956,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['7', '9.5', '5\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8956.jpg"
-  },
-  {
-    "id": 9193,
-    "problem_id": 8957,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['7', '9.5', '5\u221a{3}', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8957.jpg"
-  },
-  {
-    "id": 9194,
-    "problem_id": 8958,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['54\u00b0', '36\u00b0', '28\u00b0', '18\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8958.jpg"
-  },
-  {
-    "id": 9195,
-    "problem_id": 8959,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['54\u00b0', '36\u00b0', '28\u00b0', '18\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8959.jpg"
-  },
-  {
-    "id": 9196,
-    "problem_id": 8960,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['54\u00b0', '36\u00b0', '28\u00b0', '18\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8960.jpg"
-  },
-  {
-    "id": 9198,
-    "problem_id": 8961,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['54\u00b0', '36\u00b0', '28\u00b0', '18\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8961.jpg"
-  },
-  {
-    "id": 9199,
-    "problem_id": 8962,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['54\u00b0', '36\u00b0', '28\u00b0', '18\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8962.jpg"
-  },
-  {
-    "id": 9201,
-    "problem_id": 8963,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8963.jpg"
-  },
-  {
-    "id": 9202,
-    "problem_id": 8964,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8964.jpg"
-  },
-  {
-    "id": 9203,
-    "problem_id": 8965,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '4', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8965.jpg"
-  },
-  {
-    "id": 9204,
-    "problem_id": 8966,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '4', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8966.jpg"
-  },
-  {
-    "id": 9205,
-    "problem_id": 8967,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '4', '4\u221a{3}', '4\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8967.jpg"
-  },
-  {
-    "id": 9206,
-    "problem_id": 8968,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['90\u00b0', '68\u00b0', '58\u00b0', '44\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8968.jpg"
-  },
-  {
-    "id": 9207,
-    "problem_id": 8969,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['90\u00b0', '68\u00b0', '58\u00b0', '44\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8969.jpg"
-  },
-  {
-    "id": 9208,
-    "problem_id": 8970,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['90\u00b0', '68\u00b0', '58\u00b0', '44\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8970.jpg"
-  },
-  {
-    "id": 9209,
-    "problem_id": 8971,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['90\u00b0', '68\u00b0', '58\u00b0', '44\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8971.jpg"
-  },
-  {
-    "id": 9210,
-    "problem_id": 8972,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['90\u00b0', '68\u00b0', '58\u00b0', '44\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8972.jpg"
-  },
-  {
-    "id": 9211,
-    "problem_id": 8973,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['90\u00b0', '68\u00b0', '58\u00b0', '44\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8973.jpg"
-  },
-  {
-    "id": 9212,
-    "problem_id": 8974,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '35\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8974.jpg"
-  },
-  {
-    "id": 9213,
-    "problem_id": 8975,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '35\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8975.jpg"
-  },
-  {
-    "id": 9214,
-    "problem_id": 8976,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '35\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8976.jpg"
-  },
-  {
-    "id": 9215,
-    "problem_id": 8977,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '35\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8977.jpg"
-  },
-  {
-    "id": 9216,
-    "problem_id": 8978,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '35\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8978.jpg"
-  },
-  {
-    "id": 9217,
-    "problem_id": 8979,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['15\u00b0', '35\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8979.jpg"
-  },
-  {
-    "id": 9218,
-    "problem_id": 8980,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\u221a{5}', '2\u221a{5}', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8980.jpg"
-  },
-  {
-    "id": 9219,
-    "problem_id": 8981,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\u221a{5}', '2\u221a{5}', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8981.jpg"
-  },
-  {
-    "id": 9220,
-    "problem_id": 8982,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\u221a{5}', '2\u221a{5}', '2', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8982.jpg"
-  },
-  {
-    "id": 9221,
-    "problem_id": 8983,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, OE is perpendicular to AB. If \u2220COE\uff1d65\u00b0, then \u2220BOD is (). A, B, C, D choices are ['40\u00b0', '35\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8983.jpg"
-  },
-  {
-    "id": 9222,
-    "problem_id": 8984,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, OE is perpendicular to AB. If \u2220COE\uff1d65\u00b0, then \u2220BOD is (). A, B, C, D choices are ['40\u00b0', '35\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8984.jpg"
-  },
-  {
-    "id": 9224,
-    "problem_id": 8985,
-    "problem": "<image>As shown in the figure, AB is a tangent to circle O, and point B is the point of tangency. Connect AO and extend it to intersect circle O at point C, then connect BC. If \u2220A = 26\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['26\u00b0', '32\u00b0', '52\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8985.jpg"
-  },
-  {
-    "id": 9225,
-    "problem_id": 8986,
-    "problem": "<image>As shown in the figure, line c intersects with lines a and b, and a is parallel to b. If \u22201 is 55\u00b0, what is the degree of \u22202?. A, B, C, D choices are ['55\u00b0', '145\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8986.jpg"
-  },
-  {
-    "id": 9226,
-    "problem_id": 8987,
-    "problem": "<image>As shown in the figure, line c intersects with lines a and b, and a is parallel to b. If \u22201 is 55\u00b0, what is the degree of \u22202?. A, B, C, D choices are ['55\u00b0', '145\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8987.jpg"
-  },
-  {
-    "id": 9227,
-    "problem_id": 8988,
-    "problem": "<image>As shown in the figure, line c intersects with lines a and b, and a is parallel to b. If \u22201 is 55\u00b0, what is the degree of \u22202?. A, B, C, D choices are ['55\u00b0', '145\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8988.jpg"
-  },
-  {
-    "id": 9228,
-    "problem_id": 8989,
-    "problem": "<image>In triangle ABC, point D is the midpoint of side AB and point E is the midpoint of side BC. If the area of triangle ABC is 12, what is the area of the shaded region in the figure?. A, B, C, D choices are ['6', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8989.jpg"
-  },
-  {
-    "id": 9229,
-    "problem_id": 8990,
-    "problem": "<image>In triangle ABC, point D is the midpoint of side AB and point E is the midpoint of side BC. If the area of triangle ABC is 12, what is the area of the shaded region in the figure?. A, B, C, D choices are ['6', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8990.jpg"
-  },
-  {
-    "id": 9230,
-    "problem_id": 8991,
-    "problem": "<image>As shown in the diagram, triangle ABC is inscribed in circle O. Connect OA and OB. If \u2220ABO = 35\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['70\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8991.jpg"
-  },
-  {
-    "id": 9231,
-    "problem_id": 8992,
-    "problem": "<image>As shown in the diagram, triangle ABC is inscribed in circle O. Connect OA and OB. If \u2220ABO = 35\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['70\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8992.jpg"
-  },
-  {
-    "id": 9232,
-    "problem_id": 8993,
-    "problem": "<image>As shown in the diagram, triangle ABC is inscribed in circle O. Connect OA and OB. If \u2220ABO = 35\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['70\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8993.jpg"
-  },
-  {
-    "id": 9234,
-    "problem_id": 8994,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 8, BC = 6. Point P is a moving point on the hypotenuse AB. PE is perpendicular to AC at point E, and PF is perpendicular to BC at point F. If we connect EF, what is the minimum value of segment EF? (). A, B, C, D choices are ['1.2', '2.4', '2.5', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8994.jpg"
-  },
-  {
-    "id": 9235,
-    "problem_id": 8995,
-    "problem": "<image>As shown in the figure, diagonal AC and BD of rectangle ABCD intersect at point O. If \u2220AOB = 50\u00b0, what is the degree of \u2220OAD?. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8995.jpg"
-  },
-  {
-    "id": 9236,
-    "problem_id": 8996,
-    "problem": "<image>As shown in the figure, diagonal AC and BD of rectangle ABCD intersect at point O. If \u2220AOB = 50\u00b0, what is the degree of \u2220OAD?. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8996.jpg"
-  },
-  {
-    "id": 9237,
-    "problem_id": 8997,
-    "problem": "<image>As shown in the figure, diagonal AC and BD of rectangle ABCD intersect at point O. If \u2220AOB = 50\u00b0, what is the degree of \u2220OAD?. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8997.jpg"
-  },
-  {
-    "id": 9238,
-    "problem_id": 8998,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, CD is tangent to circle O at point C, and if \u2220BCD = 25\u00b0, then \u2220B is equal to ().. A, B, C, D choices are ['25\u00b0', '65\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8998.jpg"
-  },
-  {
-    "id": 9239,
-    "problem_id": 8999,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, CD is tangent to circle O at point C, and if \u2220BCD = 25\u00b0, then \u2220B is equal to ().. A, B, C, D choices are ['25\u00b0', '65\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/8999.jpg"
-  },
-  {
-    "id": 9240,
-    "problem_id": 9000,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, CD is tangent to circle O at point C, and if \u2220BCD = 25\u00b0, then \u2220B is equal to ().. A, B, C, D choices are ['25\u00b0', '65\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9000.jpg"
-  },
-  {
-    "id": 9242,
-    "problem_id": 9001,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, CD is tangent to circle O at point C, and if \u2220BCD = 25\u00b0, then \u2220B is equal to ().. A, B, C, D choices are ['25\u00b0', '65\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9001.jpg"
-  },
-  {
-    "id": 9243,
-    "problem_id": 9002,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\u03c0', '3\u03c0', '5\u03c0', '15\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9002.jpg"
-  },
-  {
-    "id": 9244,
-    "problem_id": 9003,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\u03c0', '3\u03c0', '5\u03c0', '15\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9003.jpg"
-  },
-  {
-    "id": 9245,
-    "problem_id": 9004,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['\u03c0', '3\u03c0', '5\u03c0', '15\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9004.jpg"
-  },
-  {
-    "id": 9246,
-    "problem_id": 9005,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9005.jpg"
-  },
-  {
-    "id": 9247,
-    "problem_id": 9006,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9006.jpg"
-  },
-  {
-    "id": 9248,
-    "problem_id": 9007,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9007.jpg"
-  },
-  {
-    "id": 9249,
-    "problem_id": 9008,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9008.jpg"
-  },
-  {
-    "id": 9250,
-    "problem_id": 9009,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9009.jpg"
-  },
-  {
-    "id": 9251,
-    "problem_id": 9010,
-    "problem": "<image>As shown in the figure, D and E are points on sides AB and BC of triangle ABC, respectively, and DE || AC. AE and CD are connected and intersect at point O. If the area of triangle BDE is 3 and the ratio of the areas of triangles DOE to COA is 1:9, then the area of triangle ABC is ().. A, B, C, D choices are ['9', '18', '27', '45'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9010.jpg"
-  },
-  {
-    "id": 9252,
-    "problem_id": 9011,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9011.jpg"
-  },
-  {
-    "id": 9253,
-    "problem_id": 9012,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9012.jpg"
-  },
-  {
-    "id": 9254,
-    "problem_id": 9013,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9013.jpg"
-  },
-  {
-    "id": 9255,
-    "problem_id": 9014,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9014.jpg"
-  },
-  {
-    "id": 9256,
-    "problem_id": 9015,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9015.jpg"
-  },
-  {
-    "id": 9257,
-    "problem_id": 9016,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9016.jpg"
-  },
-  {
-    "id": 9258,
-    "problem_id": 9017,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9017.jpg"
-  },
-  {
-    "id": 9259,
-    "problem_id": 9018,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9018.jpg"
-  },
-  {
-    "id": 9260,
-    "problem_id": 9019,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '20', '10', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9019.jpg"
-  },
-  {
-    "id": 9261,
-    "problem_id": 9020,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '20', '10', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9020.jpg"
-  },
-  {
-    "id": 9262,
-    "problem_id": 9021,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '20', '10', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9021.jpg"
-  },
-  {
-    "id": 9263,
-    "problem_id": 9022,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '20', '10', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9022.jpg"
-  },
-  {
-    "id": 9264,
-    "problem_id": 9023,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9023.jpg"
-  },
-  {
-    "id": 9265,
-    "problem_id": 9024,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9024.jpg"
-  },
-  {
-    "id": 9266,
-    "problem_id": 9025,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9025.jpg"
-  },
-  {
-    "id": 9267,
-    "problem_id": 9026,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9026.jpg"
-  },
-  {
-    "id": 9268,
-    "problem_id": 9027,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9027.jpg"
-  },
-  {
-    "id": 9269,
-    "problem_id": 9028,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9028.jpg"
-  },
-  {
-    "id": 9270,
-    "problem_id": 9029,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220C = 90\u00b0, AC = 4, BC = 3, then sin\u2220ABC = ().. A, B, C, D choices are ['0.6', '0.8', '\\\\frac{4}{3}', '0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9029.jpg"
-  },
-  {
-    "id": 9271,
-    "problem_id": 9030,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9030.jpg"
-  },
-  {
-    "id": 9272,
-    "problem_id": 9031,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9031.jpg"
-  },
-  {
-    "id": 9273,
-    "problem_id": 9032,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9032.jpg"
-  },
-  {
-    "id": 9274,
-    "problem_id": 9033,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9033.jpg"
-  },
-  {
-    "id": 9275,
-    "problem_id": 9034,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9034.jpg"
-  },
-  {
-    "id": 9276,
-    "problem_id": 9035,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9035.jpg"
-  },
-  {
-    "id": 9277,
-    "problem_id": 9036,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9036.jpg"
-  },
-  {
-    "id": 9278,
-    "problem_id": 9037,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9037.jpg"
-  },
-  {
-    "id": 9279,
-    "problem_id": 9038,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9038.jpg"
-  },
-  {
-    "id": 9280,
-    "problem_id": 9039,
-    "problem": "<image>Given the parallel lines a and b in the figure, if \u22201 = 45\u00b0 and \u22202 = 65\u00b0, what is the measure of \u22203?. A, B, C, D choices are ['110\u00b0', '100\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9039.jpg"
-  },
-  {
-    "id": 9281,
-    "problem_id": 9040,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '3', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9040.jpg"
-  },
-  {
-    "id": 9282,
-    "problem_id": 9041,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '3', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9041.jpg"
-  },
-  {
-    "id": 9283,
-    "problem_id": 9042,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '3', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9042.jpg"
-  },
-  {
-    "id": 9284,
-    "problem_id": 9043,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '3', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9043.jpg"
-  },
-  {
-    "id": 9285,
-    "problem_id": 9044,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '8', '3', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9044.jpg"
-  },
-  {
-    "id": 9286,
-    "problem_id": 9045,
-    "problem": "<image>As shown in the figure, O is a point on the line AB, and it is known that OC is perpendicular to OD, and \u2220AOC = 35\u00b0. Then \u2220BOD = ().. A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9045.jpg"
-  },
-  {
-    "id": 9287,
-    "problem_id": 9046,
-    "problem": "<image>As shown in the figure, O is a point on the line AB, and it is known that OC is perpendicular to OD, and \u2220AOC = 35\u00b0. Then \u2220BOD = ().. A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9046.jpg"
-  },
-  {
-    "id": 9288,
-    "problem_id": 9047,
-    "problem": "<image>As shown in the figure, O is a point on the line AB, and it is known that OC is perpendicular to OD, and \u2220AOC = 35\u00b0. Then \u2220BOD = ().. A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9047.jpg"
-  },
-  {
-    "id": 9289,
-    "problem_id": 9048,
-    "problem": "<image>As shown in the figure, three points A, B, and C are given on circle O. Connect AB, AC, and OC. Tangent BD intersects the extended line of OC at point D. If OC = 2 and \u2220A = 30\u00b0, the length of DB is ().. A, B, C, D choices are ['4', '2\u221a{3}', '2\u221a{2}', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9048.jpg"
-  },
-  {
-    "id": 9290,
-    "problem_id": 9049,
-    "problem": "<image>In the figure, in circle O, OA and OB are radii, AB, AC, BC are chords. If \u2220OAB = 70\u00b0, then what is the degree measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '70\u00b0', '20\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9049.jpg"
-  },
-  {
-    "id": 9291,
-    "problem_id": 9050,
-    "problem": "<image>In the figure, in circle O, OA and OB are radii, AB, AC, BC are chords. If \u2220OAB = 70\u00b0, then what is the degree measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '70\u00b0', '20\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9050.jpg"
-  },
-  {
-    "id": 9292,
-    "problem_id": 9051,
-    "problem": "<image>In the figure, in circle O, OA and OB are radii, AB, AC, BC are chords. If \u2220OAB = 70\u00b0, then what is the degree measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '70\u00b0', '20\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9051.jpg"
-  },
-  {
-    "id": 9293,
-    "problem_id": 9052,
-    "problem": "<image>In the figure, in circle O, OA and OB are radii, AB, AC, BC are chords. If \u2220OAB = 70\u00b0, then what is the degree measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '70\u00b0', '20\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9052.jpg"
-  },
-  {
-    "id": 9294,
-    "problem_id": 9053,
-    "problem": "<image>In the figure, in circle O, OA and OB are radii, AB, AC, BC are chords. If \u2220OAB = 70\u00b0, then what is the degree measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '70\u00b0', '20\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9053.jpg"
-  },
-  {
-    "id": 9295,
-    "problem_id": 9054,
-    "problem": "<image>In the figure, point O is on the line AB, and OC is perpendicular to OD. If \u2220AOC = 120\u00b0, what is the measure of \u2220BOD? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9054.jpg"
-  },
-  {
-    "id": 9296,
-    "problem_id": 9055,
-    "problem": "<image>In the figure, point O is on the line AB, and OC is perpendicular to OD. If \u2220AOC = 120\u00b0, what is the measure of \u2220BOD? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9055.jpg"
-  },
-  {
-    "id": 9297,
-    "problem_id": 9056,
-    "problem": "<image>As shown in the diagram, three points A, B, and C are on the circle O, and AB, AC, OB, and OC are connected. Tangent BD intersects the extension of OC at point D. Given that \u2220A=25\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9056.jpg"
-  },
-  {
-    "id": 9298,
-    "problem_id": 9057,
-    "problem": "<image>In the parallelogram ABCD as shown, AB = 10, BC = 6, E and F are the midpoints of AD and DC, respectively. If EF = 7, what is the perimeter of quadrilateral EACF?. A, B, C, D choices are ['20', '22', '29', '31'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9057.jpg"
-  },
-  {
-    "id": 9299,
-    "problem_id": 9058,
-    "problem": "<image>As shown in the figure, if the base radius of a cone is 1 and the length of the slant line is 3, what is the lateral area? (). A, B, C, D choices are ['2\u03c0', '3\u03c0', '6\u03c0', '8\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9058.jpg"
-  },
-  {
-    "id": 9300,
-    "problem_id": 9059,
-    "problem": "<image>As shown in the figure, if the base radius of a cone is 1 and the length of the slant line is 3, what is the lateral area? (). A, B, C, D choices are ['2\u03c0', '3\u03c0', '6\u03c0', '8\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9059.jpg"
-  },
-  {
-    "id": 9301,
-    "problem_id": 9060,
-    "problem": "<image>As shown in the figure, if the base radius of a cone is 1 and the length of the slant line is 3, what is the lateral area? (). A, B, C, D choices are ['2\u03c0', '3\u03c0', '6\u03c0', '8\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9060.jpg"
-  },
-  {
-    "id": 9302,
-    "problem_id": 9061,
-    "problem": "<image>As shown in the figure, if the base radius of a cone is 1 and the length of the slant line is 3, what is the lateral area? (). A, B, C, D choices are ['2\u03c0', '3\u03c0', '6\u03c0', '8\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9061.jpg"
-  },
-  {
-    "id": 9303,
-    "problem_id": 9062,
-    "problem": "<image>As shown in the figure, if the base radius of a cone is 1 and the length of the slant line is 3, what is the lateral area? (). A, B, C, D choices are ['2\u03c0', '3\u03c0', '6\u03c0', '8\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9062.jpg"
-  },
-  {
-    "id": 9304,
-    "problem_id": 9063,
-    "problem": "<image>As shown in the figure, if the base radius of a cone is 1 and the length of the slant line is 3, what is the lateral area? (). A, B, C, D choices are ['2\u03c0', '3\u03c0', '6\u03c0', '8\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9063.jpg"
-  },
-  {
-    "id": 9305,
-    "problem_id": 9064,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9064.jpg"
-  },
-  {
-    "id": 9306,
-    "problem_id": 9065,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9065.jpg"
-  },
-  {
-    "id": 9307,
-    "problem_id": 9066,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9066.jpg"
-  },
-  {
-    "id": 9308,
-    "problem_id": 9067,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9067.jpg"
-  },
-  {
-    "id": 9309,
-    "problem_id": 9068,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9068.jpg"
-  },
-  {
-    "id": 9311,
-    "problem_id": 9069,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9069.jpg"
-  },
-  {
-    "id": 9312,
-    "problem_id": 9070,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9070.jpg"
-  },
-  {
-    "id": 9313,
-    "problem_id": 9071,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9071.jpg"
-  },
-  {
-    "id": 9314,
-    "problem_id": 9072,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9072.jpg"
-  },
-  {
-    "id": 9315,
-    "problem_id": 9073,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['5', '8', '10', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9073.jpg"
-  },
-  {
-    "id": 9316,
-    "problem_id": 9074,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '5', '3\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9074.jpg"
-  },
-  {
-    "id": 9317,
-    "problem_id": 9075,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '5', '3\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9075.jpg"
-  },
-  {
-    "id": 9318,
-    "problem_id": 9076,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '5', '3\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9076.jpg"
-  },
-  {
-    "id": 9319,
-    "problem_id": 9077,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '5', '3\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9077.jpg"
-  },
-  {
-    "id": 9320,
-    "problem_id": 9078,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '5', '3\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9078.jpg"
-  },
-  {
-    "id": 9321,
-    "problem_id": 9079,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '5', '3\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9079.jpg"
-  },
-  {
-    "id": 9322,
-    "problem_id": 9080,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1.5', '2', '3', '0.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9080.jpg"
-  },
-  {
-    "id": 9323,
-    "problem_id": 9081,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1.5', '2', '3', '0.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9081.jpg"
-  },
-  {
-    "id": 9324,
-    "problem_id": 9082,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1.5', '2', '3', '0.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9082.jpg"
-  },
-  {
-    "id": 9325,
-    "problem_id": 9083,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1.5', '2', '3', '0.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9083.jpg"
-  },
-  {
-    "id": 9326,
-    "problem_id": 9084,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['1.5', '2', '3', '0.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9084.jpg"
-  },
-  {
-    "id": 9327,
-    "problem_id": 9085,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9085.jpg"
-  },
-  {
-    "id": 9328,
-    "problem_id": 9086,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9086.jpg"
-  },
-  {
-    "id": 9329,
-    "problem_id": 9087,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9087.jpg"
-  },
-  {
-    "id": 9330,
-    "problem_id": 9088,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '7', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9088.jpg"
-  },
-  {
-    "id": 9331,
-    "problem_id": 9089,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '7', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9089.jpg"
-  },
-  {
-    "id": 9332,
-    "problem_id": 9090,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3', '4', '7', '11'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9090.jpg"
-  },
-  {
-    "id": 9333,
-    "problem_id": 9091,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 8. D is any point on side AB, E is the midpoint of CD, and F is the midpoint of BE. What is the area of triangle ABF?. A, B, C, D choices are ['3', '2', '\\\\frac{5}{2}', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9091.jpg"
-  },
-  {
-    "id": 9334,
-    "problem_id": 9092,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 8. D is any point on side AB, E is the midpoint of CD, and F is the midpoint of BE. What is the area of triangle ABF?. A, B, C, D choices are ['3', '2', '\\\\frac{5}{2}', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9092.jpg"
-  },
-  {
-    "id": 9335,
-    "problem_id": 9093,
-    "problem": "<image>In right triangle \u25b3ABC, where \u2220CAB\uff1d90\u00b0 and \u2220ABC\uff1d70\u00b0, AD is the angle bisector of \u2220CAB and intersects the side BC at point D. A perpendicular line CE is drawn from point C to side AD in \u25b3ACD. What is the degree measure of \u2220ECD?. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9093.jpg"
-  },
-  {
-    "id": 9336,
-    "problem_id": 9094,
-    "problem": "<image>As shown in the figure, EF intersects the diagonal of parallelogram ABCD at point O, intersects AD at point E, and intersects BC at point F. It is known that AB = 4, BC = 6, and OE = 3. What is the perimeter of quadrilateral EFCD?. A, B, C, D choices are ['16', '13', '11', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9094.jpg"
-  },
-  {
-    "id": 9337,
-    "problem_id": 9095,
-    "problem": "<image>As shown in the figure, regular hexagon ABCDEF is inscribed in circle O. If AC is connected, what is the degree measure of angle BAC? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9095.jpg"
-  },
-  {
-    "id": 9338,
-    "problem_id": 9096,
-    "problem": "<image>As shown in the figure, regular hexagon ABCDEF is inscribed in circle O. If AC is connected, what is the degree measure of angle BAC? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9096.jpg"
-  },
-  {
-    "id": 9339,
-    "problem_id": 9097,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B respectively. C is a point on the circle, and AC and BC are connected. If \u2220ACB = 62\u00b0, then what is the degree measure of \u2220P?. A, B, C, D choices are ['56\u00b0', '62\u00b0', '66\u00b0', '68\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9097.jpg"
-  },
-  {
-    "id": 9340,
-    "problem_id": 9098,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to circle O at points A and B respectively. C is a point on the circle, and AC and BC are connected. If \u2220ACB = 62\u00b0, then what is the degree measure of \u2220P?. A, B, C, D choices are ['56\u00b0', '62\u00b0', '66\u00b0', '68\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9098.jpg"
-  },
-  {
-    "id": 9341,
-    "problem_id": 9099,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=10. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['11', '17', '18', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9099.jpg"
-  },
-  {
-    "id": 9342,
-    "problem_id": 9100,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=10. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['11', '17', '18', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9100.jpg"
-  },
-  {
-    "id": 9343,
-    "problem_id": 9101,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=10. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['11', '17', '18', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9101.jpg"
-  },
-  {
-    "id": 9344,
-    "problem_id": 9102,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=10. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['11', '17', '18', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9102.jpg"
-  },
-  {
-    "id": 9345,
-    "problem_id": 9103,
-    "problem": "<image>In triangle ABC, AB=AC=12 and BC=10. AD bisects angle BAC and intersects BC at point D. E is the midpoint of AC. If we connect DE, what is the perimeter of triangle CDE?. A, B, C, D choices are ['11', '17', '18', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9103.jpg"
-  },
-  {
-    "id": 9346,
-    "problem_id": 9104,
-    "problem": "<image>As shown in the diagram, EF is parallel to BC in triangle ABC. If AB = 7, BC = 5, and BE = 3, then EF = ().. A, B, C, D choices are ['\\\\frac{15}{4}', '\\\\frac{20}{3}', '\\\\frac{15}{7}', '\\\\frac{20}{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9104.jpg"
-  },
-  {
-    "id": 9347,
-    "problem_id": 9105,
-    "problem": "<image>As shown in the diagram, EF is parallel to BC in triangle ABC. If AB = 7, BC = 5, and BE = 3, then EF = ().. A, B, C, D choices are ['\\\\frac{15}{4}', '\\\\frac{20}{3}', '\\\\frac{15}{7}', '\\\\frac{20}{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9105.jpg"
-  },
-  {
-    "id": 9348,
-    "problem_id": 9106,
-    "problem": "<image>As shown in the diagram, EF is parallel to BC in triangle ABC. If AB = 7, BC = 5, and BE = 3, then EF = ().. A, B, C, D choices are ['\\\\frac{15}{4}', '\\\\frac{20}{3}', '\\\\frac{15}{7}', '\\\\frac{20}{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9106.jpg"
-  },
-  {
-    "id": 9349,
-    "problem_id": 9107,
-    "problem": "<image>As shown in the diagram, EF is parallel to BC in triangle ABC. If AB = 7, BC = 5, and BE = 3, then EF = ().. A, B, C, D choices are ['\\\\frac{15}{4}', '\\\\frac{20}{3}', '\\\\frac{15}{7}', '\\\\frac{20}{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9107.jpg"
-  },
-  {
-    "id": 9350,
-    "problem_id": 9108,
-    "problem": "<image>As shown in the diagram, EF is parallel to BC in triangle ABC. If AB = 7, BC = 5, and BE = 3, then EF = ().. A, B, C, D choices are ['\\\\frac{15}{4}', '\\\\frac{20}{3}', '\\\\frac{15}{7}', '\\\\frac{20}{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9108.jpg"
-  },
-  {
-    "id": 9351,
-    "problem_id": 9109,
-    "problem": "<image>As shown in the diagram, EF is parallel to BC in triangle ABC. If AB = 7, BC = 5, and BE = 3, then EF = ().. A, B, C, D choices are ['\\\\frac{15}{4}', '\\\\frac{20}{3}', '\\\\frac{15}{7}', '\\\\frac{20}{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9109.jpg"
-  },
-  {
-    "id": 9352,
-    "problem_id": 9110,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of side CD. If AB = 12 and OM = 4.5, what is the length of segment OB?. A, B, C, D choices are ['7', '8', '7.5', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9110.jpg"
-  },
-  {
-    "id": 9353,
-    "problem_id": 9111,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of side CD. If AB = 12 and OM = 4.5, what is the length of segment OB?. A, B, C, D choices are ['7', '8', '7.5', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9111.jpg"
-  },
-  {
-    "id": 9354,
-    "problem_id": 9112,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of side CD. If AB = 12 and OM = 4.5, what is the length of segment OB?. A, B, C, D choices are ['7', '8', '7.5', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9112.jpg"
-  },
-  {
-    "id": 9355,
-    "problem_id": 9113,
-    "problem": "<image>In parallelogram ABCD, if \u2220DBC = 25\u00b0 and \u2220BAD = 115\u00b0, then \u2220BDC = ().. A, B, C, D choices are ['25\u00b0', '30\u00b0', '40\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9113.jpg"
-  },
-  {
-    "id": 9356,
-    "problem_id": 9114,
-    "problem": "<image>In parallelogram ABCD, if \u2220DBC = 25\u00b0 and \u2220BAD = 115\u00b0, then \u2220BDC = ().. A, B, C, D choices are ['25\u00b0', '30\u00b0', '40\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9114.jpg"
-  },
-  {
-    "id": 9357,
-    "problem_id": 9115,
-    "problem": "<image>In parallelogram ABCD, if \u2220DBC = 25\u00b0 and \u2220BAD = 115\u00b0, then \u2220BDC = ().. A, B, C, D choices are ['25\u00b0', '30\u00b0', '40\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9115.jpg"
-  },
-  {
-    "id": 9358,
-    "problem_id": 9116,
-    "problem": "<image>In parallelogram ABCD, if \u2220DBC = 25\u00b0 and \u2220BAD = 115\u00b0, then \u2220BDC = ().. A, B, C, D choices are ['25\u00b0', '30\u00b0', '40\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9116.jpg"
-  },
-  {
-    "id": 9359,
-    "problem_id": 9117,
-    "problem": "<image>In parallelogram ABCD, if \u2220DBC = 25\u00b0 and \u2220BAD = 115\u00b0, then \u2220BDC = ().. A, B, C, D choices are ['25\u00b0', '30\u00b0', '40\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9117.jpg"
-  },
-  {
-    "id": 9360,
-    "problem_id": 9118,
-    "problem": "<image>In triangle ABC, D is the midpoint of AB, BE is perpendicular to AC with E as the foot of the perpendicular. If DE = 4 and AE = 6, then the length of BE is (). A, B, C, D choices are ['10', '2\u221a{5}', '8', '2\u221a{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9118.jpg"
-  },
-  {
-    "id": 9361,
-    "problem_id": 9119,
-    "problem": "<image>In triangle ABC, D is the midpoint of AB, BE is perpendicular to AC with E as the foot of the perpendicular. If DE = 4 and AE = 6, then the length of BE is (). A, B, C, D choices are ['10', '2\u221a{5}', '8', '2\u221a{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9119.jpg"
-  },
-  {
-    "id": 9362,
-    "problem_id": 9120,
-    "problem": "<image>In triangle ABC, D is the midpoint of AB, BE is perpendicular to AC with E as the foot of the perpendicular. If DE = 4 and AE = 6, then the length of BE is (). A, B, C, D choices are ['10', '2\u221a{5}', '8', '2\u221a{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9120.jpg"
-  },
-  {
-    "id": 9363,
-    "problem_id": 9121,
-    "problem": "<image>In triangle ABC, D is the midpoint of AB, BE is perpendicular to AC with E as the foot of the perpendicular. If DE = 4 and AE = 6, then the length of BE is (). A, B, C, D choices are ['10', '2\u221a{5}', '8', '2\u221a{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9121.jpg"
-  },
-  {
-    "id": 9364,
-    "problem_id": 9122,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. A right-angled triangle ruler is placed in the position shown in the figure. If \u22201=60\u00b0, what is the degree of the complement of \u22202?. A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9122.jpg"
-  },
-  {
-    "id": 9365,
-    "problem_id": 9123,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. A right-angled triangle ruler is placed in the position shown in the figure. If \u22201=60\u00b0, what is the degree of the complement of \u22202?. A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9123.jpg"
-  },
-  {
-    "id": 9366,
-    "problem_id": 9124,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. A right-angled triangle ruler is placed in the position shown in the figure. If \u22201=60\u00b0, what is the degree of the complement of \u22202?. A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9124.jpg"
-  },
-  {
-    "id": 9367,
-    "problem_id": 9125,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. A right-angled triangle ruler is placed in the position shown in the figure. If \u22201=60\u00b0, what is the degree of the complement of \u22202?. A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9125.jpg"
-  },
-  {
-    "id": 9368,
-    "problem_id": 9126,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\{1}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9126.jpg"
-  },
-  {
-    "id": 9369,
-    "problem_id": 9127,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\{1}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9127.jpg"
-  },
-  {
-    "id": 9370,
-    "problem_id": 9128,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\{1}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9128.jpg"
-  },
-  {
-    "id": 9372,
-    "problem_id": 9129,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\{1}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9129.jpg"
-  },
-  {
-    "id": 9373,
-    "problem_id": 9130,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['0.5', '0.25', '\\\\frac{1}{3}', '\\\\{1}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9130.jpg"
-  },
-  {
-    "id": 9374,
-    "problem_id": 9131,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9131.jpg"
-  },
-  {
-    "id": 9375,
-    "problem_id": 9132,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9132.jpg"
-  },
-  {
-    "id": 9376,
-    "problem_id": 9133,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9133.jpg"
-  },
-  {
-    "id": 9377,
-    "problem_id": 9134,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9134.jpg"
-  },
-  {
-    "id": 9378,
-    "problem_id": 9135,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9135.jpg"
-  },
-  {
-    "id": 9379,
-    "problem_id": 9136,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9136.jpg"
-  },
-  {
-    "id": 9380,
-    "problem_id": 9137,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9137.jpg"
-  },
-  {
-    "id": 9381,
-    "problem_id": 9138,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9138.jpg"
-  },
-  {
-    "id": 9382,
-    "problem_id": 9139,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['24', '10', '\\\\frac{24}{5}', '\\\\frac{12}{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9139.jpg"
-  },
-  {
-    "id": 9383,
-    "problem_id": 9140,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{3}', '6\u221a{3}', '4.5', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9140.jpg"
-  },
-  {
-    "id": 9384,
-    "problem_id": 9141,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{3}', '6\u221a{3}', '4.5', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9141.jpg"
-  },
-  {
-    "id": 9385,
-    "problem_id": 9142,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{3}', '6\u221a{3}', '4.5', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9142.jpg"
-  },
-  {
-    "id": 9386,
-    "problem_id": 9143,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{3}', '6\u221a{3}', '4.5', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9143.jpg"
-  },
-  {
-    "id": 9387,
-    "problem_id": 9144,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['3\u221a{3}', '6\u221a{3}', '4.5', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9144.jpg"
-  },
-  {
-    "id": 9390,
-    "problem_id": 9145,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '30', '20', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9145.jpg"
-  },
-  {
-    "id": 9391,
-    "problem_id": 9146,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '30', '20', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9146.jpg"
-  },
-  {
-    "id": 9393,
-    "problem_id": 9147,
-    "problem": "<image>Get Some Error During Process. A, B, C, D choices are ['40', '30', '20', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9147.jpg"
-  },
-  {
-    "id": 9394,
-    "problem_id": 9148,
-    "problem": "<image>In a Cartesian coordinate system, given C(3,4), a circle with center at point C is tangent to the y-axis. Points A and B are on the x-axis with OA=OB. Point P is a moving point on circle C, and \u2220APB=90\u00b0. What is the minimum value of the length of AB?. A, B, C, D choices are ['4', '3', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9148.jpg"
-  },
-  {
-    "id": 9395,
-    "problem_id": 9149,
-    "problem": "<image>In a Cartesian coordinate system, given C(3,4), a circle with center at point C is tangent to the y-axis. Points A and B are on the x-axis with OA=OB. Point P is a moving point on circle C, and \u2220APB=90\u00b0. What is the minimum value of the length of AB?. A, B, C, D choices are ['4', '3', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9149.jpg"
-  },
-  {
-    "id": 9396,
-    "problem_id": 9150,
-    "problem": "<image>In a Cartesian coordinate system, given C(3,4), a circle with center at point C is tangent to the y-axis. Points A and B are on the x-axis with OA=OB. Point P is a moving point on circle C, and \u2220APB=90\u00b0. What is the minimum value of the length of AB?. A, B, C, D choices are ['4', '3', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9150.jpg"
-  },
-  {
-    "id": 9397,
-    "problem_id": 9151,
-    "problem": "<image>In a Cartesian coordinate system, given C(3,4), a circle with center at point C is tangent to the y-axis. Points A and B are on the x-axis with OA=OB. Point P is a moving point on circle C, and \u2220APB=90\u00b0. What is the minimum value of the length of AB?. A, B, C, D choices are ['4', '3', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9151.jpg"
-  },
-  {
-    "id": 9398,
-    "problem_id": 9152,
-    "problem": "<image>A set square is placed in the position shown in the figure. If AB\u2225CD, what is the degree measure of angle 1?. A, B, C, D choices are ['60\u00b0', '75\u00b0', '80\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9152.jpg"
-  },
-  {
-    "id": 9399,
-    "problem_id": 9153,
-    "problem": "<image>A set square is placed in the position shown in the figure. If AB\u2225CD, what is the degree measure of angle 1?. A, B, C, D choices are ['60\u00b0', '75\u00b0', '80\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9153.jpg"
-  },
-  {
-    "id": 9400,
-    "problem_id": 9154,
-    "problem": "<image>A set square is placed in the position shown in the figure. If AB\u2225CD, what is the degree measure of angle 1?. A, B, C, D choices are ['60\u00b0', '75\u00b0', '80\u00b0', '105\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9154.jpg"
-  },
-  {
-    "id": 9401,
-    "problem_id": 9155,
-    "problem": "<image>As shown in the diagram, points A and B are on line l1, while points C and D are on line l2. l1 is parallel to l2, CA is perpendicular to l1, BD is perpendicular to l2, and AC = 3cm. What is the length of BD?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9155.jpg"
-  },
-  {
-    "id": 9402,
-    "problem_id": 9156,
-    "problem": "<image>As shown in the diagram, points A and B are on line l1, while points C and D are on line l2. l1 is parallel to l2, CA is perpendicular to l1, BD is perpendicular to l2, and AC = 3cm. What is the length of BD?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9156.jpg"
-  },
-  {
-    "id": 9403,
-    "problem_id": 9157,
-    "problem": "<image>As shown in the diagram, points A and B are on line l1, while points C and D are on line l2. l1 is parallel to l2, CA is perpendicular to l1, BD is perpendicular to l2, and AC = 3cm. What is the length of BD?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9157.jpg"
-  },
-  {
-    "id": 9404,
-    "problem_id": 9158,
-    "problem": "<image>As shown in the diagram, points A and B are on line l1, while points C and D are on line l2. l1 is parallel to l2, CA is perpendicular to l1, BD is perpendicular to l2, and AC = 3cm. What is the length of BD?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9158.jpg"
-  },
-  {
-    "id": 9405,
-    "problem_id": 9159,
-    "problem": "<image>As shown in the diagram, points A and B are on line l1, while points C and D are on line l2. l1 is parallel to l2, CA is perpendicular to l1, BD is perpendicular to l2, and AC = 3cm. What is the length of BD?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9159.jpg"
-  },
-  {
-    "id": 9406,
-    "problem_id": 9160,
-    "problem": "<image>As shown in the diagram, points A and B are on line l1, while points C and D are on line l2. l1 is parallel to l2, CA is perpendicular to l1, BD is perpendicular to l2, and AC = 3cm. What is the length of BD?. A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9160.jpg"
-  },
-  {
-    "id": 9407,
-    "problem_id": 9161,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is inscribed in circle O, and AC is connected. What is the degree of angle BAC? (). A, B, C, D choices are ['45\u00b0', '38\u00b0', '36\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9161.jpg"
-  },
-  {
-    "id": 9408,
-    "problem_id": 9162,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is inscribed in circle O, and AC is connected. What is the degree of angle BAC? (). A, B, C, D choices are ['45\u00b0', '38\u00b0', '36\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9162.jpg"
-  },
-  {
-    "id": 9409,
-    "problem_id": 9163,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is inscribed in circle O, and AC is connected. What is the degree of angle BAC? (). A, B, C, D choices are ['45\u00b0', '38\u00b0', '36\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9163.jpg"
-  },
-  {
-    "id": 9410,
-    "problem_id": 9164,
-    "problem": "<image>As shown in the diagram, pentagon ABCDE is inscribed in circle O, and AC is connected. What is the degree of angle BAC? (). A, B, C, D choices are ['45\u00b0', '38\u00b0', '36\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9164.jpg"
-  },
-  {
-    "id": 9411,
-    "problem_id": 9165,
-    "problem": "<image>As shown in the diagram, lines a and b intersect at point O. If \u22201 + \u22202 = 100\u00b0, then what is the measure of \u22203?. A, B, C, D choices are ['50\u00b0', '100\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9165.jpg"
-  },
-  {
-    "id": 9412,
-    "problem_id": 9166,
-    "problem": "<image>As shown in the diagram, lines a and b intersect at point O. If \u22201 + \u22202 = 100\u00b0, then what is the measure of \u22203?. A, B, C, D choices are ['50\u00b0', '100\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9166.jpg"
-  },
-  {
-    "id": 9413,
-    "problem_id": 9167,
-    "problem": "<image>As shown in the diagram, lines a and b intersect at point O. If \u22201 + \u22202 = 100\u00b0, then what is the measure of \u22203?. A, B, C, D choices are ['50\u00b0', '100\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9167.jpg"
-  },
-  {
-    "id": 9414,
-    "problem_id": 9168,
-    "problem": "<image>As shown in the diagram, lines a and b intersect at point O. If \u22201 + \u22202 = 100\u00b0, then what is the measure of \u22203?. A, B, C, D choices are ['50\u00b0', '100\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9168.jpg"
-  },
-  {
-    "id": 9415,
-    "problem_id": 9169,
-    "problem": "<image>As shown in the diagram, lines a and b intersect at point O. If \u22201 + \u22202 = 100\u00b0, then what is the measure of \u22203?. A, B, C, D choices are ['50\u00b0', '100\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9169.jpg"
-  },
-  {
-    "id": 9416,
-    "problem_id": 9170,
-    "problem": "<image>As shown in the figure, AB\u2225DG, \u2220ADG+\u2220AEF = 180\u00b0, DG bisects \u2220ADC, if \u2220B = 42\u00b0, then the degree of \u2220AEF is (). A, B, C, D choices are ['148\u00b0', '138\u00b0', '158\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9170.jpg"
-  },
-  {
-    "id": 9417,
-    "problem_id": 9171,
-    "problem": "<image>In rectangle ABCD as shown, AB=3 and the diagonals AC and BD intersect at point O. AE is perpendicular and bisects OB at point E. Find the length of AD.. A, B, C, D choices are ['4', '3\u221a{3}', '5', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9171.jpg"
-  },
-  {
-    "id": 9418,
-    "problem_id": 9172,
-    "problem": "<image>In rectangle ABCD as shown, AB=3 and the diagonals AC and BD intersect at point O. AE is perpendicular and bisects OB at point E. Find the length of AD.. A, B, C, D choices are ['4', '3\u221a{3}', '5', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9172.jpg"
-  },
-  {
-    "id": 9419,
-    "problem_id": 9173,
-    "problem": "<image>In rectangle ABCD as shown, AB=3 and the diagonals AC and BD intersect at point O. AE is perpendicular and bisects OB at point E. Find the length of AD.. A, B, C, D choices are ['4', '3\u221a{3}', '5', '5\u221a{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9173.jpg"
-  },
-  {
-    "id": 9420,
-    "problem_id": 9174,
-    "problem": "<image>In right triangle ABC with \u2220C = 90\u00b0, AD bisects \u2220BAC and intersects BC at point D. If AB = 8 and the area of triangle ABD is 16, then the length of CD is ().. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9174.jpg"
-  },
-  {
-    "id": 9421,
-    "problem_id": 9175,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If \u2220AOD = 30\u00b0, what is the degree measure of \u2220BCD?. A, B, C, D choices are ['100\u00b0', '105\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9175.jpg"
-  },
-  {
-    "id": 9422,
-    "problem_id": 9176,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, and \u2220CDB = 20\u00b0. What is the degree of \u2220ABC? (). A, B, C, D choices are ['60\u00b0', '65\u00b0', '70\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9176.jpg"
-  },
-  {
-    "id": 9425,
-    "problem_id": 9177,
-    "problem": "<image>In triangle ABC, the angle bisector of \u2220ACB intersects AB at point D. Line DE is drawn parallel to BC passing through point D, intersecting AC at point E. If \u2220AED = 80\u00b0, then the degree measure of \u2220CDE is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9177.jpg"
-  },
-  {
-    "id": 9426,
-    "problem_id": 9178,
-    "problem": "<image>In triangle ABC, the angle bisector of \u2220ACB intersects AB at point D. Line DE is drawn parallel to BC passing through point D, intersecting AC at point E. If \u2220AED = 80\u00b0, then the degree measure of \u2220CDE is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9178.jpg"
-  },
-  {
-    "id": 9427,
-    "problem_id": 9179,
-    "problem": "<image>In triangle ABC, AD is the altitude, and AE bisects angle BAC. If angle B is 50\u00b0 and angle C is 80\u00b0, what is the degree measure of angle DAE?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9179.jpg"
-  },
-  {
-    "id": 9429,
-    "problem_id": 9180,
-    "problem": "<image>In triangle ABC, AD is the altitude, and AE bisects angle BAC. If angle B is 50\u00b0 and angle C is 80\u00b0, what is the degree measure of angle DAE?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9180.jpg"
-  },
-  {
-    "id": 9430,
-    "problem_id": 9181,
-    "problem": "<image>In triangle ABC, AD is the altitude, and AE bisects angle BAC. If angle B is 50\u00b0 and angle C is 80\u00b0, what is the degree measure of angle DAE?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9181.jpg"
-  },
-  {
-    "id": 9431,
-    "problem_id": 9182,
-    "problem": "<image>As shown in the diagram, point E is the midpoint of side CD of the square ABCD, and DE = 5. What is the length of BE?. A, B, C, D choices are ['13', '12', '5\u221a{5}', '10\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9182.jpg"
-  },
-  {
-    "id": 9432,
-    "problem_id": 9183,
-    "problem": "<image>As shown in the diagram, point E is the midpoint of side CD of the square ABCD, and DE = 5. What is the length of BE?. A, B, C, D choices are ['13', '12', '5\u221a{5}', '10\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9183.jpg"
-  },
-  {
-    "id": 9433,
-    "problem_id": 9184,
-    "problem": "<image>As shown in the diagram, point E is the midpoint of side CD of the square ABCD, and DE = 5. What is the length of BE?. A, B, C, D choices are ['13', '12', '5\u221a{5}', '10\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9184.jpg"
-  },
-  {
-    "id": 9434,
-    "problem_id": 9185,
-    "problem": "<image>As shown in the diagram, point E is the midpoint of side CD of the square ABCD, and DE = 5. What is the length of BE?. A, B, C, D choices are ['13', '12', '5\u221a{5}', '10\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9185.jpg"
-  },
-  {
-    "id": 9435,
-    "problem_id": 9186,
-    "problem": "<image>As shown in the diagram, point E is the midpoint of side CD of the square ABCD, and DE = 5. What is the length of BE?. A, B, C, D choices are ['13', '12', '5\u221a{5}', '10\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9186.jpg"
-  },
-  {
-    "id": 9436,
-    "problem_id": 9187,
-    "problem": "<image>As shown in the figure, to measure the distance between two points A and B located next to a pond, point O is determined on the ground. Midpoints C and D of OA and OB are taken respectively, and it is found that CD = 10m. The distance between A and B is () meters.. A, B, C, D choices are ['5m', '10m', '20m', '40m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9187.jpg"
-  },
-  {
-    "id": 9437,
-    "problem_id": 9188,
-    "problem": "<image>As shown in the figure, to measure the distance between two points A and B located next to a pond, point O is determined on the ground. Midpoints C and D of OA and OB are taken respectively, and it is found that CD = 10m. The distance between A and B is () meters.. A, B, C, D choices are ['5m', '10m', '20m', '40m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9188.jpg"
-  },
-  {
-    "id": 9438,
-    "problem_id": 9189,
-    "problem": "<image>As shown in the figure, to measure the distance between two points A and B located next to a pond, point O is determined on the ground. Midpoints C and D of OA and OB are taken respectively, and it is found that CD = 10m. The distance between A and B is () meters.. A, B, C, D choices are ['5m', '10m', '20m', '40m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9189.jpg"
-  },
-  {
-    "id": 9439,
-    "problem_id": 9190,
-    "problem": "<image>As shown in the figure, to measure the distance between two points A and B located next to a pond, point O is determined on the ground. Midpoints C and D of OA and OB are taken respectively, and it is found that CD = 10m. The distance between A and B is () meters.. A, B, C, D choices are ['5m', '10m', '20m', '40m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9190.jpg"
-  },
-  {
-    "id": 9440,
-    "problem_id": 9191,
-    "problem": "<image>As shown in the figure, to measure the distance between two points A and B located next to a pond, point O is determined on the ground. Midpoints C and D of OA and OB are taken respectively, and it is found that CD = 10m. The distance between A and B is () meters.. A, B, C, D choices are ['5m', '10m', '20m', '40m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9191.jpg"
-  },
-  {
-    "id": 9441,
-    "problem_id": 9192,
-    "problem": "<image>As shown in the figure, to measure the distance between two points A and B located next to a pond, point O is determined on the ground. Midpoints C and D of OA and OB are taken respectively, and it is found that CD = 10m. The distance between A and B is () meters.. A, B, C, D choices are ['5m', '10m', '20m', '40m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9192.jpg"
-  },
-  {
-    "id": 9442,
-    "problem_id": 9193,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, then the length of OM + OB is () .. A, B, C, D choices are ['7', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9193.jpg"
-  },
-  {
-    "id": 9443,
-    "problem_id": 9194,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, then the length of OM + OB is () .. A, B, C, D choices are ['7', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9194.jpg"
-  },
-  {
-    "id": 9444,
-    "problem_id": 9195,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, then the length of OM + OB is () .. A, B, C, D choices are ['7', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9195.jpg"
-  },
-  {
-    "id": 9445,
-    "problem_id": 9196,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, then the length of OM + OB is () .. A, B, C, D choices are ['7', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9196.jpg"
-  },
-  {
-    "id": 9446,
-    "problem_id": 9197,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, then the length of OM + OB is () .. A, B, C, D choices are ['7', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9197.jpg"
-  },
-  {
-    "id": 9447,
-    "problem_id": 9198,
-    "problem": "<image>As shown in the figure, O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, then the length of OM + OB is () .. A, B, C, D choices are ['7', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9198.jpg"
-  },
-  {
-    "id": 9448,
-    "problem_id": 9199,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8cm\u00b2, what is the area of triangle AEF?. A, B, C, D choices are ['1cm2', '1.5cm2', '2cm2', '4cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9199.jpg"
-  },
-  {
-    "id": 9449,
-    "problem_id": 9200,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8cm\u00b2, what is the area of triangle AEF?. A, B, C, D choices are ['1cm2', '1.5cm2', '2cm2', '4cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9200.jpg"
-  },
-  {
-    "id": 9450,
-    "problem_id": 9201,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8cm\u00b2, what is the area of triangle AEF?. A, B, C, D choices are ['1cm2', '1.5cm2', '2cm2', '4cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9201.jpg"
-  },
-  {
-    "id": 9451,
-    "problem_id": 9202,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9202.jpg"
-  },
-  {
-    "id": 9452,
-    "problem_id": 9203,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9203.jpg"
-  },
-  {
-    "id": 9453,
-    "problem_id": 9204,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9204.jpg"
-  },
-  {
-    "id": 9454,
-    "problem_id": 9205,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9205.jpg"
-  },
-  {
-    "id": 9455,
-    "problem_id": 9206,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9206.jpg"
-  },
-  {
-    "id": 9456,
-    "problem_id": 9207,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9207.jpg"
-  },
-  {
-    "id": 9457,
-    "problem_id": 9208,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and AC, respectively. If the perimeter of triangle ABC is 6, then the perimeter of triangle DEF is (). A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9208.jpg"
-  },
-  {
-    "id": 9458,
-    "problem_id": 9209,
-    "problem": "<image>As shown in the diagram, BC is parallel to DE, \u22201 = 110\u00b0, \u2220AED = 80\u00b0, then the size of \u2220A is (). A, B, C, D choices are ['20\u00b0', '25\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9209.jpg"
-  },
-  {
-    "id": 9459,
-    "problem_id": 9210,
-    "problem": "<image>As shown in the figure, the diagonals of ABCD intersect at point O, and AB = 5. If the perimeter of \u25b3OCD is 23, then the sum of the two diagonals of ABCD is (). A, B, C, D choices are ['18', '28', '36', '46'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9210.jpg"
-  },
-  {
-    "id": 9460,
-    "problem_id": 9211,
-    "problem": "<image>As shown in the figure, the diagonals of ABCD intersect at point O, and AB = 5. If the perimeter of \u25b3OCD is 23, then the sum of the two diagonals of ABCD is (). A, B, C, D choices are ['18', '28', '36', '46'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9211.jpg"
-  },
-  {
-    "id": 9461,
-    "problem_id": 9212,
-    "problem": "<image>As shown in the figure, the diagonals of ABCD intersect at point O, and AB = 5. If the perimeter of \u25b3OCD is 23, then the sum of the two diagonals of ABCD is (). A, B, C, D choices are ['18', '28', '36', '46'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9212.jpg"
-  },
-  {
-    "id": 9462,
-    "problem_id": 9213,
-    "problem": "<image>As shown in the figure, the diagonals of ABCD intersect at point O, and AB = 5. If the perimeter of \u25b3OCD is 23, then the sum of the two diagonals of ABCD is (). A, B, C, D choices are ['18', '28', '36', '46'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9213.jpg"
-  },
-  {
-    "id": 9463,
-    "problem_id": 9214,
-    "problem": "<image>As shown in the figure, the diagonals of ABCD intersect at point O, and AB = 5. If the perimeter of \u25b3OCD is 23, then the sum of the two diagonals of ABCD is (). A, B, C, D choices are ['18', '28', '36', '46'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9214.jpg"
-  },
-  {
-    "id": 9464,
-    "problem_id": 9215,
-    "problem": "<image>As shown in the figure, the diagonals of ABCD intersect at point O, and AB = 5. If the perimeter of \u25b3OCD is 23, then the sum of the two diagonals of ABCD is (). A, B, C, D choices are ['18', '28', '36', '46'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9215.jpg"
-  },
-  {
-    "id": 9465,
-    "problem_id": 9216,
-    "problem": "<image>As shown in the figure, the side length of diamond ABCD is 5cm. P is a point on diagonal BD, and PH is perpendicular to AB at point H, with PH=2cm. The area of triangle PBC is (). A, B, C, D choices are ['8', '7', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9216.jpg"
-  },
-  {
-    "id": 9466,
-    "problem_id": 9217,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8cm2, what is the area of triangle AEF?. A, B, C, D choices are ['1cm2', '1.5cm2', '2cm2', '4cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9217.jpg"
-  },
-  {
-    "id": 9467,
-    "problem_id": 9218,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8cm2, what is the area of triangle AEF?. A, B, C, D choices are ['1cm2', '1.5cm2', '2cm2', '4cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9218.jpg"
-  },
-  {
-    "id": 9468,
-    "problem_id": 9219,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively. If the area of triangle ABC is 8cm2, what is the area of triangle AEF?. A, B, C, D choices are ['1cm2', '1.5cm2', '2cm2', '4cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9219.jpg"
-  },
-  {
-    "id": 9469,
-    "problem_id": 9220,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9220.jpg"
-  },
-  {
-    "id": 9470,
-    "problem_id": 9221,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9221.jpg"
-  },
-  {
-    "id": 9471,
-    "problem_id": 9222,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9222.jpg"
-  },
-  {
-    "id": 9472,
-    "problem_id": 9223,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9223.jpg"
-  },
-  {
-    "id": 9473,
-    "problem_id": 9224,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9224.jpg"
-  },
-  {
-    "id": 9474,
-    "problem_id": 9225,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9225.jpg"
-  },
-  {
-    "id": 9475,
-    "problem_id": 9226,
-    "problem": "<image>In the figure, quadrilateral ABCD is a diamond shape, AC=8cm, DB=6cm, DH\u22a5AB at H, then DH equals (). A, B, C, D choices are ['3.6', '4.8', '5', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9226.jpg"
-  },
-  {
-    "id": 9476,
-    "problem_id": 9227,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of a circle. The extension lines of AB and DC intersect at point P. If C is the midpoint of PD and PD = 6, PB = 2, then what is the length of AB?. A, B, C, D choices are ['9', '7', '3', '4.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9227.jpg"
-  },
-  {
-    "id": 9477,
-    "problem_id": 9228,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of regular hexagon ABCDEF, and point P is on \u2299O (P is not coincident with A or B). What is the degree measure of \u2220APB? (). A, B, C, D choices are ['60\u00b0', '120\u00b0', '30\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9228.jpg"
-  },
-  {
-    "id": 9478,
-    "problem_id": 9229,
-    "problem": "<image>In the figure, AB is a chord of circle O. AC is tangent to circle O at point A. Connect OA and OB. If \u2220O = 120\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['75\u00b0', '70\u00b0', '65\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9229.jpg"
-  },
-  {
-    "id": 9479,
-    "problem_id": 9230,
-    "problem": "<image>In the figure, AB is a chord of circle O. AC is tangent to circle O at point A. Connect OA and OB. If \u2220O = 120\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['75\u00b0', '70\u00b0', '65\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9230.jpg"
-  },
-  {
-    "id": 9480,
-    "problem_id": 9231,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rhombus ABCD intersect at point O, and E is the midpoint of DC. If the perimeter of the rhombus is 16, what is the length of OE?. A, B, C, D choices are ['2', '1', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9231.jpg"
-  },
-  {
-    "id": 9481,
-    "problem_id": 9232,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rhombus ABCD intersect at point O, and E is the midpoint of DC. If the perimeter of the rhombus is 16, what is the length of OE?. A, B, C, D choices are ['2', '1', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9232.jpg"
-  },
-  {
-    "id": 9482,
-    "problem_id": 9233,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rhombus ABCD intersect at point O, and E is the midpoint of DC. If the perimeter of the rhombus is 16, what is the length of OE?. A, B, C, D choices are ['2', '1', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9233.jpg"
-  },
-  {
-    "id": 9483,
-    "problem_id": 9234,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rhombus ABCD intersect at point O, and E is the midpoint of DC. If the perimeter of the rhombus is 16, what is the length of OE?. A, B, C, D choices are ['2', '1', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9234.jpg"
-  },
-  {
-    "id": 9484,
-    "problem_id": 9235,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of rhombus ABCD intersect at point O, and E is the midpoint of DC. If the perimeter of the rhombus is 16, what is the length of OE?. A, B, C, D choices are ['2', '1', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9235.jpg"
-  },
-  {
-    "id": 9485,
-    "problem_id": 9236,
-    "problem": "<image>As shown in the figure, in right triangle ABC, where \u2220C=90\u00b0, CD is the altitude on the hypotenuse AB. If AD=2 and BD=6, what is the length of AC?. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9236.jpg"
-  },
-  {
-    "id": 9486,
-    "problem_id": 9237,
-    "problem": "<image>As shown in the figure, in right triangle ABC, where \u2220C=90\u00b0, CD is the altitude on the hypotenuse AB. If AD=2 and BD=6, what is the length of AC?. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9237.jpg"
-  },
-  {
-    "id": 9487,
-    "problem_id": 9238,
-    "problem": "<image>As shown in the figure, in right triangle ABC, where \u2220C=90\u00b0, CD is the altitude on the hypotenuse AB. If AD=2 and BD=6, what is the length of AC?. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9238.jpg"
-  },
-  {
-    "id": 9488,
-    "problem_id": 9239,
-    "problem": "<image>As shown in the figure, in right triangle ABC, where \u2220C=90\u00b0, CD is the altitude on the hypotenuse AB. If AD=2 and BD=6, what is the length of AC?. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9239.jpg"
-  },
-  {
-    "id": 9489,
-    "problem_id": 9240,
-    "problem": "<image>As shown in the figure, in right triangle ABC, where \u2220C=90\u00b0, CD is the altitude on the hypotenuse AB. If AD=2 and BD=6, what is the length of AC?. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9240.jpg"
-  },
-  {
-    "id": 9490,
-    "problem_id": 9241,
-    "problem": "<image>As shown in the figure, in right triangle ABC, where \u2220C=90\u00b0, CD is the altitude on the hypotenuse AB. If AD=2 and BD=6, what is the length of AC?. A, B, C, D choices are ['4', '5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9241.jpg"
-  },
-  {
-    "id": 9491,
-    "problem_id": 9242,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9242.jpg"
-  },
-  {
-    "id": 9492,
-    "problem_id": 9243,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9243.jpg"
-  },
-  {
-    "id": 9493,
-    "problem_id": 9244,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9244.jpg"
-  },
-  {
-    "id": 9494,
-    "problem_id": 9245,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9245.jpg"
-  },
-  {
-    "id": 9495,
-    "problem_id": 9246,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9246.jpg"
-  },
-  {
-    "id": 9496,
-    "problem_id": 9247,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9247.jpg"
-  },
-  {
-    "id": 9497,
-    "problem_id": 9248,
-    "problem": "<image>\"The \"Zhao Shuangxian Diagram\" cleverly uses the relationship between areas to prove the Pythagorean theorem, which is a pride of ancient Chinese mathematics. The \"Zhao Shuangxian Diagram\" shown in the figure is made up of four identical right-angled triangles and a small square to form a large square. Let the longer leg of the right-angled triangle be a and the shorter leg be b. If (a+b)^2=26 and the area of the large square is 17, then what is the area of the small square?\". A, B, C, D choices are ['6', '7', '8', '9'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9248.jpg"
-  },
-  {
-    "id": 9498,
-    "problem_id": 9249,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9249.jpg"
-  },
-  {
-    "id": 9499,
-    "problem_id": 9250,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9250.jpg"
-  },
-  {
-    "id": 9500,
-    "problem_id": 9251,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9251.jpg"
-  },
-  {
-    "id": 9501,
-    "problem_id": 9252,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9252.jpg"
-  },
-  {
-    "id": 9502,
-    "problem_id": 9253,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9253.jpg"
-  },
-  {
-    "id": 9503,
-    "problem_id": 9254,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9254.jpg"
-  },
-  {
-    "id": 9504,
-    "problem_id": 9255,
-    "problem": "<image>As shown in the figure, the perimeter of parallelogram ABCD is 40, and the perimeter of triangle BOC is 10 more than that of triangle AOB. What is the length of BC?. A, B, C, D choices are ['20', '5', '10', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9255.jpg"
-  },
-  {
-    "id": 9505,
-    "problem_id": 9256,
-    "problem": "<image>As shown in the diagram, \u25b3ABC is congruent to \u25b3DEF, BC = 12, EC = 7, what is the length of CF?. A, B, C, D choices are ['5', '6', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9256.jpg"
-  },
-  {
-    "id": 9506,
-    "problem_id": 9257,
-    "problem": "<image>As shown in the diagram, \u25b3ABC is congruent to \u25b3DEF, BC = 12, EC = 7, what is the length of CF?. A, B, C, D choices are ['5', '6', '7', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9257.jpg"
-  },
-  {
-    "id": 9507,
-    "problem_id": 9258,
-    "problem": "<image>As shown in the figure, it is known that the diagonals of the rhombus ABCD intersect at point O, DB = 6, and AD = 5. The area of the rhombus ABCD is ().. A, B, C, D choices are ['20', '24', '30', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9258.jpg"
-  },
-  {
-    "id": 9508,
-    "problem_id": 9259,
-    "problem": "<image>As shown in the figure, it is known that the diagonals of the rhombus ABCD intersect at point O, DB = 6, and AD = 5. The area of the rhombus ABCD is ().. A, B, C, D choices are ['20', '24', '30', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9259.jpg"
-  },
-  {
-    "id": 9509,
-    "problem_id": 9260,
-    "problem": "<image>As shown in the figure, it is known that the diagonals of the rhombus ABCD intersect at point O, DB = 6, and AD = 5. The area of the rhombus ABCD is ().. A, B, C, D choices are ['20', '24', '30', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9260.jpg"
-  },
-  {
-    "id": 9510,
-    "problem_id": 9261,
-    "problem": "<image>As shown in the figure, it is known that the diagonals of the rhombus ABCD intersect at point O, DB = 6, and AD = 5. The area of the rhombus ABCD is ().. A, B, C, D choices are ['20', '24', '30', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9261.jpg"
-  },
-  {
-    "id": 9511,
-    "problem_id": 9262,
-    "problem": "<image>As shown in the figure, it is known that the diagonals of the rhombus ABCD intersect at point O, DB = 6, and AD = 5. The area of the rhombus ABCD is ().. A, B, C, D choices are ['20', '24', '30', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9262.jpg"
-  },
-  {
-    "id": 9512,
-    "problem_id": 9263,
-    "problem": "<image>In parallelogram ABCD, AB is the diameter of circle O. DC is tangent to circle O at point E, and point F is the intersection of AD and circle O. Given AB=12 and angle C=60 degrees, what is the length of arc FE?. A, B, C, D choices are ['6\u03c0', '3\u03c0', '2\u03c0', '\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9263.jpg"
-  },
-  {
-    "id": 9513,
-    "problem_id": 9264,
-    "problem": "<image>As shown in the figure, a strip of paper with parallel opposite edges is folded twice, with creases at AB and CD respectively. If CD is parallel to BE and angle 1 is 30 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9264.jpg"
-  },
-  {
-    "id": 9514,
-    "problem_id": 9265,
-    "problem": "<image>In triangle ABC, AD is the altitude of BC, and CE is the median of AB. If CD = AD = 2, what is the area of triangle DCE?. A, B, C, D choices are ['4', '3', '2', 'l'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9265.jpg"
-  },
-  {
-    "id": 9515,
-    "problem_id": 9266,
-    "problem": "<image>As shown in the figure, in right triangle CBD, if \u2220ABC = 36\u00b0, then what is the degree measure of \u2220DFE?. A, B, C, D choices are ['36\u00b0', '64\u00b0', '54\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9266.jpg"
-  },
-  {
-    "id": 9516,
-    "problem_id": 9267,
-    "problem": "<image>As shown in the figure, in right triangle CBD, if \u2220ABC = 36\u00b0, then what is the degree measure of \u2220DFE?. A, B, C, D choices are ['36\u00b0', '64\u00b0', '54\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9267.jpg"
-  },
-  {
-    "id": 9517,
-    "problem_id": 9268,
-    "problem": "<image>As shown in the figure, in right triangle CBD, if \u2220ABC = 36\u00b0, then what is the degree measure of \u2220DFE?. A, B, C, D choices are ['36\u00b0', '64\u00b0', '54\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9268.jpg"
-  },
-  {
-    "id": 9518,
-    "problem_id": 9269,
-    "problem": "<image>As shown in the figure, in right triangle CBD, if \u2220ABC = 36\u00b0, then what is the degree measure of \u2220DFE?. A, B, C, D choices are ['36\u00b0', '64\u00b0', '54\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9269.jpg"
-  },
-  {
-    "id": 9519,
-    "problem_id": 9270,
-    "problem": "<image>As shown in the figure, in right triangle CBD, if \u2220ABC = 36\u00b0, then what is the degree measure of \u2220DFE?. A, B, C, D choices are ['36\u00b0', '64\u00b0', '54\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9270.jpg"
-  },
-  {
-    "id": 9520,
-    "problem_id": 9271,
-    "problem": "<image>In triangle ABC, AB=AC, M and N are the midpoints of AB and AC, and D and E are points on BC. DN and EM are connected. If AB=13cm, BC=10cm, and DE=5cm, what is the area of the shaded region?. A, B, C, D choices are ['25', '35', '30', '42'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9271.jpg"
-  },
-  {
-    "id": 9521,
-    "problem_id": 9272,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9272.jpg"
-  },
-  {
-    "id": 9522,
-    "problem_id": 9273,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9273.jpg"
-  },
-  {
-    "id": 9523,
-    "problem_id": 9274,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9274.jpg"
-  },
-  {
-    "id": 9524,
-    "problem_id": 9275,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9275.jpg"
-  },
-  {
-    "id": 9525,
-    "problem_id": 9276,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9276.jpg"
-  },
-  {
-    "id": 9527,
-    "problem_id": 9277,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9277.jpg"
-  },
-  {
-    "id": 9528,
-    "problem_id": 9278,
-    "problem": "<image>As shown in the figure, the highways AC and BC are perpendicular to each other. The midpoint M of the highway AB is separated from point C by a lake. If the length of AB is measured to be 2.6km, what is the distance between points M and C? (). A, B, C, D choices are ['0.8km', '1.2km', '1.3km', '5.2km'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9278.jpg"
-  },
-  {
-    "id": 9529,
-    "problem_id": 9279,
-    "problem": "<image>There is a right triangle board DEF placed on triangle ABC, with the two legs DE and DF passing through points B and C respectively. In triangle ABC, \u2220DBA + \u2220DCA = 45\u00b0. What is the degree measure of \u2220A?. A, B, C, D choices are ['40\u00b0', '44\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9279.jpg"
-  },
-  {
-    "id": 9530,
-    "problem_id": 9280,
-    "problem": "<image>In the diagram, AD is the angle bisector of the isosceles right triangle ABC. If AD = 4, then CD is equal to ().. A, B, C, D choices are ['8', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9280.jpg"
-  },
-  {
-    "id": 9531,
-    "problem_id": 9281,
-    "problem": "<image>In the diagram, AD is the angle bisector of the isosceles right triangle ABC. If AD = 4, then CD is equal to ().. A, B, C, D choices are ['8', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9281.jpg"
-  },
-  {
-    "id": 9532,
-    "problem_id": 9282,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and ray AN intersects CD at point M. If \u2220A = 40\u00b0, then \u2220CMN is equal to ().. A, B, C, D choices are ['120\u00b0', '130\u00b0', '140\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9282.jpg"
-  },
-  {
-    "id": 9533,
-    "problem_id": 9283,
-    "problem": "<image>As shown in the figure, PA, PB, and circle O are tangent to points A, B, and P respectively. PA = 2, \u2220P = 60\u00b0, then AB = ().. A, B, C, D choices are ['\u221a{3}', '2', '2\u221a{3}', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9283.jpg"
-  },
-  {
-    "id": 9534,
-    "problem_id": 9284,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB=90\u00b0, \u2220B=15\u00b0, DE is perpendicular bisector of AB, intersecting BC at point E, AC=3cm, then BE equals (). A, B, C, D choices are ['6cm', '5cm', '4cm', '3cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9284.jpg"
-  },
-  {
-    "id": 9535,
-    "problem_id": 9285,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB=90\u00b0, \u2220B=15\u00b0, DE is perpendicular bisector of AB, intersecting BC at point E, AC=3cm, then BE equals (). A, B, C, D choices are ['6cm', '5cm', '4cm', '3cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9285.jpg"
-  },
-  {
-    "id": 9536,
-    "problem_id": 9286,
-    "problem": "<image>As shown in the figure, chord AB of circle O is perpendicular and bisects radius OC. AE is a tangent to circle O, intersecting the extension of OC at point E. What is the degree measure of angle CAE? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9286.jpg"
-  },
-  {
-    "id": 9537,
-    "problem_id": 9287,
-    "problem": "<image>As shown in the figure, chord AB of circle O is perpendicular and bisects radius OC. AE is a tangent to circle O, intersecting the extension of OC at point E. What is the degree measure of angle CAE? (). A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9287.jpg"
-  },
-  {
-    "id": 9538,
-    "problem_id": 9288,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9288.jpg"
-  },
-  {
-    "id": 9539,
-    "problem_id": 9289,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9289.jpg"
-  },
-  {
-    "id": 9540,
-    "problem_id": 9290,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9290.jpg"
-  },
-  {
-    "id": 9541,
-    "problem_id": 9291,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9291.jpg"
-  },
-  {
-    "id": 9542,
-    "problem_id": 9292,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9292.jpg"
-  },
-  {
-    "id": 9543,
-    "problem_id": 9293,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9293.jpg"
-  },
-  {
-    "id": 9544,
-    "problem_id": 9294,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9294.jpg"
-  },
-  {
-    "id": 9545,
-    "problem_id": 9295,
-    "problem": "<image>In the rhombus ABCD, diagonal AC and BD intersect at point O, point E is the midpoint of side AB, and OE is connected. If BD = 6 and AC = 8, what is the length of segment OE?. A, B, C, D choices are ['2.5', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9295.jpg"
-  },
-  {
-    "id": 9548,
-    "problem_id": 9296,
-    "problem": "<image>As shown in the figure, line l1 is parallel to line l2, and lines l1 and l2 are intersected by line l3. If \u22201 = 54\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['36\u00b0', '46\u00b0', '126\u00b0', '136\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9296.jpg"
-  },
-  {
-    "id": 9549,
-    "problem_id": 9297,
-    "problem": "<image>As shown in the diagram, if \u22201 = 100\u00b0 and DF is parallel to AB, then what is the measure of \u2220D?. A, B, C, D choices are ['70\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9297.jpg"
-  },
-  {
-    "id": 9551,
-    "problem_id": 9298,
-    "problem": "<image>In the figure, the diagonals AC and BD of diamond-shaped ABCD intersect at point O, and H is the midpoint of side AD. If the perimeter of diamond-shaped ABCD is 32, then the length of OH is equal to ().. A, B, C, D choices are ['4', '8', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9298.jpg"
-  },
-  {
-    "id": 9552,
-    "problem_id": 9299,
-    "problem": "<image>In the figure, the diagonals AC and BD of diamond-shaped ABCD intersect at point O, and H is the midpoint of side AD. If the perimeter of diamond-shaped ABCD is 32, then the length of OH is equal to ().. A, B, C, D choices are ['4', '8', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9299.jpg"
-  },
-  {
-    "id": 9553,
-    "problem_id": 9300,
-    "problem": "<image>In the figure, the diagonals AC and BD of diamond-shaped ABCD intersect at point O, and H is the midpoint of side AD. If the perimeter of diamond-shaped ABCD is 32, then the length of OH is equal to ().. A, B, C, D choices are ['4', '8', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9300.jpg"
-  },
-  {
-    "id": 9554,
-    "problem_id": 9301,
-    "problem": "<image>In the figure, the diagonals AC and BD of diamond-shaped ABCD intersect at point O, and H is the midpoint of side AD. If the perimeter of diamond-shaped ABCD is 32, then the length of OH is equal to ().. A, B, C, D choices are ['4', '8', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9301.jpg"
-  },
-  {
-    "id": 9555,
-    "problem_id": 9302,
-    "problem": "<image>In the figure, the diagonals AC and BD of diamond-shaped ABCD intersect at point O, and H is the midpoint of side AD. If the perimeter of diamond-shaped ABCD is 32, then the length of OH is equal to ().. A, B, C, D choices are ['4', '8', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9302.jpg"
-  },
-  {
-    "id": 9556,
-    "problem_id": 9303,
-    "problem": "<image>In the figure, the diagonals AC and BD of diamond-shaped ABCD intersect at point O, and H is the midpoint of side AD. If the perimeter of diamond-shaped ABCD is 32, then the length of OH is equal to ().. A, B, C, D choices are ['4', '8', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9303.jpg"
-  },
-  {
-    "id": 9557,
-    "problem_id": 9304,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9304.jpg"
-  },
-  {
-    "id": 9558,
-    "problem_id": 9305,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9305.jpg"
-  },
-  {
-    "id": 9559,
-    "problem_id": 9306,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9306.jpg"
-  },
-  {
-    "id": 9560,
-    "problem_id": 9307,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9307.jpg"
-  },
-  {
-    "id": 9561,
-    "problem_id": 9308,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9308.jpg"
-  },
-  {
-    "id": 9562,
-    "problem_id": 9309,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9309.jpg"
-  },
-  {
-    "id": 9563,
-    "problem_id": 9310,
-    "problem": "<image>In right triangle ABC as shown, with \u2220C = 90\u00b0 and AB = 10cm, point D is the midpoint of AB. What is the length of CD? (). A, B, C, D choices are ['7cm', '6cm', '5cm', '4cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9310.jpg"
-  },
-  {
-    "id": 9564,
-    "problem_id": 9311,
-    "problem": "<image>In the diamond-shaped ABCD, \u2220ABC = 50\u00b0, diagonal AC and BD intersect at point O, E is the midpoint of CD, and OE is connected. What is the degree measure of \u2220AOE? (). A, B, C, D choices are ['110\u00b0', '112\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9311.jpg"
-  },
-  {
-    "id": 9565,
-    "problem_id": 9312,
-    "problem": "<image>As shown in the figure, \u2220AOB is a straight angle, \u2220AOC = 40\u00b0, \u2220BOD = 26\u00b0, OM and ON are the bisectors of \u2220AOC and \u2220BOD, respectively. What is the measure of \u2220MON?. A, B, C, D choices are ['66\u00b0', '114\u00b0', '147\u00b0', '170\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9312.jpg"
-  },
-  {
-    "id": 9566,
-    "problem_id": 9313,
-    "problem": "<image>As shown in the figure, \u2220AOB is a straight angle, \u2220AOC = 40\u00b0, \u2220BOD = 26\u00b0, OM and ON are the bisectors of \u2220AOC and \u2220BOD, respectively. What is the measure of \u2220MON?. A, B, C, D choices are ['66\u00b0', '114\u00b0', '147\u00b0', '170\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9313.jpg"
-  },
-  {
-    "id": 9567,
-    "problem_id": 9314,
-    "problem": "<image>As shown in the figure, OA = OB = OC = OD, and \u2220BOC + \u2220AOD = 180\u00b0. If BC = 4 and AD = 6, what is the length of OA?. A, B, C, D choices are ['\u221a{10}', '2', '\u221a{13}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9314.jpg"
-  },
-  {
-    "id": 9568,
-    "problem_id": 9315,
-    "problem": "<image>As shown in the figure, OA = OB = OC = OD, and \u2220BOC + \u2220AOD = 180\u00b0. If BC = 4 and AD = 6, what is the length of OA?. A, B, C, D choices are ['\u221a{10}', '2', '\u221a{13}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9315.jpg"
-  },
-  {
-    "id": 9569,
-    "problem_id": 9316,
-    "problem": "<image>As shown in the figure, OA = OB = OC = OD, and \u2220BOC + \u2220AOD = 180\u00b0. If BC = 4 and AD = 6, what is the length of OA?. A, B, C, D choices are ['\u221a{10}', '2', '\u221a{13}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9316.jpg"
-  },
-  {
-    "id": 9570,
-    "problem_id": 9317,
-    "problem": "<image>As shown in the figure, OA = OB = OC = OD, and \u2220BOC + \u2220AOD = 180\u00b0. If BC = 4 and AD = 6, what is the length of OA?. A, B, C, D choices are ['\u221a{10}', '2', '\u221a{13}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9317.jpg"
-  },
-  {
-    "id": 9571,
-    "problem_id": 9318,
-    "problem": "<image>As shown in the figure, OA = OB = OC = OD, and \u2220BOC + \u2220AOD = 180\u00b0. If BC = 4 and AD = 6, what is the length of OA?. A, B, C, D choices are ['\u221a{10}', '2', '\u221a{13}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9318.jpg"
-  },
-  {
-    "id": 9572,
-    "problem_id": 9319,
-    "problem": "<image>As shown in the figure, OA = OB = OC = OD, and \u2220BOC + \u2220AOD = 180\u00b0. If BC = 4 and AD = 6, what is the length of OA?. A, B, C, D choices are ['\u221a{10}', '2', '\u221a{13}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9319.jpg"
-  },
-  {
-    "id": 9573,
-    "problem_id": 9320,
-    "problem": "<image>As shown in the figure, the lines AB and CD intersect at point O. OE is perpendicular to AB at O, and OF bisects angle DOE. If angle AOC is 32 degrees, then what is the degree measure of angle AOF?. A, B, C, D choices are ['119\u00b0', '121\u00b0', '122\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9320.jpg"
-  },
-  {
-    "id": 9574,
-    "problem_id": 9321,
-    "problem": "<image>As shown in the figure, the lines AB and CD intersect at point O. OE is perpendicular to AB at O, and OF bisects angle DOE. If angle AOC is 32 degrees, then what is the degree measure of angle AOF?. A, B, C, D choices are ['119\u00b0', '121\u00b0', '122\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9321.jpg"
-  },
-  {
-    "id": 9575,
-    "problem_id": 9322,
-    "problem": "<image>As shown in the figure, the lines AB and CD intersect at point O. OE is perpendicular to AB at O, and OF bisects angle DOE. If angle AOC is 32 degrees, then what is the degree measure of angle AOF?. A, B, C, D choices are ['119\u00b0', '121\u00b0', '122\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9322.jpg"
-  },
-  {
-    "id": 9578,
-    "problem_id": 9323,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220ACB=90\u00b0. D and E are the midpoints of sides AB and AC, respectively. Extend BC to point F such that CF=0.5\u00d7BC. If EF=5, what is the length of AB?. A, B, C, D choices are ['10', '12', '15', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9323.jpg"
-  },
-  {
-    "id": 9579,
-    "problem_id": 9324,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220ACB=90\u00b0. D and E are the midpoints of sides AB and AC, respectively. Extend BC to point F such that CF=0.5\u00d7BC. If EF=5, what is the length of AB?. A, B, C, D choices are ['10', '12', '15', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9324.jpg"
-  },
-  {
-    "id": 9580,
-    "problem_id": 9325,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220ACB=90\u00b0. D and E are the midpoints of sides AB and AC, respectively. Extend BC to point F such that CF=0.5\u00d7BC. If EF=5, what is the length of AB?. A, B, C, D choices are ['10', '12', '15', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9325.jpg"
-  },
-  {
-    "id": 9581,
-    "problem_id": 9326,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220ACB=90\u00b0. D and E are the midpoints of sides AB and AC, respectively. Extend BC to point F such that CF=0.5\u00d7BC. If EF=5, what is the length of AB?. A, B, C, D choices are ['10', '12', '15', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9326.jpg"
-  },
-  {
-    "id": 9582,
-    "problem_id": 9327,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220ACB=90\u00b0. D and E are the midpoints of sides AB and AC, respectively. Extend BC to point F such that CF=0.5\u00d7BC. If EF=5, what is the length of AB?. A, B, C, D choices are ['10', '12', '15', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9327.jpg"
-  },
-  {
-    "id": 9583,
-    "problem_id": 9328,
-    "problem": "<image>In triangle ABC as shown in the figure, where \u2220C = 90\u00b0, AB = 5, AC = 4, which of the following trigonometric functions is correct? (). A, B, C, D choices are ['sinA\uff1d0.8', 'tanA\uff1d\\\\frac{4}{3}', 'cosA\uff1d0.8', 'tanB\uff1d0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9328.jpg"
-  },
-  {
-    "id": 9584,
-    "problem_id": 9329,
-    "problem": "<image>In triangle ABC as shown in the figure, where \u2220C = 90\u00b0, AB = 5, AC = 4, which of the following trigonometric functions is correct? (). A, B, C, D choices are ['sinA\uff1d0.8', 'tanA\uff1d\\\\frac{4}{3}', 'cosA\uff1d0.8', 'tanB\uff1d0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9329.jpg"
-  },
-  {
-    "id": 9585,
-    "problem_id": 9330,
-    "problem": "<image>In triangle ABC as shown in the figure, where \u2220C = 90\u00b0, AB = 5, AC = 4, which of the following trigonometric functions is correct? (). A, B, C, D choices are ['sinA\uff1d0.8', 'tanA\uff1d\\\\frac{4}{3}', 'cosA\uff1d0.8', 'tanB\uff1d0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9330.jpg"
-  },
-  {
-    "id": 9586,
-    "problem_id": 9331,
-    "problem": "<image>In triangle ABC as shown in the figure, where \u2220C = 90\u00b0, AB = 5, AC = 4, which of the following trigonometric functions is correct? (). A, B, C, D choices are ['sinA\uff1d0.8', 'tanA\uff1d\\\\frac{4}{3}', 'cosA\uff1d0.8', 'tanB\uff1d0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9331.jpg"
-  },
-  {
-    "id": 9587,
-    "problem_id": 9332,
-    "problem": "<image>In triangle ABC as shown in the figure, where \u2220C = 90\u00b0, AB = 5, AC = 4, which of the following trigonometric functions is correct? (). A, B, C, D choices are ['sinA\uff1d0.8', 'tanA\uff1d\\\\frac{4}{3}', 'cosA\uff1d0.8', 'tanB\uff1d0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9332.jpg"
-  },
-  {
-    "id": 9588,
-    "problem_id": 9333,
-    "problem": "<image>In triangle ABC as shown in the figure, where \u2220C = 90\u00b0, AB = 5, AC = 4, which of the following trigonometric functions is correct? (). A, B, C, D choices are ['sinA\uff1d0.8', 'tanA\uff1d\\\\frac{4}{3}', 'cosA\uff1d0.8', 'tanB\uff1d0.75'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9333.jpg"
-  },
-  {
-    "id": 9589,
-    "problem_id": 9334,
-    "problem": "<image>In the figure, AD is the angle bisector of isosceles triangle ABC, and BC=10. Then CD equals (). A, B, C, D choices are ['10', '6', '5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9334.jpg"
-  },
-  {
-    "id": 9590,
-    "problem_id": 9335,
-    "problem": "<image>In the figure, AD is the angle bisector of isosceles triangle ABC, and BC=10. Then CD equals (). A, B, C, D choices are ['10', '6', '5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9335.jpg"
-  },
-  {
-    "id": 9591,
-    "problem_id": 9336,
-    "problem": "<image>In the figure, AD is the angle bisector of isosceles triangle ABC, and BC=10. Then CD equals (). A, B, C, D choices are ['10', '6', '5', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9336.jpg"
-  },
-  {
-    "id": 9593,
-    "problem_id": 9337,
-    "problem": "<image>As shown in the diagram, \u25b3DEF is obtained by translating \u25b3ABC in the direction of ray AB. If \u2220A = 33\u00b0, what is the degree of \u2220EDF? (). A, B, C, D choices are ['33\u00b0', '80\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9337.jpg"
-  },
-  {
-    "id": 9594,
-    "problem_id": 9338,
-    "problem": "<image>As shown in the diagram, \u25b3DEF is obtained by translating \u25b3ABC in the direction of ray AB. If \u2220A = 33\u00b0, what is the degree of \u2220EDF? (). A, B, C, D choices are ['33\u00b0', '80\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9338.jpg"
-  },
-  {
-    "id": 9595,
-    "problem_id": 9339,
-    "problem": "<image>As shown in the diagram, \u25b3DEF is obtained by translating \u25b3ABC in the direction of ray AB. If \u2220A = 33\u00b0, what is the degree of \u2220EDF? (). A, B, C, D choices are ['33\u00b0', '80\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9339.jpg"
-  },
-  {
-    "id": 9596,
-    "problem_id": 9340,
-    "problem": "<image>As shown in the diagram, \u25b3DEF is obtained by translating \u25b3ABC in the direction of ray AB. If \u2220A = 33\u00b0, what is the degree of \u2220EDF? (). A, B, C, D choices are ['33\u00b0', '80\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9340.jpg"
-  },
-  {
-    "id": 9597,
-    "problem_id": 9341,
-    "problem": "<image>As shown in the diagram, \u25b3DEF is obtained by translating \u25b3ABC in the direction of ray AB. If \u2220A = 33\u00b0, what is the degree of \u2220EDF? (). A, B, C, D choices are ['33\u00b0', '80\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9341.jpg"
-  },
-  {
-    "id": 9598,
-    "problem_id": 9342,
-    "problem": "<image>As shown in the diagram, \u25b3DEF is obtained by translating \u25b3ABC in the direction of ray AB. If \u2220A = 33\u00b0, what is the degree of \u2220EDF? (). A, B, C, D choices are ['33\u00b0', '80\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9342.jpg"
-  },
-  {
-    "id": 9599,
-    "problem_id": 9343,
-    "problem": "<image>In the figure, AB\u2225CD, \u22201 = 62\u00b0, FG bisects \u2220EFD. What is the degree measure of \u2220FGB?. A, B, C, D choices are ['149\u00b0', '118\u00b0', '119\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9343.jpg"
-  },
-  {
-    "id": 9600,
-    "problem_id": 9344,
-    "problem": "<image>In the figure, AB\u2225CD, \u22201 = 62\u00b0, FG bisects \u2220EFD. What is the degree measure of \u2220FGB?. A, B, C, D choices are ['149\u00b0', '118\u00b0', '119\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9344.jpg"
-  },
-  {
-    "id": 9601,
-    "problem_id": 9345,
-    "problem": "<image>In the figure, AB\u2225CD, \u22201 = 62\u00b0, FG bisects \u2220EFD. What is the degree measure of \u2220FGB?. A, B, C, D choices are ['149\u00b0', '118\u00b0', '119\u00b0', '114\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9345.jpg"
-  },
-  {
-    "id": 9602,
-    "problem_id": 9346,
-    "problem": "<image>In triangle ABC as shown, where angle ACB is 90 degrees and angle B is 60 degrees, and CD is parallel to AB, what is the measure of angle 1?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9346.jpg"
-  },
-  {
-    "id": 9603,
-    "problem_id": 9347,
-    "problem": "<image>In triangle ABC as shown, where angle ACB is 90 degrees and angle B is 60 degrees, and CD is parallel to AB, what is the measure of angle 1?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9347.jpg"
-  },
-  {
-    "id": 9604,
-    "problem_id": 9348,
-    "problem": "<image>In triangle ABC as shown, where angle ACB is 90 degrees and angle B is 60 degrees, and CD is parallel to AB, what is the measure of angle 1?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9348.jpg"
-  },
-  {
-    "id": 9605,
-    "problem_id": 9349,
-    "problem": "<image>In triangle ABC as shown, where angle ACB is 90 degrees and angle B is 60 degrees, and CD is parallel to AB, what is the measure of angle 1?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9349.jpg"
-  },
-  {
-    "id": 9606,
-    "problem_id": 9350,
-    "problem": "<image>In the diagram, AD is the median of equilateral triangle ABC, point E is on AC, and AE = AD. What is the measure of angle EDC? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9350.jpg"
-  },
-  {
-    "id": 9607,
-    "problem_id": 9351,
-    "problem": "<image>In the diagram, AD is the median of equilateral triangle ABC, point E is on AC, and AE = AD. What is the measure of angle EDC? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9351.jpg"
-  },
-  {
-    "id": 9608,
-    "problem_id": 9352,
-    "problem": "<image>In the diagram, AD is the median of equilateral triangle ABC, point E is on AC, and AE = AD. What is the measure of angle EDC? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9352.jpg"
-  },
-  {
-    "id": 9609,
-    "problem_id": 9353,
-    "problem": "<image>In the diagram, AD is the median of equilateral triangle ABC, point E is on AC, and AE = AD. What is the measure of angle EDC? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9353.jpg"
-  },
-  {
-    "id": 9610,
-    "problem_id": 9354,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9354.jpg"
-  },
-  {
-    "id": 9611,
-    "problem_id": 9355,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9355.jpg"
-  },
-  {
-    "id": 9612,
-    "problem_id": 9356,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9356.jpg"
-  },
-  {
-    "id": 9613,
-    "problem_id": 9357,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9357.jpg"
-  },
-  {
-    "id": 9614,
-    "problem_id": 9358,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9358.jpg"
-  },
-  {
-    "id": 9615,
-    "problem_id": 9359,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9359.jpg"
-  },
-  {
-    "id": 9616,
-    "problem_id": 9360,
-    "problem": "<image>As shown in the figure, P is a point outside the circle O with a radius of 3. PA is tangent to the circle O at point A. If AP = 4, then OP = ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9360.jpg"
-  },
-  {
-    "id": 9617,
-    "problem_id": 9361,
-    "problem": "<image>As shown in the figure, lines a and b are intersected by line c. Line a is parallel to line b and angle 1 is 120\u00b0. What is the degree measure of angle 2? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9361.jpg"
-  },
-  {
-    "id": 9618,
-    "problem_id": 9362,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O and CD is a chord of circle O. If \u2220CAB = 51\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['45\u00b0', '35\u00b0', '42\u00b0', '39\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9362.jpg"
-  },
-  {
-    "id": 9620,
-    "problem_id": 9363,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O and CD is a chord of circle O. If \u2220CAB = 51\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['45\u00b0', '35\u00b0', '42\u00b0', '39\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9363.jpg"
-  },
-  {
-    "id": 9621,
-    "problem_id": 9364,
-    "problem": "<image>As shown in the figure, if we remove an 80\u00b0 angle from quadrilateral ABCD to form pentagon BCDEF, then the sum of angles 1 and 2 is ().\n\n(Note: No English parts were changed in the input, as requested.). A, B, C, D choices are ['240\u00b0', '260\u00b0', '280\u00b0', '300\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9364.jpg"
-  },
-  {
-    "id": 9622,
-    "problem_id": 9365,
-    "problem": "<image>As shown in the figure, if we remove an 80\u00b0 angle from quadrilateral ABCD to form pentagon BCDEF, then the sum of angles 1 and 2 is ().\n\n(Note: No English parts were changed in the input, as requested.). A, B, C, D choices are ['240\u00b0', '260\u00b0', '280\u00b0', '300\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9365.jpg"
-  },
-  {
-    "id": 9623,
-    "problem_id": 9366,
-    "problem": "<image>As shown in the figure, if we remove an 80\u00b0 angle from quadrilateral ABCD to form pentagon BCDEF, then the sum of angles 1 and 2 is ().\n\n(Note: No English parts were changed in the input, as requested.). A, B, C, D choices are ['240\u00b0', '260\u00b0', '280\u00b0', '300\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9366.jpg"
-  },
-  {
-    "id": 9624,
-    "problem_id": 9367,
-    "problem": "<image>As shown in the figure, if we remove an 80\u00b0 angle from quadrilateral ABCD to form pentagon BCDEF, then the sum of angles 1 and 2 is ().\n\n(Note: No English parts were changed in the input, as requested.). A, B, C, D choices are ['240\u00b0', '260\u00b0', '280\u00b0', '300\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9367.jpg"
-  },
-  {
-    "id": 9625,
-    "problem_id": 9368,
-    "problem": "<image>As shown in the figure, if we remove an 80\u00b0 angle from quadrilateral ABCD to form pentagon BCDEF, then the sum of angles 1 and 2 is ().\n\n(Note: No English parts were changed in the input, as requested.). A, B, C, D choices are ['240\u00b0', '260\u00b0', '280\u00b0', '300\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9368.jpg"
-  },
-  {
-    "id": 9626,
-    "problem_id": 9369,
-    "problem": "<image>As shown in the figure, diagonals AC and BD of quadrilateral ABCD intersect at point O. Line EF passes through point O and intersects AD and BC at points E and F, respectively. If the area of ABCD is 20 cm, then what is the area of the shaded region in the figure?. A, B, C, D choices are ['12', '10', '8', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9369.jpg"
-  },
-  {
-    "id": 9627,
-    "problem_id": 9370,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9370.jpg"
-  },
-  {
-    "id": 9628,
-    "problem_id": 9371,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9371.jpg"
-  },
-  {
-    "id": 9629,
-    "problem_id": 9372,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9372.jpg"
-  },
-  {
-    "id": 9630,
-    "problem_id": 9373,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9373.jpg"
-  },
-  {
-    "id": 9631,
-    "problem_id": 9374,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9374.jpg"
-  },
-  {
-    "id": 9632,
-    "problem_id": 9375,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9375.jpg"
-  },
-  {
-    "id": 9633,
-    "problem_id": 9376,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9376.jpg"
-  },
-  {
-    "id": 9634,
-    "problem_id": 9377,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 110\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n\n**Analysis**\n\nThis problem primarily tests the understanding and application of the properties of triangles, specifically the relationship between interior and exterior angles. By using the fact that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles, we can set up an equation to solve for the unknown angle. This approach reinforces the fundamental concepts of triangle angle properties and their applications in solving geometric problems.</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9377.jpg"
-  },
-  {
-    "id": 9635,
-    "problem_id": 9378,
-    "problem": "<image>As shown in the figure, point C is a point within \u2220BAD, and CB and CD are connected. \u2220A = 80\u00b0, \u2220B = 10\u00b0, \u2220D = 40\u00b0. What is the degree of \u2220BCD? (). A, B, C, D choices are ['110\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9378.jpg"
-  },
-  {
-    "id": 9636,
-    "problem_id": 9379,
-    "problem": "<image>In the figure, AE bisects angle BAC, BE is perpendicular to AE at point E, ED is parallel to AC, and angle BAE is 34 degrees. What is the measure of angle BED?. A, B, C, D choices are ['134\u00b0', '124\u00b0', '114\u00b0', '104\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9379.jpg"
-  },
-  {
-    "id": 9637,
-    "problem_id": 9380,
-    "problem": "<image>As shown in the figure, after folding rectangle ABCD along EF, ED intersects with BF at point G. If \u2220EFG = 50\u00b0, what is the degree measure of \u2220BGE?. A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9380.jpg"
-  },
-  {
-    "id": 9638,
-    "problem_id": 9381,
-    "problem": "<image>As shown in the figure, after folding rectangle ABCD along EF, ED intersects with BF at point G. If \u2220EFG = 50\u00b0, what is the degree measure of \u2220BGE?. A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9381.jpg"
-  },
-  {
-    "id": 9639,
-    "problem_id": 9382,
-    "problem": "<image>In the diagram, points E, B, C, and D are on the same line. \u2220A = \u2220ACF, and \u2220DCF = 50\u00b0. What is the degree measure of \u2220ABE? (). A, B, C, D choices are ['50\u00b0', '130\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9382.jpg"
-  },
-  {
-    "id": 9640,
-    "problem_id": 9383,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9383.jpg"
-  },
-  {
-    "id": 9641,
-    "problem_id": 9384,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9384.jpg"
-  },
-  {
-    "id": 9642,
-    "problem_id": 9385,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9385.jpg"
-  },
-  {
-    "id": 9643,
-    "problem_id": 9386,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9386.jpg"
-  },
-  {
-    "id": 9644,
-    "problem_id": 9387,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9387.jpg"
-  },
-  {
-    "id": 9645,
-    "problem_id": 9388,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9388.jpg"
-  },
-  {
-    "id": 9646,
-    "problem_id": 9389,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9389.jpg"
-  },
-  {
-    "id": 9647,
-    "problem_id": 9390,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. If \u2220BAO = 32\u00b0, what is the degree measure of \u2220ACB?. A, B, C, D choices are ['32\u00b0', '45\u00b0', '58\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9390.jpg"
-  },
-  {
-    "id": 9648,
-    "problem_id": 9391,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9391.jpg"
-  },
-  {
-    "id": 9649,
-    "problem_id": 9392,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9392.jpg"
-  },
-  {
-    "id": 9650,
-    "problem_id": 9393,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9393.jpg"
-  },
-  {
-    "id": 9651,
-    "problem_id": 9394,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9394.jpg"
-  },
-  {
-    "id": 9652,
-    "problem_id": 9395,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9395.jpg"
-  },
-  {
-    "id": 9653,
-    "problem_id": 9396,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9396.jpg"
-  },
-  {
-    "id": 9654,
-    "problem_id": 9397,
-    "problem": "<image>As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O, and the sum of the two diagonals is 36cm. If the length of AB is 9cm, then the perimeter of triangle OCD is (). A, B, C, D choices are ['45cm', '27cm', '22.5cm', '31cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9397.jpg"
-  },
-  {
-    "id": 9655,
-    "problem_id": 9398,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. \u2220BOC = 100\u00b0. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9398.jpg"
-  },
-  {
-    "id": 9656,
-    "problem_id": 9399,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. \u2220BOC = 100\u00b0. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9399.jpg"
-  },
-  {
-    "id": 9657,
-    "problem_id": 9400,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. \u2220BOC = 100\u00b0. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9400.jpg"
-  },
-  {
-    "id": 9658,
-    "problem_id": 9401,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. \u2220BOC = 100\u00b0. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9401.jpg"
-  },
-  {
-    "id": 9659,
-    "problem_id": 9402,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. \u2220BOC = 100\u00b0. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9402.jpg"
-  },
-  {
-    "id": 9660,
-    "problem_id": 9403,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. \u2220BOC = 100\u00b0. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9403.jpg"
-  },
-  {
-    "id": 9661,
-    "problem_id": 9404,
-    "problem": "<image>As shown in the diagram, in triangle ABC, AB=AC=5, BC=3, MN is the perpendicular bisector of AB, and intersects with AC at point D. The perimeter of triangle BDC is ().. A, B, C, D choices are ['8', '10', '11', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9404.jpg"
-  },
-  {
-    "id": 9662,
-    "problem_id": 9405,
-    "problem": "<image>As shown in the diagram, in triangle ABC, AB=AC=5, BC=3, MN is the perpendicular bisector of AB, and intersects with AC at point D. The perimeter of triangle BDC is ().. A, B, C, D choices are ['8', '10', '11', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9405.jpg"
-  },
-  {
-    "id": 9663,
-    "problem_id": 9406,
-    "problem": "<image>As shown in the diagram, in triangle ABC, AB=AC=5, BC=3, MN is the perpendicular bisector of AB, and intersects with AC at point D. The perimeter of triangle BDC is ().. A, B, C, D choices are ['8', '10', '11', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9406.jpg"
-  },
-  {
-    "id": 9664,
-    "problem_id": 9407,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9407.jpg"
-  },
-  {
-    "id": 9665,
-    "problem_id": 9408,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9408.jpg"
-  },
-  {
-    "id": 9666,
-    "problem_id": 9409,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9409.jpg"
-  },
-  {
-    "id": 9667,
-    "problem_id": 9410,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9410.jpg"
-  },
-  {
-    "id": 9668,
-    "problem_id": 9411,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9411.jpg"
-  },
-  {
-    "id": 9669,
-    "problem_id": 9412,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9412.jpg"
-  },
-  {
-    "id": 9670,
-    "problem_id": 9413,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9413.jpg"
-  },
-  {
-    "id": 9671,
-    "problem_id": 9414,
-    "problem": "<image>As shown in the figure, \u2220A = 40\u00b0, \u2220CBD is the exterior angle of \u25b3ABC, and \u2220CBD = 120\u00b0. What is the size of \u2220C? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '60\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9414.jpg"
-  },
-  {
-    "id": 9672,
-    "problem_id": 9415,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9415.jpg"
-  },
-  {
-    "id": 9673,
-    "problem_id": 9416,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9416.jpg"
-  },
-  {
-    "id": 9674,
-    "problem_id": 9417,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9417.jpg"
-  },
-  {
-    "id": 9675,
-    "problem_id": 9418,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9418.jpg"
-  },
-  {
-    "id": 9676,
-    "problem_id": 9419,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9419.jpg"
-  },
-  {
-    "id": 9677,
-    "problem_id": 9420,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9420.jpg"
-  },
-  {
-    "id": 9678,
-    "problem_id": 9421,
-    "problem": "<image>In triangle ABC, the perpendicular bisector of AB intersects AB at point D and intersects BC at point E. AE is connected. If AD = 3 and the perimeter of triangle ACE is 13, then the perimeter of triangle ABC is ().. A, B, C, D choices are ['19', '16', '29', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9421.jpg"
-  },
-  {
-    "id": 9679,
-    "problem_id": 9422,
-    "problem": "<image>As shown in the figure, line a is parallel to line b and intersects with line c. If \u22201 = 36\u00b0, then what is the measure of \u22202?. A, B, C, D choices are ['36\u00b0', '54\u00b0', '100\u00b0', '144\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9422.jpg"
-  },
-  {
-    "id": 9680,
-    "problem_id": 9423,
-    "problem": "<image>As shown in the figure, AD is the median of equilateral triangle \u25b3ABC. If a point E is taken on side AC so that AE = AD, what is the degree of angle EDC? (). A, B, C, D choices are ['30\u00b0', '20\u00b0', '25\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9423.jpg"
-  },
-  {
-    "id": 9681,
-    "problem_id": 9424,
-    "problem": "<image>In circle O, if \u2220BOD = 80\u00b0, then \u2220BCD is equal to (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9424.jpg"
-  },
-  {
-    "id": 9682,
-    "problem_id": 9425,
-    "problem": "<image>In circle O, if \u2220BOD = 80\u00b0, then \u2220BCD is equal to (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9425.jpg"
-  },
-  {
-    "id": 9683,
-    "problem_id": 9426,
-    "problem": "<image>In circle O, if \u2220BOD = 80\u00b0, then \u2220BCD is equal to (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9426.jpg"
-  },
-  {
-    "id": 9684,
-    "problem_id": 9427,
-    "problem": "<image>In circle O, if \u2220BOD = 80\u00b0, then \u2220BCD is equal to (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9427.jpg"
-  },
-  {
-    "id": 9685,
-    "problem_id": 9428,
-    "problem": "<image>In circle O, if \u2220BOD = 80\u00b0, then \u2220BCD is equal to (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9428.jpg"
-  },
-  {
-    "id": 9686,
-    "problem_id": 9429,
-    "problem": "<image>In circle O, if \u2220BOD = 80\u00b0, then \u2220BCD is equal to (). A, B, C, D choices are ['80\u00b0', '100\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9429.jpg"
-  },
-  {
-    "id": 9687,
-    "problem_id": 9430,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9430.jpg"
-  },
-  {
-    "id": 9688,
-    "problem_id": 9431,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9431.jpg"
-  },
-  {
-    "id": 9689,
-    "problem_id": 9432,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9432.jpg"
-  },
-  {
-    "id": 9690,
-    "problem_id": 9433,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9433.jpg"
-  },
-  {
-    "id": 9691,
-    "problem_id": 9434,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9434.jpg"
-  },
-  {
-    "id": 9692,
-    "problem_id": 9435,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9435.jpg"
-  },
-  {
-    "id": 9693,
-    "problem_id": 9436,
-    "problem": "<image>As shown in the figure, point D and point E are respectively the midpoints of AB and AC, and DE = 3. The distance between B and C is ().. A, B, C, D choices are ['3', '6', '9', '1.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9436.jpg"
-  },
-  {
-    "id": 9694,
-    "problem_id": 9437,
-    "problem": "<image>In the figure, quadrilateral ABCD has AB=3cm, AD=4cm, BC=13cm, CD=12cm, and \u2220A=90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['12', '18', '22', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9437.jpg"
-  },
-  {
-    "id": 9695,
-    "problem_id": 9438,
-    "problem": "<image>In the figure, quadrilateral ABCD has AB=3cm, AD=4cm, BC=13cm, CD=12cm, and \u2220A=90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['12', '18', '22', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9438.jpg"
-  },
-  {
-    "id": 9696,
-    "problem_id": 9439,
-    "problem": "<image>In the figure, quadrilateral ABCD has AB=3cm, AD=4cm, BC=13cm, CD=12cm, and \u2220A=90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['12', '18', '22', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9439.jpg"
-  },
-  {
-    "id": 9697,
-    "problem_id": 9440,
-    "problem": "<image>In the figure, quadrilateral ABCD has AB=3cm, AD=4cm, BC=13cm, CD=12cm, and \u2220A=90\u00b0. What is the area of quadrilateral ABCD?. A, B, C, D choices are ['12', '18', '22', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9440.jpg"
-  },
-  {
-    "id": 9698,
-    "problem_id": 9441,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC, if OB is connected and \u2220OBC = 28\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['28\u00b0', '52\u00b0', '56\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9441.jpg"
-  },
-  {
-    "id": 9699,
-    "problem_id": 9442,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC, if OB is connected and \u2220OBC = 28\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['28\u00b0', '52\u00b0', '56\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9442.jpg"
-  },
-  {
-    "id": 9700,
-    "problem_id": 9443,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC, if OB is connected and \u2220OBC = 28\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['28\u00b0', '52\u00b0', '56\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9443.jpg"
-  },
-  {
-    "id": 9701,
-    "problem_id": 9444,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC, if OB is connected and \u2220OBC = 28\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['28\u00b0', '52\u00b0', '56\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9444.jpg"
-  },
-  {
-    "id": 9702,
-    "problem_id": 9445,
-    "problem": "<image>Given that point O is the circumcenter of triangle ABC, if OB is connected and \u2220OBC = 28\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['28\u00b0', '52\u00b0', '56\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9445.jpg"
-  },
-  {
-    "id": 9703,
-    "problem_id": 9446,
-    "problem": "<image>In triangle ABC, where BC is parallel to ED and angle C is 65 degrees, what is the degree measure of angle CED? (). A, B, C, D choices are ['65\u00b0', '115\u00b0', '135\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9446.jpg"
-  },
-  {
-    "id": 9704,
-    "problem_id": 9447,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9447.jpg"
-  },
-  {
-    "id": 9705,
-    "problem_id": 9448,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9448.jpg"
-  },
-  {
-    "id": 9706,
-    "problem_id": 9449,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9449.jpg"
-  },
-  {
-    "id": 9707,
-    "problem_id": 9450,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9450.jpg"
-  },
-  {
-    "id": 9708,
-    "problem_id": 9451,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9451.jpg"
-  },
-  {
-    "id": 9709,
-    "problem_id": 9452,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9452.jpg"
-  },
-  {
-    "id": 9710,
-    "problem_id": 9453,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9453.jpg"
-  },
-  {
-    "id": 9711,
-    "problem_id": 9454,
-    "problem": "<image>In the rectangle ABCD, diagonal AC = 4, triangle AOB is an equilateral triangle as shown in the figure. What is the length of AD?. A, B, C, D choices are ['2', '3', '2\u221a{2}', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9454.jpg"
-  },
-  {
-    "id": 9712,
-    "problem_id": 9455,
-    "problem": "<image>In triangle ABC, the altitude AD intersects with the median CE at point F. If AD = CE = 8 and FD = 2, what is the value of AB?. A, B, C, D choices are ['2\u221a{21}', '6\u221a{2}', '10', '4\u221a{7}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9455.jpg"
-  },
-  {
-    "id": 9713,
-    "problem_id": 9456,
-    "problem": "<image>In triangle ABC and triangle DEF, AB=DE, BC=EF, and \u2220B+\u2220E=180\u00b0. If the area of triangle ABC is 48cm2, then what is the area of triangle DEF?. A, B, C, D choices are ['48cm2', '24cm2', '54cm2', '96cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9456.jpg"
-  },
-  {
-    "id": 9714,
-    "problem_id": 9457,
-    "problem": "<image>In triangle ABC and triangle DEF, AB=DE, BC=EF, and \u2220B+\u2220E=180\u00b0. If the area of triangle ABC is 48cm2, then what is the area of triangle DEF?. A, B, C, D choices are ['48cm2', '24cm2', '54cm2', '96cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9457.jpg"
-  },
-  {
-    "id": 9715,
-    "problem_id": 9458,
-    "problem": "<image>In triangle ABC and triangle DEF, AB=DE, BC=EF, and \u2220B+\u2220E=180\u00b0. If the area of triangle ABC is 48cm2, then what is the area of triangle DEF?. A, B, C, D choices are ['48cm2', '24cm2', '54cm2', '96cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9458.jpg"
-  },
-  {
-    "id": 9716,
-    "problem_id": 9459,
-    "problem": "<image>In triangle ABC and triangle DEF, AB=DE, BC=EF, and \u2220B+\u2220E=180\u00b0. If the area of triangle ABC is 48cm2, then what is the area of triangle DEF?. A, B, C, D choices are ['48cm2', '24cm2', '54cm2', '96cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9459.jpg"
-  },
-  {
-    "id": 9717,
-    "problem_id": 9460,
-    "problem": "<image>In triangle ABC and triangle DEF, AB=DE, BC=EF, and \u2220B+\u2220E=180\u00b0. If the area of triangle ABC is 48cm2, then what is the area of triangle DEF?. A, B, C, D choices are ['48cm2', '24cm2', '54cm2', '96cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9460.jpg"
-  },
-  {
-    "id": 9718,
-    "problem_id": 9461,
-    "problem": "<image>In triangle ABC and triangle DEF, AB=DE, BC=EF, and \u2220B+\u2220E=180\u00b0. If the area of triangle ABC is 48cm2, then what is the area of triangle DEF?. A, B, C, D choices are ['48cm2', '24cm2', '54cm2', '96cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9461.jpg"
-  },
-  {
-    "id": 9719,
-    "problem_id": 9462,
-    "problem": "<image>In triangle ABC, D and E are on AB and AC respectively, and DE is parallel to BC. If AD = 0.5 \u00d7 DB and the area of triangle ADE is 3, then the area of quadrilateral DBCE is ().. A, B, C, D choices are ['12', '15', '24', '27'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9462.jpg"
-  },
-  {
-    "id": 9720,
-    "problem_id": 9463,
-    "problem": "<image>In triangle ABC, D and E are on AB and AC respectively, and DE is parallel to BC. If AD = 0.5 \u00d7 DB and the area of triangle ADE is 3, then the area of quadrilateral DBCE is ().. A, B, C, D choices are ['12', '15', '24', '27'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9463.jpg"
-  },
-  {
-    "id": 9721,
-    "problem_id": 9464,
-    "problem": "<image>In triangle ABC, D and E are on AB and AC respectively, and DE is parallel to BC. If AD = 0.5 \u00d7 DB and the area of triangle ADE is 3, then the area of quadrilateral DBCE is ().. A, B, C, D choices are ['12', '15', '24', '27'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9464.jpg"
-  },
-  {
-    "id": 9722,
-    "problem_id": 9465,
-    "problem": "<image>In triangle ABC, D and E are on AB and AC respectively, and DE is parallel to BC. If AD = 0.5 \u00d7 DB and the area of triangle ADE is 3, then the area of quadrilateral DBCE is ().. A, B, C, D choices are ['12', '15', '24', '27'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9465.jpg"
-  },
-  {
-    "id": 9723,
-    "problem_id": 9466,
-    "problem": "<image>In triangle ABC, D and E are on AB and AC respectively, and DE is parallel to BC. If AD = 0.5 \u00d7 DB and the area of triangle ADE is 3, then the area of quadrilateral DBCE is ().. A, B, C, D choices are ['12', '15', '24', '27'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9466.jpg"
-  },
-  {
-    "id": 9724,
-    "problem_id": 9467,
-    "problem": "<image>As shown in the figure, AB\u2225CD, \u2220A\uff1d50\u00b0, \u2220C\uff1d20\u00b0, then \u2220E\uff1d\uff08\uff09. A, B, C, D choices are ['20\u00b0', '30\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9467.jpg"
-  },
-  {
-    "id": 9725,
-    "problem_id": 9468,
-    "problem": "<image>As shown in the figure, AB\u2225CD, \u2220A\uff1d50\u00b0, \u2220C\uff1d20\u00b0, then \u2220E\uff1d\uff08\uff09. A, B, C, D choices are ['20\u00b0', '30\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9468.jpg"
-  },
-  {
-    "id": 9726,
-    "problem_id": 9469,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, \u22201:\u22202 = 7:11, then what is the degree of \u22202? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9469.jpg"
-  },
-  {
-    "id": 9727,
-    "problem_id": 9470,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, \u22201:\u22202 = 7:11, then what is the degree of \u22202? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9470.jpg"
-  },
-  {
-    "id": 9729,
-    "problem_id": 9471,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, \u22201:\u22202 = 7:11, then what is the degree of \u22202? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9471.jpg"
-  },
-  {
-    "id": 9730,
-    "problem_id": 9472,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, \u22201:\u22202 = 7:11, then what is the degree of \u22202? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9472.jpg"
-  },
-  {
-    "id": 9731,
-    "problem_id": 9473,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, \u22201:\u22202 = 7:11, then what is the degree of \u22202? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9473.jpg"
-  },
-  {
-    "id": 9732,
-    "problem_id": 9474,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9474.jpg"
-  },
-  {
-    "id": 9733,
-    "problem_id": 9475,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9475.jpg"
-  },
-  {
-    "id": 9734,
-    "problem_id": 9476,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9476.jpg"
-  },
-  {
-    "id": 9735,
-    "problem_id": 9477,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9477.jpg"
-  },
-  {
-    "id": 9736,
-    "problem_id": 9478,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9478.jpg"
-  },
-  {
-    "id": 9737,
-    "problem_id": 9479,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9479.jpg"
-  },
-  {
-    "id": 9738,
-    "problem_id": 9480,
-    "problem": "<image>In the right triangle ABC as shown in the figure, \u2220BAC\uff1d90\u00b0. Squares are constructed outwardly on sides AB, CA, and BC. The area of square ABIH is 25 and the area of square ACFG is 144. What is the area of square BDEC?. A, B, C, D choices are ['130', '119', '169', '120'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9480.jpg"
-  },
-  {
-    "id": 9739,
-    "problem_id": 9481,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. If the area of quadrilateral BCED is 15, then the area of triangle ABC is (). A, B, C, D choices are ['30', '25', '22.5', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9481.jpg"
-  },
-  {
-    "id": 9740,
-    "problem_id": 9482,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. If the area of quadrilateral BCED is 15, then the area of triangle ABC is (). A, B, C, D choices are ['30', '25', '22.5', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9482.jpg"
-  },
-  {
-    "id": 9741,
-    "problem_id": 9483,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. If the area of quadrilateral BCED is 15, then the area of triangle ABC is (). A, B, C, D choices are ['30', '25', '22.5', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9483.jpg"
-  },
-  {
-    "id": 9742,
-    "problem_id": 9484,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. If the area of quadrilateral BCED is 15, then the area of triangle ABC is (). A, B, C, D choices are ['30', '25', '22.5', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9484.jpg"
-  },
-  {
-    "id": 9743,
-    "problem_id": 9485,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AB and AC, respectively. If the area of quadrilateral BCED is 15, then the area of triangle ABC is (). A, B, C, D choices are ['30', '25', '22.5', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9485.jpg"
-  },
-  {
-    "id": 9744,
-    "problem_id": 9486,
-    "problem": "<image>In triangle ABC, DE is the perpendicular bisector of AC and intersects BC and AC at points D and E, respectively. The perimeter of triangle ABC is 18 and AE = 3. What is the perimeter of triangle ABD?. A, B, C, D choices are ['12', '15', '18', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9486.jpg"
-  },
-  {
-    "id": 9745,
-    "problem_id": 9487,
-    "problem": "<image>In triangle ABC, DE is the perpendicular bisector of AC and intersects BC and AC at points D and E, respectively. The perimeter of triangle ABC is 18 and AE = 3. What is the perimeter of triangle ABD?. A, B, C, D choices are ['12', '15', '18', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9487.jpg"
-  },
-  {
-    "id": 9746,
-    "problem_id": 9488,
-    "problem": "<image>In triangle ABC, DE is the perpendicular bisector of AC and intersects BC and AC at points D and E, respectively. The perimeter of triangle ABC is 18 and AE = 3. What is the perimeter of triangle ABD?. A, B, C, D choices are ['12', '15', '18', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9488.jpg"
-  },
-  {
-    "id": 9747,
-    "problem_id": 9489,
-    "problem": "<image>As shown in the figure, AB is the diameter of a semicircle, C and D are two points on the semicircle, and \u2220CAB = 24\u00b0. What is the degree measure of \u2220ADC? (). A, B, C, D choices are ['124\u00b0', '114\u00b0', '116\u00b0', '126\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9489.jpg"
-  },
-  {
-    "id": 9748,
-    "problem_id": 9490,
-    "problem": "<image>As shown in the figure, the rectangular paper strip ABCD is folded with crease EF. After folding, points C and D fall at points C' and D' respectively. DE intersects BF at point G. Given that \u2220BGD' = 26\u00b0, the degree of angle \u03b1 is () . A, B, C, D choices are ['77\u00b0', '64\u00b0', '26\u00b0', '87\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9490.jpg"
-  },
-  {
-    "id": 9749,
-    "problem_id": 9491,
-    "problem": "<image>As shown in the figure, the rectangular paper strip ABCD is folded with crease EF. After folding, points C and D fall at points C' and D' respectively. DE intersects BF at point G. Given that \u2220BGD' = 26\u00b0, the degree of angle \u03b1 is () . A, B, C, D choices are ['77\u00b0', '64\u00b0', '26\u00b0', '87\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9491.jpg"
-  },
-  {
-    "id": 9750,
-    "problem_id": 9492,
-    "problem": "<image>As shown in the figure, the rectangular paper strip ABCD is folded with crease EF. After folding, points C and D fall at points C' and D' respectively. DE intersects BF at point G. Given that \u2220BGD' = 26\u00b0, the degree of angle \u03b1 is () . A, B, C, D choices are ['77\u00b0', '64\u00b0', '26\u00b0', '87\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9492.jpg"
-  },
-  {
-    "id": 9751,
-    "problem_id": 9493,
-    "problem": "<image>Given AB\u2225CD and \u22201\uff1d135\u00b0 as shown in the figure, what is the degree of \u2220A?. A, B, C, D choices are ['40\u00b0', '45\u00b0', '135\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9493.jpg"
-  },
-  {
-    "id": 9752,
-    "problem_id": 9494,
-    "problem": "<image>Given AB\u2225CD and \u22201\uff1d135\u00b0 as shown in the figure, what is the degree of \u2220A?. A, B, C, D choices are ['40\u00b0', '45\u00b0', '135\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9494.jpg"
-  },
-  {
-    "id": 9753,
-    "problem_id": 9495,
-    "problem": "<image>Given AB\u2225CD and \u22201\uff1d135\u00b0 as shown in the figure, what is the degree of \u2220A?. A, B, C, D choices are ['40\u00b0', '45\u00b0', '135\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9495.jpg"
-  },
-  {
-    "id": 9754,
-    "problem_id": 9496,
-    "problem": "<image>Given AB\u2225CD and \u22201\uff1d135\u00b0 as shown in the figure, what is the degree of \u2220A?. A, B, C, D choices are ['40\u00b0', '45\u00b0', '135\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9496.jpg"
-  },
-  {
-    "id": 9755,
-    "problem_id": 9497,
-    "problem": "<image>Given AB\u2225CD and \u22201\uff1d135\u00b0 as shown in the figure, what is the degree of \u2220A?. A, B, C, D choices are ['40\u00b0', '45\u00b0', '135\u00b0', '145\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9497.jpg"
-  },
-  {
-    "id": 9756,
-    "problem_id": 9498,
-    "problem": "<image>As shown in the diagram, BC is the diameter of circle O, and AB is a chord of circle O. If \u2220AOC = 58\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['20\u00b0', '25\u00b0', '29\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9498.jpg"
-  },
-  {
-    "id": 9757,
-    "problem_id": 9499,
-    "problem": "<image>In the figure, if \u2220D = 120\u00b0 in diamond ABCD, then \u22201 = (). A, B, C, D choices are ['30\u00b0', '25\u00b0', '60\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9499.jpg"
-  },
-  {
-    "id": 9758,
-    "problem_id": 9500,
-    "problem": "<image>In the figure, if \u2220D = 120\u00b0 in diamond ABCD, then \u22201 = (). A, B, C, D choices are ['30\u00b0', '25\u00b0', '60\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9500.jpg"
-  },
-  {
-    "id": 9759,
-    "problem_id": 9501,
-    "problem": "<image>In the figure, if \u2220D = 120\u00b0 in diamond ABCD, then \u22201 = (). A, B, C, D choices are ['30\u00b0', '25\u00b0', '60\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9501.jpg"
-  },
-  {
-    "id": 9760,
-    "problem_id": 9502,
-    "problem": "<image>In the figure, if \u2220D = 120\u00b0 in diamond ABCD, then \u22201 = (). A, B, C, D choices are ['30\u00b0', '25\u00b0', '60\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9502.jpg"
-  },
-  {
-    "id": 9761,
-    "problem_id": 9503,
-    "problem": "<image>In the figure, CF is the angle bisector of \u2220ACM, CF\u2225AB, and \u2220ACF\uff1d50\u00b0. Then, what is the degree of angle \u2220B?. A, B, C, D choices are ['80\u00b0', '40\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9503.jpg"
-  },
-  {
-    "id": 9762,
-    "problem_id": 9504,
-    "problem": "<image>In the figure, CF is the angle bisector of \u2220ACM, CF\u2225AB, and \u2220ACF\uff1d50\u00b0. Then, what is the degree of angle \u2220B?. A, B, C, D choices are ['80\u00b0', '40\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9504.jpg"
-  },
-  {
-    "id": 9763,
-    "problem_id": 9505,
-    "problem": "<image>In the figure, CF is the angle bisector of \u2220ACM, CF\u2225AB, and \u2220ACF\uff1d50\u00b0. Then, what is the degree of angle \u2220B?. A, B, C, D choices are ['80\u00b0', '40\u00b0', '60\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9505.jpg"
-  },
-  {
-    "id": 9764,
-    "problem_id": 9506,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. What is the area of the shaded triangle AEF?. A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9506.jpg"
-  },
-  {
-    "id": 9765,
-    "problem_id": 9507,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. What is the area of the shaded triangle AEF?. A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9507.jpg"
-  },
-  {
-    "id": 9766,
-    "problem_id": 9508,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. What is the area of the shaded triangle AEF?. A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9508.jpg"
-  },
-  {
-    "id": 9767,
-    "problem_id": 9509,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. What is the area of the shaded triangle AEF?. A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9509.jpg"
-  },
-  {
-    "id": 9768,
-    "problem_id": 9510,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of BC, AD, and CE, respectively, and the area of triangle ABC is 12cm2. What is the area of the shaded triangle AEF?. A, B, C, D choices are ['1', '1.5', '2', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9510.jpg"
-  },
-  {
-    "id": 9769,
-    "problem_id": 9511,
-    "problem": "<image>In the figure, DE is the perpendicular bisector of side AB of triangle ABC, with D as the foot of the perpendicular. DE intersects AC at point E, and AC=9, BC=5. What is the perimeter of triangle BEC?. A, B, C, D choices are ['12', '13', '14', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9511.jpg"
-  },
-  {
-    "id": 9770,
-    "problem_id": 9512,
-    "problem": "<image>In the diamond-shaped figure ABCD, if \u2220D = 140\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9512.jpg"
-  },
-  {
-    "id": 9771,
-    "problem_id": 9513,
-    "problem": "<image>In the diamond-shaped figure ABCD, if \u2220D = 140\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9513.jpg"
-  },
-  {
-    "id": 9772,
-    "problem_id": 9514,
-    "problem": "<image>In the diamond-shaped figure ABCD, if \u2220D = 140\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9514.jpg"
-  },
-  {
-    "id": 9773,
-    "problem_id": 9515,
-    "problem": "<image>In the diamond-shaped figure ABCD, if \u2220D = 140\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9515.jpg"
-  },
-  {
-    "id": 9774,
-    "problem_id": 9516,
-    "problem": "<image>In the diamond-shaped figure ABCD, if \u2220D = 140\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9516.jpg"
-  },
-  {
-    "id": 9775,
-    "problem_id": 9517,
-    "problem": "<image>In the diamond-shaped figure ABCD, if \u2220D = 140\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9517.jpg"
-  },
-  {
-    "id": 9776,
-    "problem_id": 9518,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 10, AD is the median of side BC, E is any point on AD, and BE and CE are connected. The area of the shaded part in the figure is ().. A, B, C, D choices are ['4', '5', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9518.jpg"
-  },
-  {
-    "id": 9777,
-    "problem_id": 9519,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O, and OA and OC are connected. If \u2220AOC = 116\u00b0, what is the degree of \u2220ADC? (). A, B, C, D choices are ['122\u00b0', '120\u00b0', '117\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9519.jpg"
-  },
-  {
-    "id": 9778,
-    "problem_id": 9520,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O, and OA and OC are connected. If \u2220AOC = 116\u00b0, what is the degree of \u2220ADC? (). A, B, C, D choices are ['122\u00b0', '120\u00b0', '117\u00b0', '116\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9520.jpg"
-  },
-  {
-    "id": 9779,
-    "problem_id": 9521,
-    "problem": "<image>As shown in the figure, OE is perpendicular to AB, and the line CD passes through point O. If \u2220COA = 35\u00b0, what is the complement of \u2220BOD?. A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9521.jpg"
-  },
-  {
-    "id": 9780,
-    "problem_id": 9522,
-    "problem": "<image>As shown in the figure, OE is perpendicular to AB, and the line CD passes through point O. If \u2220COA = 35\u00b0, what is the complement of \u2220BOD?. A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9522.jpg"
-  },
-  {
-    "id": 9781,
-    "problem_id": 9523,
-    "problem": "<image>As shown in the figure, AD is parallel to BC, \u2220ABD = \u2220D, \u2220A = 110\u00b0, then what is the degree of \u2220DBC? (). A, B, C, D choices are ['70\u00b0', '35\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9523.jpg"
-  },
-  {
-    "id": 9782,
-    "problem_id": 9524,
-    "problem": "<image>As shown in the figure, AD is parallel to BC, \u2220ABD = \u2220D, \u2220A = 110\u00b0, then what is the degree of \u2220DBC? (). A, B, C, D choices are ['70\u00b0', '35\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9524.jpg"
-  },
-  {
-    "id": 9783,
-    "problem_id": 9525,
-    "problem": "<image>As shown in the figure, AD is parallel to BC, \u2220ABD = \u2220D, \u2220A = 110\u00b0, then what is the degree of \u2220DBC? (). A, B, C, D choices are ['70\u00b0', '35\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9525.jpg"
-  },
-  {
-    "id": 9784,
-    "problem_id": 9526,
-    "problem": "<image>As shown in the figure, DE is the median of \u25b3ABC, point F is on DE, and \u2220AFB = 90\u00b0. If AB = 5 and BC = 8, the length of EF is ().. A, B, C, D choices are ['2.5', '1.5', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9526.jpg"
-  },
-  {
-    "id": 9785,
-    "problem_id": 9527,
-    "problem": "<image>In the figure, extend BC to point E in ABCD. If \u2220A = 100\u00b0, what is the measure of \u2220DCE?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9527.jpg"
-  },
-  {
-    "id": 9786,
-    "problem_id": 9528,
-    "problem": "<image>In the figure, extend BC to point E in ABCD. If \u2220A = 100\u00b0, what is the measure of \u2220DCE?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9528.jpg"
-  },
-  {
-    "id": 9787,
-    "problem_id": 9529,
-    "problem": "<image>As shown in the figure, \u2220MON = 60\u00b0. \u2460 Draw arcs with a radius of 2cm and center at point O, intersecting OM and ON at points A and C respectively. \u2461 Draw arcs with a radius of 2cm and center at points A and C respectively, and the two arcs intersect at point B. \u2462 Connect AB and BC. What is the area of quadrilateral OABC?. A, B, C, D choices are ['4\u221a{3}', '2\u221a{3}', '4', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9529.jpg"
-  },
-  {
-    "id": 9789,
-    "problem_id": 9530,
-    "problem": "<image>In triangle ABC, line BD is perpendicular and bisects AC. If \u2220A = 20\u00b0, what is the measure of \u2220CBD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9530.jpg"
-  },
-  {
-    "id": 9790,
-    "problem_id": 9531,
-    "problem": "<image>In triangle ABC, line BD is perpendicular and bisects AC. If \u2220A = 20\u00b0, what is the measure of \u2220CBD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9531.jpg"
-  },
-  {
-    "id": 9791,
-    "problem_id": 9532,
-    "problem": "<image>In triangle ABC, line BD is perpendicular and bisects AC. If \u2220A = 20\u00b0, what is the measure of \u2220CBD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9532.jpg"
-  },
-  {
-    "id": 9792,
-    "problem_id": 9533,
-    "problem": "<image>In triangle ABC, line BD is perpendicular and bisects AC. If \u2220A = 20\u00b0, what is the measure of \u2220CBD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9533.jpg"
-  },
-  {
-    "id": 9793,
-    "problem_id": 9534,
-    "problem": "<image>In triangle ABC, line BD is perpendicular and bisects AC. If \u2220A = 20\u00b0, what is the measure of \u2220CBD?. A, B, C, D choices are ['20\u00b0', '30\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9534.jpg"
-  },
-  {
-    "id": 9794,
-    "problem_id": 9535,
-    "problem": "<image>As shown in the figure, CE is the angle bisector of the exterior angle \u2220ACD of triangle ABC. If \u2220B=35\u00b0 and \u2220ACE=60\u00b0, then \u2220A=().. A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9535.jpg"
-  },
-  {
-    "id": 9795,
-    "problem_id": 9536,
-    "problem": "<image>As shown in the figure, CE is the angle bisector of the exterior angle \u2220ACD of triangle ABC. If \u2220B=35\u00b0 and \u2220ACE=60\u00b0, then \u2220A=().. A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9536.jpg"
-  },
-  {
-    "id": 9796,
-    "problem_id": 9537,
-    "problem": "<image>As shown in the figure, CE is the angle bisector of the exterior angle \u2220ACD of triangle ABC. If \u2220B=35\u00b0 and \u2220ACE=60\u00b0, then \u2220A=().. A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9537.jpg"
-  },
-  {
-    "id": 9797,
-    "problem_id": 9538,
-    "problem": "<image>As shown in the figure, CE is the angle bisector of the exterior angle \u2220ACD of triangle ABC. If \u2220B=35\u00b0 and \u2220ACE=60\u00b0, then \u2220A=().. A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9538.jpg"
-  },
-  {
-    "id": 9798,
-    "problem_id": 9539,
-    "problem": "<image>As shown in the figure, PA and PB are tangents of circle O, with A and B as the tangent points. Point C is on circle O, and \u2220ACB = 52\u00b0. What is the measure of \u2220APB?. A, B, C, D choices are ['104\u00b0', '76\u00b0', '128\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9539.jpg"
-  },
-  {
-    "id": 9799,
-    "problem_id": 9540,
-    "problem": "<image>As shown in the figure, PA and PB are tangents of circle O, with A and B as the tangent points. Point C is on circle O, and \u2220ACB = 52\u00b0. What is the measure of \u2220APB?. A, B, C, D choices are ['104\u00b0', '76\u00b0', '128\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9540.jpg"
-  },
-  {
-    "id": 9801,
-    "problem_id": 9541,
-    "problem": "<image>As shown in the figure, PA and PB are tangents of circle O, with A and B as the tangent points. Point C is on circle O, and \u2220ACB = 52\u00b0. What is the measure of \u2220APB?. A, B, C, D choices are ['104\u00b0', '76\u00b0', '128\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9541.jpg"
-  },
-  {
-    "id": 9802,
-    "problem_id": 9542,
-    "problem": "<image>As shown in the figure, PA and PB are tangents of circle O, with A and B as the tangent points. Point C is on circle O, and \u2220ACB = 52\u00b0. What is the measure of \u2220APB?. A, B, C, D choices are ['104\u00b0', '76\u00b0', '128\u00b0', '63\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9542.jpg"
-  },
-  {
-    "id": 9803,
-    "problem_id": 9543,
-    "problem": "<image>In triangle ABC, \u2220C = 90\u00b0, BD bisects \u2220ABC and intersects AC at point D. If DC = 3 and AB = 8, what is the area of triangle ABD?. A, B, C, D choices are ['8', '12', '16', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9543.jpg"
-  },
-  {
-    "id": 9804,
-    "problem_id": 9544,
-    "problem": "<image>In trapezoid ABCD shown in the figure, AB\u2225DC, AB\u22a5BC, E is the midpoint of AD, and BE is connected. If \u2220EBA = 30\u00b0 and BE = 6, then the area of trapezoid ABCD is (). A, B, C, D choices are ['6\u221a{3}', '9\u221a{3}', '15\u221a{3}', '18\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9544.jpg"
-  },
-  {
-    "id": 9805,
-    "problem_id": 9545,
-    "problem": "<image>In trapezoid ABCD shown in the figure, AB\u2225DC, AB\u22a5BC, E is the midpoint of AD, and BE is connected. If \u2220EBA = 30\u00b0 and BE = 6, then the area of trapezoid ABCD is (). A, B, C, D choices are ['6\u221a{3}', '9\u221a{3}', '15\u221a{3}', '18\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9545.jpg"
-  },
-  {
-    "id": 9806,
-    "problem_id": 9546,
-    "problem": "<image>In trapezoid ABCD shown in the figure, AB\u2225DC, AB\u22a5BC, E is the midpoint of AD, and BE is connected. If \u2220EBA = 30\u00b0 and BE = 6, then the area of trapezoid ABCD is (). A, B, C, D choices are ['6\u221a{3}', '9\u221a{3}', '15\u221a{3}', '18\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9546.jpg"
-  },
-  {
-    "id": 9807,
-    "problem_id": 9547,
-    "problem": "<image>As shown in the diagram, line a\u2225b\u2225c, the right angle vertex of a right triangle board lies on line b. If \u22201 = 54\u00b0, then \u22202 = ().. A, B, C, D choices are ['24\u00b0', '36\u00b0', '54\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9547.jpg"
-  },
-  {
-    "id": 9808,
-    "problem_id": 9548,
-    "problem": "<image>As shown in the diagram, line a\u2225b\u2225c, the right angle vertex of a right triangle board lies on line b. If \u22201 = 54\u00b0, then \u22202 = ().. A, B, C, D choices are ['24\u00b0', '36\u00b0', '54\u00b0', '64\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9548.jpg"
-  },
-  {
-    "id": 9810,
-    "problem_id": 9549,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9549.jpg"
-  },
-  {
-    "id": 9811,
-    "problem_id": 9550,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9550.jpg"
-  },
-  {
-    "id": 9812,
-    "problem_id": 9551,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9551.jpg"
-  },
-  {
-    "id": 9813,
-    "problem_id": 9552,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9552.jpg"
-  },
-  {
-    "id": 9814,
-    "problem_id": 9553,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9553.jpg"
-  },
-  {
-    "id": 9815,
-    "problem_id": 9554,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9554.jpg"
-  },
-  {
-    "id": 9816,
-    "problem_id": 9555,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9555.jpg"
-  },
-  {
-    "id": 9817,
-    "problem_id": 9556,
-    "problem": "<image>In triangle ABC as shown in the figure, \u2220ABC = 90\u00b0. Squares are constructed outwardly on the sides BC, AB, and AC, and their areas are denoted as S1, S2, and S3 respectively. If S2 = 6 and S3 = 10, then the side length of the square with area S1 is (). A, B, C, D choices are ['1', '2', '3', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9556.jpg"
-  },
-  {
-    "id": 9818,
-    "problem_id": 9557,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, where \u2220BOC = 120\u00b0 and BO = 4. What is the length of side BC of the rectangle?. A, B, C, D choices are ['6', '8', '6\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9557.jpg"
-  },
-  {
-    "id": 9819,
-    "problem_id": 9558,
-    "problem": "<image>In triangle ABC, point D and E are on sides AB and AC respectively, and DE is parallel to BC. It is known that AD=3, DB=4, and AE=6. Find the length of EC.. A, B, C, D choices are ['14', '6', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9558.jpg"
-  },
-  {
-    "id": 9820,
-    "problem_id": 9559,
-    "problem": "<image>In triangle ABC, point D and E are on sides AB and AC respectively, and DE is parallel to BC. It is known that AD=3, DB=4, and AE=6. Find the length of EC.. A, B, C, D choices are ['14', '6', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9559.jpg"
-  },
-  {
-    "id": 9821,
-    "problem_id": 9560,
-    "problem": "<image>In triangle ABC, point D and E are on sides AB and AC respectively, and DE is parallel to BC. It is known that AD=3, DB=4, and AE=6. Find the length of EC.. A, B, C, D choices are ['14', '6', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9560.jpg"
-  },
-  {
-    "id": 9822,
-    "problem_id": 9561,
-    "problem": "<image>In triangle ABC, point D and E are on sides AB and AC respectively, and DE is parallel to BC. It is known that AD=3, DB=4, and AE=6. Find the length of EC.. A, B, C, D choices are ['14', '6', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9561.jpg"
-  },
-  {
-    "id": 9823,
-    "problem_id": 9562,
-    "problem": "<image>In triangle ABC, point D and E are on sides AB and AC respectively, and DE is parallel to BC. It is known that AD=3, DB=4, and AE=6. Find the length of EC.. A, B, C, D choices are ['14', '6', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9562.jpg"
-  },
-  {
-    "id": 9824,
-    "problem_id": 9563,
-    "problem": "<image>In triangle ABC, point D and E are on sides AB and AC respectively, and DE is parallel to BC. It is known that AD=3, DB=4, and AE=6. Find the length of EC.. A, B, C, D choices are ['14', '6', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9563.jpg"
-  },
-  {
-    "id": 9825,
-    "problem_id": 9564,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, \u2220CBD = 90\u00b0, BD = BC, then what is the degree of \u22201? (). A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9564.jpg"
-  },
-  {
-    "id": 9826,
-    "problem_id": 9565,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, \u2220CBD = 90\u00b0, BD = BC, then what is the degree of \u22201? (). A, B, C, D choices are ['45\u00b0', '60\u00b0', '75\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9565.jpg"
-  },
-  {
-    "id": 9828,
-    "problem_id": 9566,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC, and H and G are points on side BC such that HG = 0.5\u00d7BC. If the area of triangle ABC is 12, the shaded area in the figure is ().. A, B, C, D choices are ['6', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9566.jpg"
-  },
-  {
-    "id": 9829,
-    "problem_id": 9567,
-    "problem": "<image>In triangle ABC, G is an arbitrary point on side BC, and D, E, F are the midpoints of AG, BD, and CE, respectively. If the area of triangle ABC is 48, then what is the area of triangle DEF?. A, B, C, D choices are ['4.8', '6', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9567.jpg"
-  },
-  {
-    "id": 9830,
-    "problem_id": 9568,
-    "problem": "<image>In triangle ABC, G is an arbitrary point on side BC, and D, E, F are the midpoints of AG, BD, and CE, respectively. If the area of triangle ABC is 48, then what is the area of triangle DEF?. A, B, C, D choices are ['4.8', '6', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9568.jpg"
-  },
-  {
-    "id": 9831,
-    "problem_id": 9569,
-    "problem": "<image>In triangle ABC, G is an arbitrary point on side BC, and D, E, F are the midpoints of AG, BD, and CE, respectively. If the area of triangle ABC is 48, then what is the area of triangle DEF?. A, B, C, D choices are ['4.8', '6', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9569.jpg"
-  },
-  {
-    "id": 9832,
-    "problem_id": 9570,
-    "problem": "<image>In triangle ABC, G is an arbitrary point on side BC, and D, E, F are the midpoints of AG, BD, and CE, respectively. If the area of triangle ABC is 48, then what is the area of triangle DEF?. A, B, C, D choices are ['4.8', '6', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9570.jpg"
-  },
-  {
-    "id": 9833,
-    "problem_id": 9571,
-    "problem": "<image>In triangle ABC, G is an arbitrary point on side BC, and D, E, F are the midpoints of AG, BD, and CE, respectively. If the area of triangle ABC is 48, then what is the area of triangle DEF?. A, B, C, D choices are ['4.8', '6', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9571.jpg"
-  },
-  {
-    "id": 9834,
-    "problem_id": 9572,
-    "problem": "<image>In triangle ABC, G is an arbitrary point on side BC, and D, E, F are the midpoints of AG, BD, and CE, respectively. If the area of triangle ABC is 48, then what is the area of triangle DEF?. A, B, C, D choices are ['4.8', '6', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9572.jpg"
-  },
-  {
-    "id": 9835,
-    "problem_id": 9573,
-    "problem": "<image>In triangle ABC, point D and E are the midpoints of BC and AD, respectively. It is also given that EF = 2FC and the area of triangle ABC is 12. What is the area of triangle BEF?. A, B, C, D choices are ['5', '4.5', '4', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9573.jpg"
-  },
-  {
-    "id": 9836,
-    "problem_id": 9574,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9574.jpg"
-  },
-  {
-    "id": 9837,
-    "problem_id": 9575,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9575.jpg"
-  },
-  {
-    "id": 9838,
-    "problem_id": 9576,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9576.jpg"
-  },
-  {
-    "id": 9839,
-    "problem_id": 9577,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9577.jpg"
-  },
-  {
-    "id": 9840,
-    "problem_id": 9578,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9578.jpg"
-  },
-  {
-    "id": 9841,
-    "problem_id": 9579,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9579.jpg"
-  },
-  {
-    "id": 9842,
-    "problem_id": 9580,
-    "problem": "<image>As shown in the diagram, PA is tangent to circle O at point A, and PB is tangent to circle O at point B. If PA = 3, then PB = ().. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9580.jpg"
-  },
-  {
-    "id": 9843,
-    "problem_id": 9581,
-    "problem": "<image>As shown in the figure, point O is the midpoint of diagonal AC of rectangle ABCD, and point M is the midpoint of AD. If AB = 5 and BC = 12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['24', '21', '23', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9581.jpg"
-  },
-  {
-    "id": 9844,
-    "problem_id": 9582,
-    "problem": "<image>As shown in the figure, point O is the midpoint of diagonal AC of rectangle ABCD, and point M is the midpoint of AD. If AB = 5 and BC = 12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['24', '21', '23', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9582.jpg"
-  },
-  {
-    "id": 9845,
-    "problem_id": 9583,
-    "problem": "<image>As shown in the figure, point O is the midpoint of diagonal AC of rectangle ABCD, and point M is the midpoint of AD. If AB = 5 and BC = 12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['24', '21', '23', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9583.jpg"
-  },
-  {
-    "id": 9846,
-    "problem_id": 9584,
-    "problem": "<image>As shown in the figure, point O is the midpoint of diagonal AC of rectangle ABCD, and point M is the midpoint of AD. If AB = 5 and BC = 12, what is the perimeter of quadrilateral ABOM?. A, B, C, D choices are ['24', '21', '23', '20'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9584.jpg"
-  },
-  {
-    "id": 9847,
-    "problem_id": 9585,
-    "problem": "<image>In the figure, Rt\u25b3ABC, \u2220ACB = 90\u00b0, \u2220BAC = 30\u00b0, BC = 2cm. When rotating around the straight line AC for one complete revolution, what is the lateral area of the resulting cone?. A, B, C, D choices are ['16\u03c0cm2', '8\u03c0cm2', '4\u03c0cm2', '2\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9585.jpg"
-  },
-  {
-    "id": 9848,
-    "problem_id": 9586,
-    "problem": "<image>In the figure, Rt\u25b3ABC, \u2220ACB = 90\u00b0, \u2220BAC = 30\u00b0, BC = 2cm. When rotating around the straight line AC for one complete revolution, what is the lateral area of the resulting cone?. A, B, C, D choices are ['16\u03c0cm2', '8\u03c0cm2', '4\u03c0cm2', '2\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9586.jpg"
-  },
-  {
-    "id": 9849,
-    "problem_id": 9587,
-    "problem": "<image>In the figure, Rt\u25b3ABC, \u2220ACB = 90\u00b0, \u2220BAC = 30\u00b0, BC = 2cm. When rotating around the straight line AC for one complete revolution, what is the lateral area of the resulting cone?. A, B, C, D choices are ['16\u03c0cm2', '8\u03c0cm2', '4\u03c0cm2', '2\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9587.jpg"
-  },
-  {
-    "id": 9850,
-    "problem_id": 9588,
-    "problem": "<image>In the figure, Rt\u25b3ABC, \u2220ACB = 90\u00b0, \u2220BAC = 30\u00b0, BC = 2cm. When rotating around the straight line AC for one complete revolution, what is the lateral area of the resulting cone?. A, B, C, D choices are ['16\u03c0cm2', '8\u03c0cm2', '4\u03c0cm2', '2\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9588.jpg"
-  },
-  {
-    "id": 9851,
-    "problem_id": 9589,
-    "problem": "<image>In the figure, Rt\u25b3ABC, \u2220ACB = 90\u00b0, \u2220BAC = 30\u00b0, BC = 2cm. When rotating around the straight line AC for one complete revolution, what is the lateral area of the resulting cone?. A, B, C, D choices are ['16\u03c0cm2', '8\u03c0cm2', '4\u03c0cm2', '2\u03c0cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9589.jpg"
-  },
-  {
-    "id": 9852,
-    "problem_id": 9590,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9590.jpg"
-  },
-  {
-    "id": 9853,
-    "problem_id": 9591,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9591.jpg"
-  },
-  {
-    "id": 9854,
-    "problem_id": 9592,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9592.jpg"
-  },
-  {
-    "id": 9855,
-    "problem_id": 9593,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9593.jpg"
-  },
-  {
-    "id": 9856,
-    "problem_id": 9594,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9594.jpg"
-  },
-  {
-    "id": 9857,
-    "problem_id": 9595,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9595.jpg"
-  },
-  {
-    "id": 9858,
-    "problem_id": 9596,
-    "problem": "<image>As shown in the figure, in order to measure the distance between points A and B along the edge of a pond, a point C is taken on the same side of line AB. Line CA is then extended to point D, and line CB is extended to point E, such that A and B are the midpoints of CD and CE, respectively. If DE = 18m, what is the length of line segment AB?. A, B, C, D choices are ['12m', '10m', '9m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9596.jpg"
-  },
-  {
-    "id": 9860,
-    "problem_id": 9597,
-    "problem": "<image>As shown in the figure, DE is parallel to AB, and if \u2220A = 40\u00b0, then \u2220ACE = ().. A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9597.jpg"
-  },
-  {
-    "id": 9861,
-    "problem_id": 9598,
-    "problem": "<image>As shown in the figure, DE is parallel to AB, and if \u2220A = 40\u00b0, then \u2220ACE = ().. A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9598.jpg"
-  },
-  {
-    "id": 9862,
-    "problem_id": 9599,
-    "problem": "<image>As shown in the figure, DE is parallel to AB, and if \u2220A = 40\u00b0, then \u2220ACE = ().. A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9599.jpg"
-  },
-  {
-    "id": 9863,
-    "problem_id": 9600,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB = 90\u00b0, AC = 5, AB = 13, point D is the midpoint of AC, DE is drawn parallel to BC passing through point D, and intersects AB at point E. The length of DE is (). A, B, C, D choices are ['8', '7', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9600.jpg"
-  },
-  {
-    "id": 9864,
-    "problem_id": 9601,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB = 90\u00b0, AC = 5, AB = 13, point D is the midpoint of AC, DE is drawn parallel to BC passing through point D, and intersects AB at point E. The length of DE is (). A, B, C, D choices are ['8', '7', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9601.jpg"
-  },
-  {
-    "id": 9865,
-    "problem_id": 9602,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB = 90\u00b0, AC = 5, AB = 13, point D is the midpoint of AC, DE is drawn parallel to BC passing through point D, and intersects AB at point E. The length of DE is (). A, B, C, D choices are ['8', '7', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9602.jpg"
-  },
-  {
-    "id": 9866,
-    "problem_id": 9603,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB = 90\u00b0, AC = 5, AB = 13, point D is the midpoint of AC, DE is drawn parallel to BC passing through point D, and intersects AB at point E. The length of DE is (). A, B, C, D choices are ['8', '7', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9603.jpg"
-  },
-  {
-    "id": 9867,
-    "problem_id": 9604,
-    "problem": "<image>As shown in the figure, in triangle ABC, \u2220ACB = 90\u00b0, AC = 5, AB = 13, point D is the midpoint of AC, DE is drawn parallel to BC passing through point D, and intersects AB at point E. The length of DE is (). A, B, C, D choices are ['8', '7', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9604.jpg"
-  },
-  {
-    "id": 9868,
-    "problem_id": 9605,
-    "problem": "<image>In the figure, in quadrilateral ABCD, AE is perpendicular to BC at point E, and AF is perpendicular to CD at point F, with AE = 3cm and AF = 4cm. If the perimeter of ABCD is 56cm, what is the length of BC?. A, B, C, D choices are ['14cm', '16cm', '28cm', '32cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9605.jpg"
-  },
-  {
-    "id": 9869,
-    "problem_id": 9606,
-    "problem": "<image>As shown in the diagram, BC is parallel to AE, point D is on AE, \u2220C = 120\u00b0, and DB bisects \u2220ADC. What is the measure of \u2220B?. A, B, C, D choices are ['30\u00b0', '20\u00b0', '35\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9606.jpg"
-  },
-  {
-    "id": 9870,
-    "problem_id": 9607,
-    "problem": "<image>As shown in the diagram, BC is parallel to AE, point D is on AE, \u2220C = 120\u00b0, and DB bisects \u2220ADC. What is the measure of \u2220B?. A, B, C, D choices are ['30\u00b0', '20\u00b0', '35\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9607.jpg"
-  },
-  {
-    "id": 9871,
-    "problem_id": 9608,
-    "problem": "<image>After filling a cylindrical container with a diameter of 26cm with some water, the cross-section is shown in the figure. If the maximum depth of the water is 8cm, the width of the water surface AB is ().. A, B, C, D choices are ['12cm', '18cm', '20cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9608.jpg"
-  },
-  {
-    "id": 9872,
-    "problem_id": 9609,
-    "problem": "<image>After filling a cylindrical container with a diameter of 26cm with some water, the cross-section is shown in the figure. If the maximum depth of the water is 8cm, the width of the water surface AB is ().. A, B, C, D choices are ['12cm', '18cm', '20cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9609.jpg"
-  },
-  {
-    "id": 9873,
-    "problem_id": 9610,
-    "problem": "<image>After filling a cylindrical container with a diameter of 26cm with some water, the cross-section is shown in the figure. If the maximum depth of the water is 8cm, the width of the water surface AB is ().. A, B, C, D choices are ['12cm', '18cm', '20cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9610.jpg"
-  },
-  {
-    "id": 9874,
-    "problem_id": 9611,
-    "problem": "<image>After filling a cylindrical container with a diameter of 26cm with some water, the cross-section is shown in the figure. If the maximum depth of the water is 8cm, the width of the water surface AB is ().. A, B, C, D choices are ['12cm', '18cm', '20cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9611.jpg"
-  },
-  {
-    "id": 9875,
-    "problem_id": 9612,
-    "problem": "<image>After filling a cylindrical container with a diameter of 26cm with some water, the cross-section is shown in the figure. If the maximum depth of the water is 8cm, the width of the water surface AB is ().. A, B, C, D choices are ['12cm', '18cm', '20cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9612.jpg"
-  },
-  {
-    "id": 9876,
-    "problem_id": 9613,
-    "problem": "<image>In triangle ABC, AB = 3 and AC = 2. When angle B is at its maximum, what is the length of BC?. A, B, C, D choices are ['1', '5', '\u221a{13}', '\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9613.jpg"
-  },
-  {
-    "id": 9877,
-    "problem_id": 9614,
-    "problem": "<image>In the figure, AB is the diameter of circle O, and point C and point D are two points on circle O. Connect CA, CD, and AD. If \u2220CAB = 50\u00b0, what is the degree measure of \u2220ADC?. A, B, C, D choices are ['110\u00b0', '120\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9614.jpg"
-  },
-  {
-    "id": 9878,
-    "problem_id": 9615,
-    "problem": "<image>In the figure, AB is the diameter of circle O, and point C and point D are two points on circle O. Connect CA, CD, and AD. If \u2220CAB = 50\u00b0, what is the degree measure of \u2220ADC?. A, B, C, D choices are ['110\u00b0', '120\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9615.jpg"
-  },
-  {
-    "id": 9879,
-    "problem_id": 9616,
-    "problem": "<image>In the right triangle ABC as shown, \u2220BAC = 90\u00b0, AB = 3, AC = 4, P is a moving point on the side BC, PE \u22a5 AB at E, PF \u22a5 AC at F, and M is the midpoint of EF. What is the minimum value of AM?. A, B, C, D choices are ['2.4', '2', '1.5', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9616.jpg"
-  },
-  {
-    "id": 9880,
-    "problem_id": 9617,
-    "problem": "<image>In the right triangle ABC as shown, \u2220BAC = 90\u00b0, AB = 3, AC = 4, P is a moving point on the side BC, PE \u22a5 AB at E, PF \u22a5 AC at F, and M is the midpoint of EF. What is the minimum value of AM?. A, B, C, D choices are ['2.4', '2', '1.5', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9617.jpg"
-  },
-  {
-    "id": 9881,
-    "problem_id": 9618,
-    "problem": "<image>In the right triangle ABC as shown, \u2220BAC = 90\u00b0, AB = 3, AC = 4, P is a moving point on the side BC, PE \u22a5 AB at E, PF \u22a5 AC at F, and M is the midpoint of EF. What is the minimum value of AM?. A, B, C, D choices are ['2.4', '2', '1.5', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9618.jpg"
-  },
-  {
-    "id": 9882,
-    "problem_id": 9619,
-    "problem": "<image>In the right triangle ABC as shown, \u2220BAC = 90\u00b0, AB = 3, AC = 4, P is a moving point on the side BC, PE \u22a5 AB at E, PF \u22a5 AC at F, and M is the midpoint of EF. What is the minimum value of AM?. A, B, C, D choices are ['2.4', '2', '1.5', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9619.jpg"
-  },
-  {
-    "id": 9883,
-    "problem_id": 9620,
-    "problem": "<image>In the right triangle ABC as shown, \u2220BAC = 90\u00b0, AB = 3, AC = 4, P is a moving point on the side BC, PE \u22a5 AB at E, PF \u22a5 AC at F, and M is the midpoint of EF. What is the minimum value of AM?. A, B, C, D choices are ['2.4', '2', '1.5', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9620.jpg"
-  },
-  {
-    "id": 9884,
-    "problem_id": 9621,
-    "problem": "<image>In the right triangle ABC as shown, \u2220BAC = 90\u00b0, AB = 3, AC = 4, P is a moving point on the side BC, PE \u22a5 AB at E, PF \u22a5 AC at F, and M is the midpoint of EF. What is the minimum value of AM?. A, B, C, D choices are ['2.4', '2', '1.5', '1.2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9621.jpg"
-  },
-  {
-    "id": 9885,
-    "problem_id": 9622,
-    "problem": "<image>In the diamond ABCD shown in the figure, \u2220ABC=60\u00b0 and AB=4. If points E, F, G, and H are the midpoints of sides AB, BC, CD, and DA respectively, and EF, FG, GH, and HE are connected, what is the area of quadrilateral EFGH?. A, B, C, D choices are ['8', '6\u221a{3}', '4\u221a{3}', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9622.jpg"
-  },
-  {
-    "id": 9886,
-    "problem_id": 9623,
-    "problem": "<image>As shown in the figure, line l is parallel to line m. Vertex B of equilateral triangle ABC lies on line m, and side BC forms an acute angle of 18\u00b0 with line m. What is the degree measure of angle \u03b1? (). A, B, C, D choices are ['60\u00b0', '42\u00b0', '36\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9623.jpg"
-  },
-  {
-    "id": 9887,
-    "problem_id": 9624,
-    "problem": "<image>As shown in the figure, line l is parallel to line m. Vertex B of equilateral triangle ABC lies on line m, and side BC forms an acute angle of 18\u00b0 with line m. What is the degree measure of angle \u03b1? (). A, B, C, D choices are ['60\u00b0', '42\u00b0', '36\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9624.jpg"
-  },
-  {
-    "id": 9888,
-    "problem_id": 9625,
-    "problem": "<image>In the figure, in rectangle ABCD, point E is on BC, and AE bisects \u2220BAC. AE = CE, BE = 2. What is the area of rectangle ABCD?. A, B, C, D choices are ['24\u221a{3}', '24', '12\u221a{3}', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9625.jpg"
-  },
-  {
-    "id": 9889,
-    "problem_id": 9626,
-    "problem": "<image>In the figure, in rectangle ABCD, point E is on BC, and AE bisects \u2220BAC. AE = CE, BE = 2. What is the area of rectangle ABCD?. A, B, C, D choices are ['24\u221a{3}', '24', '12\u221a{3}', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9626.jpg"
-  },
-  {
-    "id": 9890,
-    "problem_id": 9627,
-    "problem": "<image>As shown in the figure, it is known that the perimeter of triangle ABC is 21. OB and OC bisect angles ABC and ACB respectively. OD is perpendicular to BC at point D, and OD = 4. What is the area of triangle ABC?. A, B, C, D choices are ['25', '42', '84', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9627.jpg"
-  },
-  {
-    "id": 9891,
-    "problem_id": 9628,
-    "problem": "<image>As shown in the figure, it is known that the perimeter of triangle ABC is 21. OB and OC bisect angles ABC and ACB respectively. OD is perpendicular to BC at point D, and OD = 4. What is the area of triangle ABC?. A, B, C, D choices are ['25', '42', '84', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9628.jpg"
-  },
-  {
-    "id": 9892,
-    "problem_id": 9629,
-    "problem": "<image>As shown in the figure, it is known that the perimeter of triangle ABC is 21. OB and OC bisect angles ABC and ACB respectively. OD is perpendicular to BC at point D, and OD = 4. What is the area of triangle ABC?. A, B, C, D choices are ['25', '42', '84', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9629.jpg"
-  },
-  {
-    "id": 9893,
-    "problem_id": 9630,
-    "problem": "<image>As shown in the figure, it is known that the perimeter of triangle ABC is 21. OB and OC bisect angles ABC and ACB respectively. OD is perpendicular to BC at point D, and OD = 4. What is the area of triangle ABC?. A, B, C, D choices are ['25', '42', '84', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9630.jpg"
-  },
-  {
-    "id": 9894,
-    "problem_id": 9631,
-    "problem": "<image>As shown in the figure, it is known that the perimeter of triangle ABC is 21. OB and OC bisect angles ABC and ACB respectively. OD is perpendicular to BC at point D, and OD = 4. What is the area of triangle ABC?. A, B, C, D choices are ['25', '42', '84', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9631.jpg"
-  },
-  {
-    "id": 9895,
-    "problem_id": 9632,
-    "problem": "<image>As shown in the figure, it is known that the perimeter of triangle ABC is 21. OB and OC bisect angles ABC and ACB respectively. OD is perpendicular to BC at point D, and OD = 4. What is the area of triangle ABC?. A, B, C, D choices are ['25', '42', '84', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9632.jpg"
-  },
-  {
-    "id": 9896,
-    "problem_id": 9633,
-    "problem": "<image>As shown in the figure, AD is the median of side BC in triangle ABC, E and F are the midpoints of AD and BE, respectively. If the area of triangle BFD is 1, then the area of triangle ABC is (). A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9633.jpg"
-  },
-  {
-    "id": 9897,
-    "problem_id": 9634,
-    "problem": "<image>As shown in the figure, AD is the median of side BC in triangle ABC, E and F are the midpoints of AD and BE, respectively. If the area of triangle BFD is 1, then the area of triangle ABC is (). A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9634.jpg"
-  },
-  {
-    "id": 9898,
-    "problem_id": 9635,
-    "problem": "<image>As shown in the figure, AD is the median of side BC in triangle ABC, E and F are the midpoints of AD and BE, respectively. If the area of triangle BFD is 1, then the area of triangle ABC is (). A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9635.jpg"
-  },
-  {
-    "id": 9899,
-    "problem_id": 9636,
-    "problem": "<image>As shown in the figure, AD is the median of side BC in triangle ABC, E and F are the midpoints of AD and BE, respectively. If the area of triangle BFD is 1, then the area of triangle ABC is (). A, B, C, D choices are ['3', '8', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9636.jpg"
-  },
-  {
-    "id": 9900,
-    "problem_id": 9637,
-    "problem": "<image>As shown in the figure, line c intersects with lines a and b. If a || b and \u22201 = 55\u00b0, then \u22202 = ().. A, B, C, D choices are ['60\u00b0', '55\u00b0', '50\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9637.jpg"
-  },
-  {
-    "id": 9901,
-    "problem_id": 9638,
-    "problem": "<image>As shown in the figure, line c intersects with lines a and b. If a || b and \u22201 = 55\u00b0, then \u22202 = ().. A, B, C, D choices are ['60\u00b0', '55\u00b0', '50\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9638.jpg"
-  },
-  {
-    "id": 9902,
-    "problem_id": 9639,
-    "problem": "<image>As shown in the figure, AB\u2225ED and CD\u2225EF. If \u22201=145\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9639.jpg"
-  },
-  {
-    "id": 9903,
-    "problem_id": 9640,
-    "problem": "<image>As shown in the figure, AB\u2225ED and CD\u2225EF. If \u22201=145\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9640.jpg"
-  },
-  {
-    "id": 9904,
-    "problem_id": 9641,
-    "problem": "<image>As shown in the figure, AB\u2225ED and CD\u2225EF. If \u22201=145\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9641.jpg"
-  },
-  {
-    "id": 9905,
-    "problem_id": 9642,
-    "problem": "<image>As shown in the figure, AB\u2225ED and CD\u2225EF. If \u22201=145\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9642.jpg"
-  },
-  {
-    "id": 9906,
-    "problem_id": 9643,
-    "problem": "<image>As shown in the figure, AB\u2225ED and CD\u2225EF. If \u22201=145\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9643.jpg"
-  },
-  {
-    "id": 9907,
-    "problem_id": 9644,
-    "problem": "<image>As shown in the figure, AB\u2225ED and CD\u2225EF. If \u22201=145\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9644.jpg"
-  },
-  {
-    "id": 9908,
-    "problem_id": 9645,
-    "problem": "<image>In the figure, in right triangle ABC, \u2220ACB=90\u00b0, CD is the altitude of AB, CE is the median of AB, AD=2, CE=5, then CD=().. A, B, C, D choices are ['2', '3', '4', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9645.jpg"
-  },
-  {
-    "id": 9909,
-    "problem_id": 9646,
-    "problem": "<image>In the figure, in right triangle ABC, \u2220ACB=90\u00b0, CD is the altitude of AB, CE is the median of AB, AD=2, CE=5, then CD=().. A, B, C, D choices are ['2', '3', '4', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9646.jpg"
-  },
-  {
-    "id": 9910,
-    "problem_id": 9647,
-    "problem": "<image>In the figure, in right triangle ABC, \u2220ACB=90\u00b0, CD is the altitude of AB, CE is the median of AB, AD=2, CE=5, then CD=().. A, B, C, D choices are ['2', '3', '4', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9647.jpg"
-  },
-  {
-    "id": 9911,
-    "problem_id": 9648,
-    "problem": "<image>In the figure, in right triangle ABC, \u2220ACB=90\u00b0, CD is the altitude of AB, CE is the median of AB, AD=2, CE=5, then CD=().. A, B, C, D choices are ['2', '3', '4', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9648.jpg"
-  },
-  {
-    "id": 9912,
-    "problem_id": 9649,
-    "problem": "<image>In the figure, in right triangle ABC, \u2220ACB=90\u00b0, CD is the altitude of AB, CE is the median of AB, AD=2, CE=5, then CD=().. A, B, C, D choices are ['2', '3', '4', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9649.jpg"
-  },
-  {
-    "id": 9913,
-    "problem_id": 9650,
-    "problem": "<image>In the figure, in right triangle ABC, \u2220ACB=90\u00b0, CD is the altitude of AB, CE is the median of AB, AD=2, CE=5, then CD=().. A, B, C, D choices are ['2', '3', '4', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9650.jpg"
-  },
-  {
-    "id": 9914,
-    "problem_id": 9651,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9651.jpg"
-  },
-  {
-    "id": 9915,
-    "problem_id": 9652,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9652.jpg"
-  },
-  {
-    "id": 9916,
-    "problem_id": 9653,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9653.jpg"
-  },
-  {
-    "id": 9917,
-    "problem_id": 9654,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9654.jpg"
-  },
-  {
-    "id": 9918,
-    "problem_id": 9655,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9655.jpg"
-  },
-  {
-    "id": 9919,
-    "problem_id": 9656,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9656.jpg"
-  },
-  {
-    "id": 9920,
-    "problem_id": 9657,
-    "problem": "<image>In parallelogram ABCD, diagonal AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, then what is the perimeter of triangle DOC?. A, B, C, D choices are ['39', '31', '33', '25'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9657.jpg"
-  },
-  {
-    "id": 9921,
-    "problem_id": 9658,
-    "problem": "<image>As shown in the figure, AB and CD intersect at point O, and AD is parallel to CB. If AO = 2, BO = 3, and OD = 2.4, then CO is equal to ().. A, B, C, D choices are ['2.4', '3', '4', '3.6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9658.jpg"
-  },
-  {
-    "id": 9922,
-    "problem_id": 9659,
-    "problem": "<image>In triangle ABC, AD is the bisector of angle BAC. AD is extended to point E such that AD = DE, and BE is connected. If AB = 3AC and the area of triangle BDE is 9, what is the area of triangle ABC?. A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9659.jpg"
-  },
-  {
-    "id": 9923,
-    "problem_id": 9660,
-    "problem": "<image>In triangle ABC, AD is the bisector of angle BAC. AD is extended to point E such that AD = DE, and BE is connected. If AB = 3AC and the area of triangle BDE is 9, what is the area of triangle ABC?. A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9660.jpg"
-  },
-  {
-    "id": 9924,
-    "problem_id": 9661,
-    "problem": "<image>In triangle ABC, AD is the bisector of angle BAC. AD is extended to point E such that AD = DE, and BE is connected. If AB = 3AC and the area of triangle BDE is 9, what is the area of triangle ABC?. A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9661.jpg"
-  },
-  {
-    "id": 9925,
-    "problem_id": 9662,
-    "problem": "<image>In right triangle ABC, as shown in the figure, \u2220BAC=90\u00b0, AB=6, AC=8. P is a moving point on the hypotenuse BC. PE is perpendicular to AB at point E, PF is perpendicular to AC at point F. EF intersects AP at point O. What is the minimum value of OF?. A, B, C, D choices are ['4.8', '1.2', '3.6', '2.4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9662.jpg"
-  },
-  {
-    "id": 9926,
-    "problem_id": 9663,
-    "problem": "<image>In right triangle ABC, as shown in the figure, \u2220BAC=90\u00b0, AB=6, AC=8. P is a moving point on the hypotenuse BC. PE is perpendicular to AB at point E, PF is perpendicular to AC at point F. EF intersects AP at point O. What is the minimum value of OF?. A, B, C, D choices are ['4.8', '1.2', '3.6', '2.4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9663.jpg"
-  },
-  {
-    "id": 9927,
-    "problem_id": 9664,
-    "problem": "<image>In right triangle ABC, as shown in the figure, \u2220BAC=90\u00b0, AB=6, AC=8. P is a moving point on the hypotenuse BC. PE is perpendicular to AB at point E, PF is perpendicular to AC at point F. EF intersects AP at point O. What is the minimum value of OF?. A, B, C, D choices are ['4.8', '1.2', '3.6', '2.4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9664.jpg"
-  },
-  {
-    "id": 9928,
-    "problem_id": 9665,
-    "problem": "<image>As shown in the figure, BC is the diameter of circle O, and points A and D are on circle O. If \u2220ACB = 32\u00b0, what is the measure of \u2220ADC? (). A, B, C, D choices are ['68\u00b0', '62\u00b0', '58\u00b0', '52\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9665.jpg"
-  },
-  {
-    "id": 9929,
-    "problem_id": 9666,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9666.jpg"
-  },
-  {
-    "id": 9930,
-    "problem_id": 9667,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9667.jpg"
-  },
-  {
-    "id": 9931,
-    "problem_id": 9668,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9668.jpg"
-  },
-  {
-    "id": 9932,
-    "problem_id": 9669,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9669.jpg"
-  },
-  {
-    "id": 9933,
-    "problem_id": 9670,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9670.jpg"
-  },
-  {
-    "id": 9934,
-    "problem_id": 9671,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9671.jpg"
-  },
-  {
-    "id": 9935,
-    "problem_id": 9672,
-    "problem": "<image>As shown in the figure, line a intersects with line b at point A when it is intersected by line c. Line b is perpendicular to line c, and the angle 1 is 60\u00b0. If we want to make line b parallel to line a, we can rotate line b clockwise around point A. (). A, B, C, D choices are ['60\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9672.jpg"
-  },
-  {
-    "id": 9936,
-    "problem_id": 9673,
-    "problem": "<image>In the figure, if AD = 6 cm and AB = 4 cm, what is the perimeter of ABCD? (). A, B, C, D choices are ['12cm', '20cm', '16cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9673.jpg"
-  },
-  {
-    "id": 9937,
-    "problem_id": 9674,
-    "problem": "<image>In the figure, if AD = 6 cm and AB = 4 cm, what is the perimeter of ABCD? (). A, B, C, D choices are ['12cm', '20cm', '16cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9674.jpg"
-  },
-  {
-    "id": 9938,
-    "problem_id": 9675,
-    "problem": "<image>In the figure, if AD = 6 cm and AB = 4 cm, what is the perimeter of ABCD? (). A, B, C, D choices are ['12cm', '20cm', '16cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9675.jpg"
-  },
-  {
-    "id": 9939,
-    "problem_id": 9676,
-    "problem": "<image>In the figure, if AD = 6 cm and AB = 4 cm, what is the perimeter of ABCD? (). A, B, C, D choices are ['12cm', '20cm', '16cm', '24cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9676.jpg"
-  },
-  {
-    "id": 9940,
-    "problem_id": 9677,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9677.jpg"
-  },
-  {
-    "id": 9941,
-    "problem_id": 9678,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9678.jpg"
-  },
-  {
-    "id": 9942,
-    "problem_id": 9679,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9679.jpg"
-  },
-  {
-    "id": 9943,
-    "problem_id": 9680,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9680.jpg"
-  },
-  {
-    "id": 9944,
-    "problem_id": 9681,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9681.jpg"
-  },
-  {
-    "id": 9945,
-    "problem_id": 9682,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9682.jpg"
-  },
-  {
-    "id": 9946,
-    "problem_id": 9683,
-    "problem": "<image>As shown in the figure, points B, C, and D are collinear. \u2220B = 56\u00b0, \u2220ACD = 120\u00b0, then what is the degree of \u2220A?. A, B, C, D choices are ['56\u00b0', '64\u00b0', '60\u00b0', '176\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9683.jpg"
-  },
-  {
-    "id": 9947,
-    "problem_id": 9684,
-    "problem": "<image>In triangle ABC, point D is on side BC, and E and F are the midpoints of AD and BE, respectively. If the area of triangle CEF is 5, what is the area of triangle ABC?. A, B, C, D choices are ['15', '20', '25', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9684.jpg"
-  },
-  {
-    "id": 9948,
-    "problem_id": 9685,
-    "problem": "<image>In triangle ABC, M is the midpoint of BC, AD bisects \u2220BAC, BD \u22a5 AD, AB = 12, AC = 22. What is the length of MD?. A, B, C, D choices are ['5', '6', '11', '5.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9685.jpg"
-  },
-  {
-    "id": 9949,
-    "problem_id": 9686,
-    "problem": "<image>In triangle ABC, M is the midpoint of BC, AD bisects \u2220BAC, BD \u22a5 AD, AB = 12, AC = 22. What is the length of MD?. A, B, C, D choices are ['5', '6', '11', '5.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9686.jpg"
-  },
-  {
-    "id": 9950,
-    "problem_id": 9687,
-    "problem": "<image>As shown in the figure, line AB passes through point O. If OC is perpendicular to OD and angle 1 is 36 degrees, what is the size of angle 2?. A, B, C, D choices are ['74\u00b0', '64\u00b0', '54\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9687.jpg"
-  },
-  {
-    "id": 9951,
-    "problem_id": 9688,
-    "problem": "<image>As shown in the figure, line AB passes through point O. If OC is perpendicular to OD and angle 1 is 36 degrees, what is the size of angle 2?. A, B, C, D choices are ['74\u00b0', '64\u00b0', '54\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9688.jpg"
-  },
-  {
-    "id": 9952,
-    "problem_id": 9689,
-    "problem": "<image>As shown in the figure, line AB passes through point O. If OC is perpendicular to OD and angle 1 is 36 degrees, what is the size of angle 2?. A, B, C, D choices are ['74\u00b0', '64\u00b0', '54\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9689.jpg"
-  },
-  {
-    "id": 9953,
-    "problem_id": 9690,
-    "problem": "<image>As shown in the figure, line AB passes through point O. If OC is perpendicular to OD and angle 1 is 36 degrees, what is the size of angle 2?. A, B, C, D choices are ['74\u00b0', '64\u00b0', '54\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9690.jpg"
-  },
-  {
-    "id": 9954,
-    "problem_id": 9691,
-    "problem": "<image>As shown in the figure, point P is an external point of circle O, PA is a tangent of circle O, and A is the point of tangency. Line PO intersects circle O at point B, \u2220P = 30\u00b0, and OB = 4. What is the length of segment AP?. A, B, C, D choices are ['4', '4\u221a{3}', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9691.jpg"
-  },
-  {
-    "id": 9955,
-    "problem_id": 9692,
-    "problem": "<image>As shown in the figure, point P is an external point of circle O, PA is a tangent of circle O, and A is the point of tangency. Line PO intersects circle O at point B, \u2220P = 30\u00b0, and OB = 4. What is the length of segment AP?. A, B, C, D choices are ['4', '4\u221a{3}', '8', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9692.jpg"
-  },
-  {
-    "id": 9956,
-    "problem_id": 9693,
-    "problem": "<image>In triangle ABC, it is known that points D, E, and F are the midpoints of sides BC, AB, and AC, respectively, and the area of triangle ABC is 12. The area of the shaded region is ().. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9693.jpg"
-  },
-  {
-    "id": 9957,
-    "problem_id": 9694,
-    "problem": "<image>In triangle ABC, it is known that points D, E, and F are the midpoints of sides BC, AB, and AC, respectively, and the area of triangle ABC is 12. The area of the shaded region is ().. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9694.jpg"
-  },
-  {
-    "id": 9959,
-    "problem_id": 9695,
-    "problem": "<image>In triangle ABC, it is known that points D, E, and F are the midpoints of sides BC, AB, and AC, respectively, and the area of triangle ABC is 12. The area of the shaded region is ().. A, B, C, D choices are ['2', '4', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9695.jpg"
-  },
-  {
-    "id": 9960,
-    "problem_id": 9696,
-    "problem": "<image>As shown in the diagram, the perimeter of diamond ABCD is 24cm. Diagonals AC and BD intersect at point O. E is the midpoint of AD. If OE is connected, the length of segment OE is equal to () cm.. A, B, C, D choices are ['3cm', '4cm', '2.5cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9696.jpg"
-  },
-  {
-    "id": 9961,
-    "problem_id": 9697,
-    "problem": "<image>As shown in the diagram, the perimeter of diamond ABCD is 24cm. Diagonals AC and BD intersect at point O. E is the midpoint of AD. If OE is connected, the length of segment OE is equal to () cm.. A, B, C, D choices are ['3cm', '4cm', '2.5cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9697.jpg"
-  },
-  {
-    "id": 9962,
-    "problem_id": 9698,
-    "problem": "<image>As shown in the diagram, the perimeter of diamond ABCD is 24cm. Diagonals AC and BD intersect at point O. E is the midpoint of AD. If OE is connected, the length of segment OE is equal to () cm.. A, B, C, D choices are ['3cm', '4cm', '2.5cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9698.jpg"
-  },
-  {
-    "id": 9963,
-    "problem_id": 9699,
-    "problem": "<image>As shown in the diagram, the perimeter of diamond ABCD is 24cm. Diagonals AC and BD intersect at point O. E is the midpoint of AD. If OE is connected, the length of segment OE is equal to () cm.. A, B, C, D choices are ['3cm', '4cm', '2.5cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9699.jpg"
-  },
-  {
-    "id": 9964,
-    "problem_id": 9700,
-    "problem": "<image>As shown in the diagram, the perimeter of diamond ABCD is 24cm. Diagonals AC and BD intersect at point O. E is the midpoint of AD. If OE is connected, the length of segment OE is equal to () cm.. A, B, C, D choices are ['3cm', '4cm', '2.5cm', '2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9700.jpg"
-  },
-  {
-    "id": 9965,
-    "problem_id": 9701,
-    "problem": "<image>In parallelogram ABCD, AC and BD intersect at point O, AB is perpendicular to AC. If AB = 4 and AC = 6, what is the perimeter of triangle COD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9701.jpg"
-  },
-  {
-    "id": 9966,
-    "problem_id": 9702,
-    "problem": "<image>In parallelogram ABCD, AC and BD intersect at point O, AB is perpendicular to AC. If AB = 4 and AC = 6, what is the perimeter of triangle COD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9702.jpg"
-  },
-  {
-    "id": 9967,
-    "problem_id": 9703,
-    "problem": "<image>As shown in the figure, if the vertex of a square ruler is placed on one side of a ruler, and \u22201 = 24\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['24\u00b0', '56\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9703.jpg"
-  },
-  {
-    "id": 9968,
-    "problem_id": 9704,
-    "problem": "<image>As shown in the figure, if the vertex of a square ruler is placed on one side of a ruler, and \u22201 = 24\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['24\u00b0', '56\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9704.jpg"
-  },
-  {
-    "id": 9969,
-    "problem_id": 9705,
-    "problem": "<image>As shown in the figure, if the vertex of a square ruler is placed on one side of a ruler, and \u22201 = 24\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['24\u00b0', '56\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9705.jpg"
-  },
-  {
-    "id": 9970,
-    "problem_id": 9706,
-    "problem": "<image>As shown in the figure, if the vertex of a square ruler is placed on one side of a ruler, and \u22201 = 24\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['24\u00b0', '56\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9706.jpg"
-  },
-  {
-    "id": 9971,
-    "problem_id": 9707,
-    "problem": "<image>As shown in the figure, if the vertex of a square ruler is placed on one side of a ruler, and \u22201 = 24\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['24\u00b0', '56\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9707.jpg"
-  },
-  {
-    "id": 9972,
-    "problem_id": 9708,
-    "problem": "<image>As shown in the figure, if the vertex of a square ruler is placed on one side of a ruler, and \u22201 = 24\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['24\u00b0', '56\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9708.jpg"
-  },
-  {
-    "id": 9974,
-    "problem_id": 9709,
-    "problem": "<image>As shown in the figure, two straight lines a and b intersect at point O. If \u22201 = 60\u00b0, then \u22202 = (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9709.jpg"
-  },
-  {
-    "id": 9975,
-    "problem_id": 9710,
-    "problem": "<image>As shown in the figure, two straight lines a and b intersect at point O. If \u22201 = 60\u00b0, then \u22202 = (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9710.jpg"
-  },
-  {
-    "id": 9976,
-    "problem_id": 9711,
-    "problem": "<image>As shown in the figure, two straight lines a and b intersect at point O. If \u22201 = 60\u00b0, then \u22202 = (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9711.jpg"
-  },
-  {
-    "id": 9977,
-    "problem_id": 9712,
-    "problem": "<image>As shown in the figure, two straight lines a and b intersect at point O. If \u22201 = 60\u00b0, then \u22202 = (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9712.jpg"
-  },
-  {
-    "id": 9978,
-    "problem_id": 9713,
-    "problem": "<image>As shown in the figure, two straight lines a and b intersect at point O. If \u22201 = 60\u00b0, then \u22202 = (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9713.jpg"
-  },
-  {
-    "id": 9979,
-    "problem_id": 9714,
-    "problem": "<image>As shown in the figure, two straight lines a and b intersect at point O. If \u22201 = 60\u00b0, then \u22202 = (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9714.jpg"
-  },
-  {
-    "id": 9980,
-    "problem_id": 9715,
-    "problem": "<image>A right-angled triangle board is placed as shown in the figure. Point C is on the extension line of FD, AB\u2225CF, \u2220F\uff1d\u2220ACB\uff1d90\u00b0, \u2220A\uff1d60\u00b0. What is the degree measure of \u2220DBC? (). A, B, C, D choices are ['45\u00b0', '25\u00b0', '15\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9715.jpg"
-  },
-  {
-    "id": 9981,
-    "problem_id": 9716,
-    "problem": "<image>As shown in the diagram, a tall tree is broken into three sections at points 3m and 5m above the ground. The middle section AB is parallel to the ground. The top of the tree falls 6m away from the bottom of the tree. What was the height of the tree before it was broken?. A, B, C, D choices are ['9m', '14m', '11m', '10m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9716.jpg"
-  },
-  {
-    "id": 9982,
-    "problem_id": 9717,
-    "problem": "<image>In triangle ABC, points D and E are the midpoints of BC and BA, respectively. If AC = 4, then DE = ().. A, B, C, D choices are ['1', '2', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9717.jpg"
-  },
-  {
-    "id": 9983,
-    "problem_id": 9718,
-    "problem": "<image>In triangle ABC, points D and E are the midpoints of BC and BA, respectively. If AC = 4, then DE = ().. A, B, C, D choices are ['1', '2', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9718.jpg"
-  },
-  {
-    "id": 9984,
-    "problem_id": 9719,
-    "problem": "<image>In triangle ABC, points D and E are the midpoints of BC and BA, respectively. If AC = 4, then DE = ().. A, B, C, D choices are ['1', '2', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9719.jpg"
-  },
-  {
-    "id": 9985,
-    "problem_id": 9720,
-    "problem": "<image>In triangle ABC, points D and E are the midpoints of BC and BA, respectively. If AC = 4, then DE = ().. A, B, C, D choices are ['1', '2', '4', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9720.jpg"
-  },
-  {
-    "id": 9986,
-    "problem_id": 9721,
-    "problem": "<image>In circle \u2299O with radius 1, extend diameter AB to point C such that BC = OA. CD is a tangent to circle \u2299O at point D. What is the length of AD?. A, B, C, D choices are ['1', '\u221a{3}', '2', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9721.jpg"
-  },
-  {
-    "id": 9987,
-    "problem_id": 9722,
-    "problem": "<image>In circle \u2299O with radius 1, extend diameter AB to point C such that BC = OA. CD is a tangent to circle \u2299O at point D. What is the length of AD?. A, B, C, D choices are ['1', '\u221a{3}', '2', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9722.jpg"
-  },
-  {
-    "id": 9988,
-    "problem_id": 9723,
-    "problem": "<image>In circle \u2299O with radius 1, extend diameter AB to point C such that BC = OA. CD is a tangent to circle \u2299O at point D. What is the length of AD?. A, B, C, D choices are ['1', '\u221a{3}', '2', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9723.jpg"
-  },
-  {
-    "id": 9989,
-    "problem_id": 9724,
-    "problem": "<image>In circle \u2299O with radius 1, extend diameter AB to point C such that BC = OA. CD is a tangent to circle \u2299O at point D. What is the length of AD?. A, B, C, D choices are ['1', '\u221a{3}', '2', '2\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9724.jpg"
-  },
-  {
-    "id": 9990,
-    "problem_id": 9725,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9725.jpg"
-  },
-  {
-    "id": 9991,
-    "problem_id": 9726,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9726.jpg"
-  },
-  {
-    "id": 9992,
-    "problem_id": 9727,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9727.jpg"
-  },
-  {
-    "id": 9993,
-    "problem_id": 9728,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9728.jpg"
-  },
-  {
-    "id": 9994,
-    "problem_id": 9729,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9729.jpg"
-  },
-  {
-    "id": 9995,
-    "problem_id": 9730,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9730.jpg"
-  },
-  {
-    "id": 9996,
-    "problem_id": 9731,
-    "problem": "<image>As shown in the figure, the two diagonals of rectangle ABCD intersect at point O, and \u2220AOB = 60\u00b0, AB = 2. The length of side BC of the rectangle is ().. A, B, C, D choices are ['2', '4', '2\u221a{3}', '4\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9731.jpg"
-  },
-  {
-    "id": 9997,
-    "problem_id": 9732,
-    "problem": "<image>In the figure, the size of angle EAG in regular octagon ABCDEFGH is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9732.jpg"
-  },
-  {
-    "id": 9998,
-    "problem_id": 9733,
-    "problem": "<image>In the figure, the size of angle EAG in regular octagon ABCDEFGH is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9733.jpg"
-  },
-  {
-    "id": 9999,
-    "problem_id": 9734,
-    "problem": "<image>In the figure, the size of angle EAG in regular octagon ABCDEFGH is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9734.jpg"
-  },
-  {
-    "id": 10000,
-    "problem_id": 9735,
-    "problem": "<image>In parallelogram ABCD, O is the intersection point of AC and BD. A line perpendicular to AC passing through point O intersects side AD at point E. If the perimeter of triangle CDE is 11cm, then what is the perimeter of parallelogram ABCD?. A, B, C, D choices are ['20cm', '22cm', '24cm', '26cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9735.jpg"
-  },
-  {
-    "id": 10001,
-    "problem_id": 9736,
-    "problem": "<image>In triangle ABC, it is known that D, E, and F are the midpoints of BC, AD, and BE, respectively. If the area of triangle BED is 3cm2, then the area of triangle ABC is ().. A, B, C, D choices are ['24', '12', '9', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9736.jpg"
-  },
-  {
-    "id": 10002,
-    "problem_id": 9737,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9737.jpg"
-  },
-  {
-    "id": 10003,
-    "problem_id": 9738,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9738.jpg"
-  },
-  {
-    "id": 10004,
-    "problem_id": 9739,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9739.jpg"
-  },
-  {
-    "id": 10005,
-    "problem_id": 9740,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9740.jpg"
-  },
-  {
-    "id": 10006,
-    "problem_id": 9741,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9741.jpg"
-  },
-  {
-    "id": 10007,
-    "problem_id": 9742,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9742.jpg"
-  },
-  {
-    "id": 10008,
-    "problem_id": 9743,
-    "problem": "<image>If a set square is stacked as shown in the figure, what is the degree of angle 1? (). A, B, C, D choices are ['90\u00b0', '100\u00b0', '105\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9743.jpg"
-  },
-  {
-    "id": 10009,
-    "problem_id": 9744,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9744.jpg"
-  },
-  {
-    "id": 10010,
-    "problem_id": 9745,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9745.jpg"
-  },
-  {
-    "id": 10011,
-    "problem_id": 9746,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9746.jpg"
-  },
-  {
-    "id": 10012,
-    "problem_id": 9747,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9747.jpg"
-  },
-  {
-    "id": 10013,
-    "problem_id": 9748,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9748.jpg"
-  },
-  {
-    "id": 10014,
-    "problem_id": 9749,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9749.jpg"
-  },
-  {
-    "id": 10015,
-    "problem_id": 9750,
-    "problem": "<image>In the figure, points A, B, and C are all on circle O. If \u2220ACB = 70\u00b0, what is the degree measure of \u2220OAB?. A, B, C, D choices are ['10\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9750.jpg"
-  },
-  {
-    "id": 10016,
-    "problem_id": 9751,
-    "problem": "<image>As shown in the figure, 25 and 169 are the areas of two squares respectively. What is the area of the square represented by letter B?. A, B, C, D choices are ['12', '13', '144', '194'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9751.jpg"
-  },
-  {
-    "id": 10017,
-    "problem_id": 9752,
-    "problem": "<image>As shown in the figure, 25 and 169 are the areas of two squares respectively. What is the area of the square represented by letter B?. A, B, C, D choices are ['12', '13', '144', '194'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9752.jpg"
-  },
-  {
-    "id": 10018,
-    "problem_id": 9753,
-    "problem": "<image>As shown in the figure, 25 and 169 are the areas of two squares respectively. What is the area of the square represented by letter B?. A, B, C, D choices are ['12', '13', '144', '194'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9753.jpg"
-  },
-  {
-    "id": 10019,
-    "problem_id": 9754,
-    "problem": "<image>As shown in the figure, 25 and 169 are the areas of two squares respectively. What is the area of the square represented by letter B?. A, B, C, D choices are ['12', '13', '144', '194'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9754.jpg"
-  },
-  {
-    "id": 10020,
-    "problem_id": 9755,
-    "problem": "<image>As shown in the figure, 25 and 169 are the areas of two squares respectively. What is the area of the square represented by letter B?. A, B, C, D choices are ['12', '13', '144', '194'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9755.jpg"
-  },
-  {
-    "id": 10022,
-    "problem_id": 9756,
-    "problem": "<image>As shown in the figure, AB\u2225CD, \u2220FEB\uff1d70\u00b0, the angle bisector of \u2220EFD, FG, intersects AB at point G. The degree measure of \u2220EFG is ().. A, B, C, D choices are ['63\u00b0', '53\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9756.jpg"
-  },
-  {
-    "id": 10023,
-    "problem_id": 9757,
-    "problem": "<image>As shown in the figure, AB\u2225CD, \u2220FEB\uff1d70\u00b0, the angle bisector of \u2220EFD, FG, intersects AB at point G. The degree measure of \u2220EFG is ().. A, B, C, D choices are ['63\u00b0', '53\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9757.jpg"
-  },
-  {
-    "id": 10024,
-    "problem_id": 9758,
-    "problem": "<image>In the inscribed quadrilateral ABCD of circle O as shown in the figure, if \u2220BOD = 100\u00b0, then what is the degree measure of \u2220BCD?. A, B, C, D choices are ['130\u00b0', '100\u00b0', '80\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9758.jpg"
-  },
-  {
-    "id": 10025,
-    "problem_id": 9759,
-    "problem": "<image>In the inscribed quadrilateral ABCD of circle O as shown in the figure, if \u2220BOD = 100\u00b0, then what is the degree measure of \u2220BCD?. A, B, C, D choices are ['130\u00b0', '100\u00b0', '80\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9759.jpg"
-  },
-  {
-    "id": 10026,
-    "problem_id": 9760,
-    "problem": "<image>In the inscribed quadrilateral ABCD of circle O as shown in the figure, if \u2220BOD = 100\u00b0, then what is the degree measure of \u2220BCD?. A, B, C, D choices are ['130\u00b0', '100\u00b0', '80\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9760.jpg"
-  },
-  {
-    "id": 10027,
-    "problem_id": 9761,
-    "problem": "<image>In the inscribed quadrilateral ABCD of circle O as shown in the figure, if \u2220BOD = 100\u00b0, then what is the degree measure of \u2220BCD?. A, B, C, D choices are ['130\u00b0', '100\u00b0', '80\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9761.jpg"
-  },
-  {
-    "id": 10028,
-    "problem_id": 9762,
-    "problem": "<image>In the inscribed quadrilateral ABCD of circle O as shown in the figure, if \u2220BOD = 100\u00b0, then what is the degree measure of \u2220BCD?. A, B, C, D choices are ['130\u00b0', '100\u00b0', '80\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9762.jpg"
-  },
-  {
-    "id": 10029,
-    "problem_id": 9763,
-    "problem": "<image>As shown in the diagram, line AB and CD intersect at point O, and OE bisects angle AOC. If angle BOD is 70 degrees, then angle AOE equals () .. A, B, C, D choices are ['145\u00b0', '110\u00b0', '35\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9763.jpg"
-  },
-  {
-    "id": 10031,
-    "problem_id": 9764,
-    "problem": "<image>As shown in the figure, it is known that line a is parallel to line b. The right-angled triangle ABC has its right angle vertex C on line b. If \u22201 = 60\u00b0, then \u22202 = ().. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9764.jpg"
-  },
-  {
-    "id": 10032,
-    "problem_id": 9765,
-    "problem": "<image>As shown in the figure, it is known that line a is parallel to line b. The right-angled triangle ABC has its right angle vertex C on line b. If \u22201 = 60\u00b0, then \u22202 = ().. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9765.jpg"
-  },
-  {
-    "id": 10033,
-    "problem_id": 9766,
-    "problem": "<image>As shown in the figure, it is known that line a is parallel to line b. The right-angled triangle ABC has its right angle vertex C on line b. If \u22201 = 60\u00b0, then \u22202 = ().. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9766.jpg"
-  },
-  {
-    "id": 10034,
-    "problem_id": 9767,
-    "problem": "<image>As shown in the figure, if the diagonals AC and BD of the rhombus ABCD are 8 and 6 respectively, then the perimeter of the rhombus ABCD is (). A, B, C, D choices are ['14', '20', '24', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9767.jpg"
-  },
-  {
-    "id": 10035,
-    "problem_id": 9768,
-    "problem": "<image>As shown in the figure, if the diagonals AC and BD of the rhombus ABCD are 8 and 6 respectively, then the perimeter of the rhombus ABCD is (). A, B, C, D choices are ['14', '20', '24', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9768.jpg"
-  },
-  {
-    "id": 10036,
-    "problem_id": 9769,
-    "problem": "<image>As shown in the figure, if the diagonals AC and BD of the rhombus ABCD are 8 and 6 respectively, then the perimeter of the rhombus ABCD is (). A, B, C, D choices are ['14', '20', '24', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9769.jpg"
-  },
-  {
-    "id": 10037,
-    "problem_id": 9770,
-    "problem": "<image>As shown in the figure, if the diagonals AC and BD of the rhombus ABCD are 8 and 6 respectively, then the perimeter of the rhombus ABCD is (). A, B, C, D choices are ['14', '20', '24', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9770.jpg"
-  },
-  {
-    "id": 10038,
-    "problem_id": 9771,
-    "problem": "<image>As shown in the figure, if the diagonals AC and BD of the rhombus ABCD are 8 and 6 respectively, then the perimeter of the rhombus ABCD is (). A, B, C, D choices are ['14', '20', '24', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9771.jpg"
-  },
-  {
-    "id": 10039,
-    "problem_id": 9772,
-    "problem": "<image>In circle O, as shown in the diagram, if \u2220OAC+\u2220C=50\u00b0, what is the measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9772.jpg"
-  },
-  {
-    "id": 10040,
-    "problem_id": 9773,
-    "problem": "<image>In circle O, as shown in the diagram, if \u2220OAC+\u2220C=50\u00b0, what is the measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9773.jpg"
-  },
-  {
-    "id": 10041,
-    "problem_id": 9774,
-    "problem": "<image>In the right triangle ABC shown in the figure, \u2220ACB = 90\u00b0, CD is the altitude, and if \u2220BCD = 30\u00b0 and BD = 1, then the length of AB is ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9774.jpg"
-  },
-  {
-    "id": 10042,
-    "problem_id": 9775,
-    "problem": "<image>In the right triangle ABC shown in the figure, \u2220ACB = 90\u00b0, CD is the altitude, and if \u2220BCD = 30\u00b0 and BD = 1, then the length of AB is ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9775.jpg"
-  },
-  {
-    "id": 10043,
-    "problem_id": 9776,
-    "problem": "<image>As shown in the figure, it is known that the area of ABCD is 48. E is the midpoint of AB and DE is connected. What is the area of \u25b3ODE?. A, B, C, D choices are ['8', '6', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9776.jpg"
-  },
-  {
-    "id": 10044,
-    "problem_id": 9777,
-    "problem": "<image>As shown in the figure, if the rectangular paper ABCD is folded along the diagonal BD, point C falls on point E, and BE intersects AD at point F. If \u2220EDF = 42\u00b0, what is the degree of \u2220DBE? (). A, B, C, D choices are ['21\u00b0', '23\u00b0', '24\u00b0', '42\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9777.jpg"
-  },
-  {
-    "id": 10045,
-    "problem_id": 9778,
-    "problem": "<image>Given AB \u2225 CD, \u22201 = 95\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['85\u00b0', '75\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9778.jpg"
-  },
-  {
-    "id": 10047,
-    "problem_id": 9779,
-    "problem": "<image>Given AB \u2225 CD, \u22201 = 95\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['85\u00b0', '75\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9779.jpg"
-  },
-  {
-    "id": 10048,
-    "problem_id": 9780,
-    "problem": "<image>Given AB \u2225 CD, \u22201 = 95\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['85\u00b0', '75\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9780.jpg"
-  },
-  {
-    "id": 10049,
-    "problem_id": 9781,
-    "problem": "<image>Given AB \u2225 CD, \u22201 = 95\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['85\u00b0', '75\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9781.jpg"
-  },
-  {
-    "id": 10050,
-    "problem_id": 9782,
-    "problem": "<image>Given AB \u2225 CD, \u22201 = 95\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['85\u00b0', '75\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9782.jpg"
-  },
-  {
-    "id": 10051,
-    "problem_id": 9783,
-    "problem": "<image>Given AB \u2225 CD, \u22201 = 95\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['85\u00b0', '75\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9783.jpg"
-  },
-  {
-    "id": 10052,
-    "problem_id": 9784,
-    "problem": "<image>As shown in the figure, the area of rhombus ABCD is 24cm2, the length of diagonal BD is 6cm, point O is the midpoint of BD, line AE is perpendicular to BC at point A and intersects the extension of CB at point E. Connect OE, the length of segment OE is ().. A, B, C, D choices are ['3cm', '4cm', '4.8cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9784.jpg"
-  },
-  {
-    "id": 10053,
-    "problem_id": 9785,
-    "problem": "<image>As shown in the figure, the area of rhombus ABCD is 24cm2, the length of diagonal BD is 6cm, point O is the midpoint of BD, line AE is perpendicular to BC at point A and intersects the extension of CB at point E. Connect OE, the length of segment OE is ().. A, B, C, D choices are ['3cm', '4cm', '4.8cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9785.jpg"
-  },
-  {
-    "id": 10054,
-    "problem_id": 9786,
-    "problem": "<image>As shown in the figure, the area of rhombus ABCD is 24cm2, the length of diagonal BD is 6cm, point O is the midpoint of BD, line AE is perpendicular to BC at point A and intersects the extension of CB at point E. Connect OE, the length of segment OE is ().. A, B, C, D choices are ['3cm', '4cm', '4.8cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9786.jpg"
-  },
-  {
-    "id": 10055,
-    "problem_id": 9787,
-    "problem": "<image>As shown in the figure, the area of rhombus ABCD is 24cm2, the length of diagonal BD is 6cm, point O is the midpoint of BD, line AE is perpendicular to BC at point A and intersects the extension of CB at point E. Connect OE, the length of segment OE is ().. A, B, C, D choices are ['3cm', '4cm', '4.8cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9787.jpg"
-  },
-  {
-    "id": 10056,
-    "problem_id": 9788,
-    "problem": "<image>As shown in the figure, the area of rhombus ABCD is 24cm2, the length of diagonal BD is 6cm, point O is the midpoint of BD, line AE is perpendicular to BC at point A and intersects the extension of CB at point E. Connect OE, the length of segment OE is ().. A, B, C, D choices are ['3cm', '4cm', '4.8cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9788.jpg"
-  },
-  {
-    "id": 10057,
-    "problem_id": 9789,
-    "problem": "<image>As shown in the figure, the area of rhombus ABCD is 24cm2, the length of diagonal BD is 6cm, point O is the midpoint of BD, line AE is perpendicular to BC at point A and intersects the extension of CB at point E. Connect OE, the length of segment OE is ().. A, B, C, D choices are ['3cm', '4cm', '4.8cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9789.jpg"
-  },
-  {
-    "id": 10058,
-    "problem_id": 9790,
-    "problem": "<image>As shown in the figure, BE and CF are the altitudes of triangle ABC, M is the midpoint of BC, EF = 5, and BC = 8. The perimeter of triangle EFM is ().. A, B, C, D choices are ['13', '15', '18', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9790.jpg"
-  },
-  {
-    "id": 10059,
-    "problem_id": 9791,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9791.jpg"
-  },
-  {
-    "id": 10060,
-    "problem_id": 9792,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9792.jpg"
-  },
-  {
-    "id": 10061,
-    "problem_id": 9793,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9793.jpg"
-  },
-  {
-    "id": 10062,
-    "problem_id": 9794,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9794.jpg"
-  },
-  {
-    "id": 10063,
-    "problem_id": 9795,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9795.jpg"
-  },
-  {
-    "id": 10064,
-    "problem_id": 9796,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9796.jpg"
-  },
-  {
-    "id": 10065,
-    "problem_id": 9797,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9797.jpg"
-  },
-  {
-    "id": 10066,
-    "problem_id": 9798,
-    "problem": "<image>In quadrilateral ABCD, as shown in the figure, \u2220D = \u2220ACB = 90\u00b0, CD = 12, AD = 16, and BC = 15. Find the value of AB.. A, B, C, D choices are ['20', '25', '35', '30'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9798.jpg"
-  },
-  {
-    "id": 10068,
-    "problem_id": 9799,
-    "problem": "<image>As shown in the figure, line l1 is parallel to line l2, \u22201 = 50\u00b0, \u22202 = 75\u00b0, then \u22203 = ().. A, B, C, D choices are ['55\u00b0', '60\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9799.jpg"
-  },
-  {
-    "id": 10069,
-    "problem_id": 9800,
-    "problem": "<image>As shown in the figure, line l1 is parallel to line l2, \u22201 = 50\u00b0, \u22202 = 75\u00b0, then \u22203 = ().. A, B, C, D choices are ['55\u00b0', '60\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9800.jpg"
-  },
-  {
-    "id": 10070,
-    "problem_id": 9801,
-    "problem": "<image>As shown in the figure, line l1 is parallel to line l2, \u22201 = 50\u00b0, \u22202 = 75\u00b0, then \u22203 = ().. A, B, C, D choices are ['55\u00b0', '60\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9801.jpg"
-  },
-  {
-    "id": 10071,
-    "problem_id": 9802,
-    "problem": "<image>As shown in the figure, line l1 is parallel to line l2, \u22201 = 50\u00b0, \u22202 = 75\u00b0, then \u22203 = ().. A, B, C, D choices are ['55\u00b0', '60\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9802.jpg"
-  },
-  {
-    "id": 10073,
-    "problem_id": 9803,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, \u22201\uff1d90\u00b0, \u22202\uff1d32\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['68\u00b0', '102\u00b0', '122\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9803.jpg"
-  },
-  {
-    "id": 10074,
-    "problem_id": 9804,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9804.jpg"
-  },
-  {
-    "id": 10075,
-    "problem_id": 9805,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9805.jpg"
-  },
-  {
-    "id": 10076,
-    "problem_id": 9806,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9806.jpg"
-  },
-  {
-    "id": 10077,
-    "problem_id": 9807,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9807.jpg"
-  },
-  {
-    "id": 10078,
-    "problem_id": 9808,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9808.jpg"
-  },
-  {
-    "id": 10079,
-    "problem_id": 9809,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9809.jpg"
-  },
-  {
-    "id": 10080,
-    "problem_id": 9810,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9810.jpg"
-  },
-  {
-    "id": 10081,
-    "problem_id": 9811,
-    "problem": "<image>As shown in the figure, A, B, and C are three points on the circle O. \u2220ABC = 50\u00b0, what is the degree of \u2220AOC?. A, B, C, D choices are ['25\u00b0', '65\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9811.jpg"
-  },
-  {
-    "id": 10082,
-    "problem_id": 9812,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9812.jpg"
-  },
-  {
-    "id": 10083,
-    "problem_id": 9813,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9813.jpg"
-  },
-  {
-    "id": 10084,
-    "problem_id": 9814,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9814.jpg"
-  },
-  {
-    "id": 10085,
-    "problem_id": 9815,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9815.jpg"
-  },
-  {
-    "id": 10086,
-    "problem_id": 9816,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9816.jpg"
-  },
-  {
-    "id": 10087,
-    "problem_id": 9817,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9817.jpg"
-  },
-  {
-    "id": 10088,
-    "problem_id": 9818,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9818.jpg"
-  },
-  {
-    "id": 10089,
-    "problem_id": 9819,
-    "problem": "<image>In triangle ABC, AC=4. D and E are the midpoints of AB and CB, respectively. What is the length of DE?. A, B, C, D choices are ['2', '1.5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9819.jpg"
-  },
-  {
-    "id": 10090,
-    "problem_id": 9820,
-    "problem": "<image>As shown in the figure, in quadrilateral ABCD, AB = 15, BC = 12, CD = 16, AD = 25, and \u2220C = 90\u00b0. The area of quadrilateral ABCD is (). A, B, C, D choices are ['246', '296', '592', '220'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9820.jpg"
-  },
-  {
-    "id": 10091,
-    "problem_id": 9821,
-    "problem": "<image>As shown in the figure, in quadrilateral ABCD, AB = 15, BC = 12, CD = 16, AD = 25, and \u2220C = 90\u00b0. The area of quadrilateral ABCD is (). A, B, C, D choices are ['246', '296', '592', '220'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9821.jpg"
-  },
-  {
-    "id": 10092,
-    "problem_id": 9822,
-    "problem": "<image>As shown in the figure, in quadrilateral ABCD, AB = 15, BC = 12, CD = 16, AD = 25, and \u2220C = 90\u00b0. The area of quadrilateral ABCD is (). A, B, C, D choices are ['246', '296', '592', '220'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9822.jpg"
-  },
-  {
-    "id": 10093,
-    "problem_id": 9823,
-    "problem": "<image>As shown in the figure, in quadrilateral ABCD, AB = 15, BC = 12, CD = 16, AD = 25, and \u2220C = 90\u00b0. The area of quadrilateral ABCD is (). A, B, C, D choices are ['246', '296', '592', '220'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9823.jpg"
-  },
-  {
-    "id": 10094,
-    "problem_id": 9824,
-    "problem": "<image>As shown in the figure, in quadrilateral ABCD, AB = 15, BC = 12, CD = 16, AD = 25, and \u2220C = 90\u00b0. The area of quadrilateral ABCD is (). A, B, C, D choices are ['246', '296', '592', '220'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9824.jpg"
-  },
-  {
-    "id": 10095,
-    "problem_id": 9825,
-    "problem": "<image>In triangle ABC, AC=8cm, BC=6cm, and AB=10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the area of triangle DEF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9825.jpg"
-  },
-  {
-    "id": 10096,
-    "problem_id": 9826,
-    "problem": "<image>In triangle ABC, AC=8cm, BC=6cm, and AB=10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the area of triangle DEF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9826.jpg"
-  },
-  {
-    "id": 10097,
-    "problem_id": 9827,
-    "problem": "<image>In triangle ABC, AC=8cm, BC=6cm, and AB=10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the area of triangle DEF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9827.jpg"
-  },
-  {
-    "id": 10098,
-    "problem_id": 9828,
-    "problem": "<image>In triangle ABC, AC=8cm, BC=6cm, and AB=10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the area of triangle DEF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9828.jpg"
-  },
-  {
-    "id": 10099,
-    "problem_id": 9829,
-    "problem": "<image>In triangle ABC, AC=8cm, BC=6cm, and AB=10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the area of triangle DEF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9829.jpg"
-  },
-  {
-    "id": 10100,
-    "problem_id": 9830,
-    "problem": "<image>In triangle ABC, AC=8cm, BC=6cm, and AB=10cm. D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the area of triangle DEF?. A, B, C, D choices are ['6', '12', '24', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9830.jpg"
-  },
-  {
-    "id": 10101,
-    "problem_id": 9831,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, point B is on line b, and AB is perpendicular to BC. Angle 1 is 55 degrees. What is the degree of angle 2?. A, B, C, D choices are ['25\u00b0', '35\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9831.jpg"
-  },
-  {
-    "id": 10102,
-    "problem_id": 9832,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9832.jpg"
-  },
-  {
-    "id": 10103,
-    "problem_id": 9833,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9833.jpg"
-  },
-  {
-    "id": 10104,
-    "problem_id": 9834,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9834.jpg"
-  },
-  {
-    "id": 10105,
-    "problem_id": 9835,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9835.jpg"
-  },
-  {
-    "id": 10106,
-    "problem_id": 9836,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9836.jpg"
-  },
-  {
-    "id": 10107,
-    "problem_id": 9837,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9837.jpg"
-  },
-  {
-    "id": 10108,
-    "problem_id": 9838,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9838.jpg"
-  },
-  {
-    "id": 10109,
-    "problem_id": 9839,
-    "problem": "<image>In the equilateral triangle ABC shown in the figure, points D and E are on sides AB and AC, respectively. If \u25b3ADE\u223d\u25b3ABC and AD:AB=0.25, and BC=8cm, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['2cm', '3cm', '6cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9839.jpg"
-  },
-  {
-    "id": 10110,
-    "problem_id": 9840,
-    "problem": "<image>In the rhombus ABCD, with BC = 10, point E lies on BD, F is the midpoint of AD, FE is perpendicular to BD, and the foot of the perpendicular is E. If EF = 4, what is the length of BD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9840.jpg"
-  },
-  {
-    "id": 10111,
-    "problem_id": 9841,
-    "problem": "<image>In the rhombus ABCD, with BC = 10, point E lies on BD, F is the midpoint of AD, FE is perpendicular to BD, and the foot of the perpendicular is E. If EF = 4, what is the length of BD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9841.jpg"
-  },
-  {
-    "id": 10112,
-    "problem_id": 9842,
-    "problem": "<image>In the rhombus ABCD, with BC = 10, point E lies on BD, F is the midpoint of AD, FE is perpendicular to BD, and the foot of the perpendicular is E. If EF = 4, what is the length of BD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9842.jpg"
-  },
-  {
-    "id": 10113,
-    "problem_id": 9843,
-    "problem": "<image>In the rhombus ABCD, with BC = 10, point E lies on BD, F is the midpoint of AD, FE is perpendicular to BD, and the foot of the perpendicular is E. If EF = 4, what is the length of BD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9843.jpg"
-  },
-  {
-    "id": 10114,
-    "problem_id": 9844,
-    "problem": "<image>In the rhombus ABCD, with BC = 10, point E lies on BD, F is the midpoint of AD, FE is perpendicular to BD, and the foot of the perpendicular is E. If EF = 4, what is the length of BD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9844.jpg"
-  },
-  {
-    "id": 10115,
-    "problem_id": 9845,
-    "problem": "<image>In the rhombus ABCD, with BC = 10, point E lies on BD, F is the midpoint of AD, FE is perpendicular to BD, and the foot of the perpendicular is E. If EF = 4, what is the length of BD?. A, B, C, D choices are ['8', '10', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9845.jpg"
-  },
-  {
-    "id": 10116,
-    "problem_id": 9846,
-    "problem": "<image>As shown in the diagram, \u2220AOB = 90\u00b0, OE is the bisector of \u2220AOB, OD is the bisector of \u2220BOC, if \u2220EOD=60\u00b0, then \u2220EOC = (). A, B, C, D choices are ['75\u00b0', '90\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9846.jpg"
-  },
-  {
-    "id": 10117,
-    "problem_id": 9847,
-    "problem": "<image>As shown in the diagram, \u2220AOB = 90\u00b0, OE is the bisector of \u2220AOB, OD is the bisector of \u2220BOC, if \u2220EOD=60\u00b0, then \u2220EOC = (). A, B, C, D choices are ['75\u00b0', '90\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9847.jpg"
-  },
-  {
-    "id": 10118,
-    "problem_id": 9848,
-    "problem": "<image>As shown in the diagram, \u2220AOB = 90\u00b0, OE is the bisector of \u2220AOB, OD is the bisector of \u2220BOC, if \u2220EOD=60\u00b0, then \u2220EOC = (). A, B, C, D choices are ['75\u00b0', '90\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9848.jpg"
-  },
-  {
-    "id": 10119,
-    "problem_id": 9849,
-    "problem": "<image>As shown in the diagram, \u2220AOB = 90\u00b0, OE is the bisector of \u2220AOB, OD is the bisector of \u2220BOC, if \u2220EOD=60\u00b0, then \u2220EOC = (). A, B, C, D choices are ['75\u00b0', '90\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9849.jpg"
-  },
-  {
-    "id": 10120,
-    "problem_id": 9850,
-    "problem": "<image>As shown in the diagram, \u2220AOB = 90\u00b0, OE is the bisector of \u2220AOB, OD is the bisector of \u2220BOC, if \u2220EOD=60\u00b0, then \u2220EOC = (). A, B, C, D choices are ['75\u00b0', '90\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9850.jpg"
-  },
-  {
-    "id": 10122,
-    "problem_id": 9851,
-    "problem": "<image>As shown in the diagram, \u2220AOB = 90\u00b0, OE is the bisector of \u2220AOB, OD is the bisector of \u2220BOC, if \u2220EOD=60\u00b0, then \u2220EOC = (). A, B, C, D choices are ['75\u00b0', '90\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9851.jpg"
-  },
-  {
-    "id": 10123,
-    "problem_id": 9852,
-    "problem": "<image>As shown in the figure, lines AB and CD intersect at point O, where EO is perpendicular to AB with O as the foot of the altitude. If \u2220COA = 30\u00b0, what is the measure of \u2220EOD? (). A, B, C, D choices are ['60\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9852.jpg"
-  },
-  {
-    "id": 10125,
-    "problem_id": 9853,
-    "problem": "<image>As shown in the figure, lines AB and CD intersect at point O, where EO is perpendicular to AB with O as the foot of the altitude. If \u2220COA = 30\u00b0, what is the measure of \u2220EOD? (). A, B, C, D choices are ['60\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9853.jpg"
-  },
-  {
-    "id": 10126,
-    "problem_id": 9854,
-    "problem": "<image>As shown in the figure, lines AB and CD intersect at point O, where EO is perpendicular to AB with O as the foot of the altitude. If \u2220COA = 30\u00b0, what is the measure of \u2220EOD? (). A, B, C, D choices are ['60\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9854.jpg"
-  },
-  {
-    "id": 10127,
-    "problem_id": 9855,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9855.jpg"
-  },
-  {
-    "id": 10128,
-    "problem_id": 9856,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9856.jpg"
-  },
-  {
-    "id": 10129,
-    "problem_id": 9857,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9857.jpg"
-  },
-  {
-    "id": 10130,
-    "problem_id": 9858,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9858.jpg"
-  },
-  {
-    "id": 10131,
-    "problem_id": 9859,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9859.jpg"
-  },
-  {
-    "id": 10132,
-    "problem_id": 9860,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9860.jpg"
-  },
-  {
-    "id": 10133,
-    "problem_id": 9861,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9861.jpg"
-  },
-  {
-    "id": 10134,
-    "problem_id": 9862,
-    "problem": "<image>In parallelogram ABCD, if \u2220A + \u2220C = 130\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['130\u00b0', '115\u00b0', '105\u00b0', '95\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9862.jpg"
-  },
-  {
-    "id": 10135,
-    "problem_id": 9863,
-    "problem": "<image>In the figure, AO and BO bisect angles CAB and CBA respectively, and the distance from point O to AB is OD=2. If the perimeter of triangle ABC is 28, what is the area of triangle ABC?. A, B, C, D choices are ['7', '14', '21', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9863.jpg"
-  },
-  {
-    "id": 10136,
-    "problem_id": 9864,
-    "problem": "<image>In the figure, AO and BO bisect angles CAB and CBA respectively, and the distance from point O to AB is OD=2. If the perimeter of triangle ABC is 28, what is the area of triangle ABC?. A, B, C, D choices are ['7', '14', '21', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9864.jpg"
-  },
-  {
-    "id": 10137,
-    "problem_id": 9865,
-    "problem": "<image>In the figure, AO and BO bisect angles CAB and CBA respectively, and the distance from point O to AB is OD=2. If the perimeter of triangle ABC is 28, what is the area of triangle ABC?. A, B, C, D choices are ['7', '14', '21', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9865.jpg"
-  },
-  {
-    "id": 10138,
-    "problem_id": 9866,
-    "problem": "<image>In the figure, AO and BO bisect angles CAB and CBA respectively, and the distance from point O to AB is OD=2. If the perimeter of triangle ABC is 28, what is the area of triangle ABC?. A, B, C, D choices are ['7', '14', '21', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9866.jpg"
-  },
-  {
-    "id": 10139,
-    "problem_id": 9867,
-    "problem": "<image>In the figure, AO and BO bisect angles CAB and CBA respectively, and the distance from point O to AB is OD=2. If the perimeter of triangle ABC is 28, what is the area of triangle ABC?. A, B, C, D choices are ['7', '14', '21', '28'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9867.jpg"
-  },
-  {
-    "id": 10140,
-    "problem_id": 9868,
-    "problem": "<image>As shown in the figure, triangle ABC is an inscribed triangle of circle O, and AB=AC. The extension of BO intersects AC at point D. If \u2220ABD=23\u00b0, then the degree of \u2220A is ().. A, B, C, D choices are ['23\u00b0', '32\u00b0', '46\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9868.jpg"
-  },
-  {
-    "id": 10141,
-    "problem_id": 9869,
-    "problem": "<image>As shown in the figure, DE\u2225BC, BE bisects \u2220ABC. If \u22201 = 68\u00b0, what is the degree measure of \u2220CBE? (). A, B, C, D choices are ['34\u00b0', '32\u00b0', '22\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9869.jpg"
-  },
-  {
-    "id": 10142,
-    "problem_id": 9870,
-    "problem": "<image>As shown in the figure, DE\u2225BC, BE bisects \u2220ABC. If \u22201 = 68\u00b0, what is the degree measure of \u2220CBE? (). A, B, C, D choices are ['34\u00b0', '32\u00b0', '22\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9870.jpg"
-  },
-  {
-    "id": 10145,
-    "problem_id": 9871,
-    "problem": "<image>As shown in the figure, if lines a, b, and c intersect at one point, what is the degree of \u22201 + \u22202 + \u22203? (). A, B, C, D choices are ['90\u00b0', '120\u00b0', '135\u00b0', '180\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9871.jpg"
-  },
-  {
-    "id": 10146,
-    "problem_id": 9872,
-    "problem": "<image>As shown in the figure, if lines a, b, and c intersect at one point, what is the degree of \u22201 + \u22202 + \u22203? (). A, B, C, D choices are ['90\u00b0', '120\u00b0', '135\u00b0', '180\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9872.jpg"
-  },
-  {
-    "id": 10147,
-    "problem_id": 9873,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9873.jpg"
-  },
-  {
-    "id": 10148,
-    "problem_id": 9874,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9874.jpg"
-  },
-  {
-    "id": 10149,
-    "problem_id": 9875,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9875.jpg"
-  },
-  {
-    "id": 10151,
-    "problem_id": 9876,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9876.jpg"
-  },
-  {
-    "id": 10152,
-    "problem_id": 9877,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9877.jpg"
-  },
-  {
-    "id": 10153,
-    "problem_id": 9878,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9878.jpg"
-  },
-  {
-    "id": 10154,
-    "problem_id": 9879,
-    "problem": "<image>Given the diagram, if \u22201 = 58\u00b0 and \u2220B = 60\u00b0, then what is \u22202?. A, B, C, D choices are ['108\u00b0', '62\u00b0', '118\u00b0', '128\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9879.jpg"
-  },
-  {
-    "id": 10155,
-    "problem_id": 9880,
-    "problem": "<image>In triangle ABC, point D is the midpoint of side AB and point E is the midpoint of side BC. If the area of triangle ABC is 12, what is the area of the shaded region in the figure?. A, B, C, D choices are ['6', '4', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9880.jpg"
-  },
-  {
-    "id": 10156,
-    "problem_id": 9881,
-    "problem": "<image>As shown in the figure, it is known that in triangle ABC, O is the intersection point of the angle bisectors of \u2220ABC and \u2220ACB, OD\u22a5BC at D, the perimeter of triangle ABC is 20, OD\uff1d5. What is the area of triangle ABC?. A, B, C, D choices are ['100', '50', '25', '300'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9881.jpg"
-  },
-  {
-    "id": 10157,
-    "problem_id": 9882,
-    "problem": "<image>As shown in the figure, it is known that in triangle ABC, O is the intersection point of the angle bisectors of \u2220ABC and \u2220ACB, OD\u22a5BC at D, the perimeter of triangle ABC is 20, OD\uff1d5. What is the area of triangle ABC?. A, B, C, D choices are ['100', '50', '25', '300'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9882.jpg"
-  },
-  {
-    "id": 10158,
-    "problem_id": 9883,
-    "problem": "<image>As shown in the figure, it is known that in triangle ABC, O is the intersection point of the angle bisectors of \u2220ABC and \u2220ACB, OD\u22a5BC at D, the perimeter of triangle ABC is 20, OD\uff1d5. What is the area of triangle ABC?. A, B, C, D choices are ['100', '50', '25', '300'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9883.jpg"
-  },
-  {
-    "id": 10159,
-    "problem_id": 9884,
-    "problem": "<image>As shown in the figure, it is known that in triangle ABC, O is the intersection point of the angle bisectors of \u2220ABC and \u2220ACB, OD\u22a5BC at D, the perimeter of triangle ABC is 20, OD\uff1d5. What is the area of triangle ABC?. A, B, C, D choices are ['100', '50', '25', '300'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9884.jpg"
-  },
-  {
-    "id": 10160,
-    "problem_id": 9885,
-    "problem": "<image>As shown in the figure, it is known that in triangle ABC, O is the intersection point of the angle bisectors of \u2220ABC and \u2220ACB, OD\u22a5BC at D, the perimeter of triangle ABC is 20, OD\uff1d5. What is the area of triangle ABC?. A, B, C, D choices are ['100', '50', '25', '300'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9885.jpg"
-  },
-  {
-    "id": 10161,
-    "problem_id": 9886,
-    "problem": "<image>In triangle ABC, AB=AC, point D is on AC, and 2BCDE is constructed with CB and CD as sides. If \u2220A=40\u00b0, then what is the degree measure of \u2220E?. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9886.jpg"
-  },
-  {
-    "id": 10162,
-    "problem_id": 9887,
-    "problem": "<image>In triangle ABC, AB=AC, point D is on AC, and 2BCDE is constructed with CB and CD as sides. If \u2220A=40\u00b0, then what is the degree measure of \u2220E?. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9887.jpg"
-  },
-  {
-    "id": 10164,
-    "problem_id": 9888,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and the right-angled triangle ABC has its right angle vertex C on line b. If angle 1 is 54 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['36\u00b0', '44\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9888.jpg"
-  },
-  {
-    "id": 10165,
-    "problem_id": 9889,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and the right-angled triangle ABC has its right angle vertex C on line b. If angle 1 is 54 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['36\u00b0', '44\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9889.jpg"
-  },
-  {
-    "id": 10166,
-    "problem_id": 9890,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9890.jpg"
-  },
-  {
-    "id": 10167,
-    "problem_id": 9891,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9891.jpg"
-  },
-  {
-    "id": 10168,
-    "problem_id": 9892,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9892.jpg"
-  },
-  {
-    "id": 10169,
-    "problem_id": 9893,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9893.jpg"
-  },
-  {
-    "id": 10170,
-    "problem_id": 9894,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9894.jpg"
-  },
-  {
-    "id": 10171,
-    "problem_id": 9895,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9895.jpg"
-  },
-  {
-    "id": 10172,
-    "problem_id": 9896,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9896.jpg"
-  },
-  {
-    "id": 10173,
-    "problem_id": 9897,
-    "problem": "<image>Given that AO is perpendicular to BO and angle 1 is 35 degrees in the figure, what is the degree measure of angle 2?. A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9897.jpg"
-  },
-  {
-    "id": 10174,
-    "problem_id": 9898,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of sides BC and BA, respectively. If the area of triangle ABC is 32, then what is the area of triangle DEB?. A, B, C, D choices are ['0', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9898.jpg"
-  },
-  {
-    "id": 10175,
-    "problem_id": 9899,
-    "problem": "<image>In the figure, a combination of 6 squares with equal side lengths, what is the degree of \u22201+\u22202+\u22203? (). A, B, C, D choices are ['45\u00b0', '90\u00b0', '135\u00b0', '225\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9899.jpg"
-  },
-  {
-    "id": 10177,
-    "problem_id": 9900,
-    "problem": "<image>In triangle ABC, point D is on side BC, and points E and F are the midpoints of AD and CE, respectively. If the area of triangle BEF is 3, what is the area of triangle ABC?. A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9900.jpg"
-  },
-  {
-    "id": 10178,
-    "problem_id": 9901,
-    "problem": "<image>In triangle ABC, point D is on side BC, and points E and F are the midpoints of AD and CE, respectively. If the area of triangle BEF is 3, what is the area of triangle ABC?. A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9901.jpg"
-  },
-  {
-    "id": 10179,
-    "problem_id": 9902,
-    "problem": "<image>In triangle ABC, point D is on side BC, and points E and F are the midpoints of AD and CE, respectively. If the area of triangle BEF is 3, what is the area of triangle ABC?. A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9902.jpg"
-  },
-  {
-    "id": 10180,
-    "problem_id": 9903,
-    "problem": "<image>In triangle ABC, point D is on side BC, and points E and F are the midpoints of AD and CE, respectively. If the area of triangle BEF is 3, what is the area of triangle ABC?. A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9903.jpg"
-  },
-  {
-    "id": 10181,
-    "problem_id": 9904,
-    "problem": "<image>In triangle ABC, point D is on side BC, and points E and F are the midpoints of AD and CE, respectively. If the area of triangle BEF is 3, what is the area of triangle ABC?. A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9904.jpg"
-  },
-  {
-    "id": 10182,
-    "problem_id": 9905,
-    "problem": "<image>As shown in the figure, OC bisects \u2220AOB, point P is a point on OC, PM is perpendicular to OB at point M, and point N is a moving point on the ray OA. If OM = 4 and OP = 5, the minimum value of PN is ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9905.jpg"
-  },
-  {
-    "id": 10183,
-    "problem_id": 9906,
-    "problem": "<image>As shown in the figure, OC bisects \u2220AOB, point P is a point on OC, PM is perpendicular to OB at point M, and point N is a moving point on the ray OA. If OM = 4 and OP = 5, the minimum value of PN is ().. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9906.jpg"
-  },
-  {
-    "id": 10184,
-    "problem_id": 9907,
-    "problem": "<image>In triangle ABC, AD is the median of BC, BE is the median of ABD on the AD side. If the area of triangle ABC is 20, then the area of triangle ABE is ().. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9907.jpg"
-  },
-  {
-    "id": 10185,
-    "problem_id": 9908,
-    "problem": "<image>In triangle ABC, AD is the median of BC, BE is the median of ABD on the AD side. If the area of triangle ABC is 20, then the area of triangle ABE is ().. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9908.jpg"
-  },
-  {
-    "id": 10186,
-    "problem_id": 9909,
-    "problem": "<image>In triangle ABC, AD is the median of BC, BE is the median of ABD on the AD side. If the area of triangle ABC is 20, then the area of triangle ABE is ().. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9909.jpg"
-  },
-  {
-    "id": 10187,
-    "problem_id": 9910,
-    "problem": "<image>In triangle ABC, AD is the median of BC, BE is the median of ABD on the AD side. If the area of triangle ABC is 20, then the area of triangle ABE is ().. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9910.jpg"
-  },
-  {
-    "id": 10188,
-    "problem_id": 9911,
-    "problem": "<image>In triangle ABC, AD is the median of BC, BE is the median of ABD on the AD side. If the area of triangle ABC is 20, then the area of triangle ABE is ().. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9911.jpg"
-  },
-  {
-    "id": 10189,
-    "problem_id": 9912,
-    "problem": "<image>In triangle ABC, AD is the median of BC, BE is the median of ABD on the AD side. If the area of triangle ABC is 20, then the area of triangle ABE is ().. A, B, C, D choices are ['10', '6', '5', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9912.jpg"
-  },
-  {
-    "id": 10190,
-    "problem_id": 9913,
-    "problem": "<image>As shown in the figure, points A, B, C, and D are all on the circle O. AB = AC, BD is the diameter of the circle O, and CD is connected. If \u2220A = 36\u00b0, then what is the degree measure of \u2220ACD?. A, B, C, D choices are ['18\u00b0', '30\u00b0', '36\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9913.jpg"
-  },
-  {
-    "id": 10191,
-    "problem_id": 9914,
-    "problem": "<image>As shown in the figure, the quadrilateral paper ABCD is folded along MN, and points A and D are respectively placed at points A1 and D1. If \u22201 + \u22202 = 130\u00b0, then \u2220B + \u2220C = (). A, B, C, D choices are ['115\u00b0', '130\u00b0', '135\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9914.jpg"
-  },
-  {
-    "id": 10192,
-    "problem_id": 9915,
-    "problem": "<image>In right triangle ABC as shown, with angle ACB = 90\u00b0 and angle A = 30\u00b0, D, E, and F are the midpoints of AB, AC, and AD respectively. If BC = 2, what is the length of EF?. A, B, C, D choices are ['0.5', '1', '1.5', '\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9915.jpg"
-  },
-  {
-    "id": 10193,
-    "problem_id": 9916,
-    "problem": "<image>In right triangle ABC as shown, with angle ACB = 90\u00b0 and angle A = 30\u00b0, D, E, and F are the midpoints of AB, AC, and AD respectively. If BC = 2, what is the length of EF?. A, B, C, D choices are ['0.5', '1', '1.5', '\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9916.jpg"
-  },
-  {
-    "id": 10194,
-    "problem_id": 9917,
-    "problem": "<image>In right triangle ABC as shown, with angle ACB = 90\u00b0 and angle A = 30\u00b0, D, E, and F are the midpoints of AB, AC, and AD respectively. If BC = 2, what is the length of EF?. A, B, C, D choices are ['0.5', '1', '1.5', '\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9917.jpg"
-  },
-  {
-    "id": 10195,
-    "problem_id": 9918,
-    "problem": "<image>In right triangle ABC as shown, with angle ACB = 90\u00b0 and angle A = 30\u00b0, D, E, and F are the midpoints of AB, AC, and AD respectively. If BC = 2, what is the length of EF?. A, B, C, D choices are ['0.5', '1', '1.5', '\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9918.jpg"
-  },
-  {
-    "id": 10197,
-    "problem_id": 9919,
-    "problem": "<image>As shown in the figure, the two chords AB and CD of circle O intersect at point P. AC and BD intersect at point E. \u2220AED = 105\u00b0 and \u2220P = 55\u00b0, then what is the measure of \u2220ACD?. A, B, C, D choices are ['60\u00b0', '70\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9919.jpg"
-  },
-  {
-    "id": 10199,
-    "problem_id": 9920,
-    "problem": "<image>Given that point D and point E are the midpoints of sides AB and AC of triangle ABC, point G is the midpoint of EC. Connect DG and extend it to intersect the extended line of BC at point F. If the area of triangle GCF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9920.jpg"
-  },
-  {
-    "id": 10200,
-    "problem_id": 9921,
-    "problem": "<image>Given that point D and point E are the midpoints of sides AB and AC of triangle ABC, point G is the midpoint of EC. Connect DG and extend it to intersect the extended line of BC at point F. If the area of triangle GCF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9921.jpg"
-  },
-  {
-    "id": 10201,
-    "problem_id": 9922,
-    "problem": "<image>Given that point D and point E are the midpoints of sides AB and AC of triangle ABC, point G is the midpoint of EC. Connect DG and extend it to intersect the extended line of BC at point F. If the area of triangle GCF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9922.jpg"
-  },
-  {
-    "id": 10202,
-    "problem_id": 9923,
-    "problem": "<image>Given that point D and point E are the midpoints of sides AB and AC of triangle ABC, point G is the midpoint of EC. Connect DG and extend it to intersect the extended line of BC at point F. If the area of triangle GCF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['10', '12', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9923.jpg"
-  },
-  {
-    "id": 10203,
-    "problem_id": 9924,
-    "problem": "<image>In the rectangle ABCD, F is the midpoint of BC, E is a point on AD, and \u2220ECD=30\u00b0, \u2220BEC=90\u00b0, EF=4cm. What is the area of the rectangle? (). A, B, C, D choices are ['16cm2', '8\u221a{3}cm2', '16\u221a{3}cm2', '32cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9924.jpg"
-  },
-  {
-    "id": 10204,
-    "problem_id": 9925,
-    "problem": "<image>In the rectangle ABCD, F is the midpoint of BC, E is a point on AD, and \u2220ECD=30\u00b0, \u2220BEC=90\u00b0, EF=4cm. What is the area of the rectangle? (). A, B, C, D choices are ['16cm2', '8\u221a{3}cm2', '16\u221a{3}cm2', '32cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9925.jpg"
-  },
-  {
-    "id": 10205,
-    "problem_id": 9926,
-    "problem": "<image>In the rectangle ABCD, F is the midpoint of BC, E is a point on AD, and \u2220ECD=30\u00b0, \u2220BEC=90\u00b0, EF=4cm. What is the area of the rectangle? (). A, B, C, D choices are ['16cm2', '8\u221a{3}cm2', '16\u221a{3}cm2', '32cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9926.jpg"
-  },
-  {
-    "id": 10206,
-    "problem_id": 9927,
-    "problem": "<image>In the rectangle ABCD, F is the midpoint of BC, E is a point on AD, and \u2220ECD=30\u00b0, \u2220BEC=90\u00b0, EF=4cm. What is the area of the rectangle? (). A, B, C, D choices are ['16cm2', '8\u221a{3}cm2', '16\u221a{3}cm2', '32cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9927.jpg"
-  },
-  {
-    "id": 10207,
-    "problem_id": 9928,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond shape. The coordinates of points A and B are (\u221a{3}, 0) and (0, 1) respectively. Points C and D are on the coordinate axis. What is the perimeter of diamond ABCD?. A, B, C, D choices are ['8', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9928.jpg"
-  },
-  {
-    "id": 10208,
-    "problem_id": 9929,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond shape. The coordinates of points A and B are (\u221a{3}, 0) and (0, 1) respectively. Points C and D are on the coordinate axis. What is the perimeter of diamond ABCD?. A, B, C, D choices are ['8', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9929.jpg"
-  },
-  {
-    "id": 10209,
-    "problem_id": 9930,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond shape. The coordinates of points A and B are (\u221a{3}, 0) and (0, 1) respectively. Points C and D are on the coordinate axis. What is the perimeter of diamond ABCD?. A, B, C, D choices are ['8', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9930.jpg"
-  },
-  {
-    "id": 10210,
-    "problem_id": 9931,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond shape. The coordinates of points A and B are (\u221a{3}, 0) and (0, 1) respectively. Points C and D are on the coordinate axis. What is the perimeter of diamond ABCD?. A, B, C, D choices are ['8', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9931.jpg"
-  },
-  {
-    "id": 10211,
-    "problem_id": 9932,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond shape. The coordinates of points A and B are (\u221a{3}, 0) and (0, 1) respectively. Points C and D are on the coordinate axis. What is the perimeter of diamond ABCD?. A, B, C, D choices are ['8', '4', '6', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9932.jpg"
-  },
-  {
-    "id": 10212,
-    "problem_id": 9933,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b, line c intersects lines a and b at points D and E respectively, and ray DF is perpendicular to line c. If \u22201 = 32\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['67\u00b0', '48\u00b0', '32\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9933.jpg"
-  },
-  {
-    "id": 10213,
-    "problem_id": 9934,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b, line c intersects lines a and b at points D and E respectively, and ray DF is perpendicular to line c. If \u22201 = 32\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['67\u00b0', '48\u00b0', '32\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9934.jpg"
-  },
-  {
-    "id": 10214,
-    "problem_id": 9935,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 8. D is any point on side AB, E is the midpoint of CD, and F is the midpoint of BE. What is the area of triangle ABF?. A, B, C, D choices are ['3', '2', '2.5', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9935.jpg"
-  },
-  {
-    "id": 10215,
-    "problem_id": 9936,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 8. D is any point on side AB, E is the midpoint of CD, and F is the midpoint of BE. What is the area of triangle ABF?. A, B, C, D choices are ['3', '2', '2.5', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9936.jpg"
-  },
-  {
-    "id": 10216,
-    "problem_id": 9937,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 8. D is any point on side AB, E is the midpoint of CD, and F is the midpoint of BE. What is the area of triangle ABF?. A, B, C, D choices are ['3', '2', '2.5', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9937.jpg"
-  },
-  {
-    "id": 10217,
-    "problem_id": 9938,
-    "problem": "<image>As shown in the figure, the area of triangle ABC is 8. D is any point on side AB, E is the midpoint of CD, and F is the midpoint of BE. What is the area of triangle ABF?. A, B, C, D choices are ['3', '2', '2.5', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9938.jpg"
-  },
-  {
-    "id": 10218,
-    "problem_id": 9939,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9939.jpg"
-  },
-  {
-    "id": 10219,
-    "problem_id": 9940,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9940.jpg"
-  },
-  {
-    "id": 10220,
-    "problem_id": 9941,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9941.jpg"
-  },
-  {
-    "id": 10221,
-    "problem_id": 9942,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9942.jpg"
-  },
-  {
-    "id": 10222,
-    "problem_id": 9943,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9943.jpg"
-  },
-  {
-    "id": 10223,
-    "problem_id": 9944,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9944.jpg"
-  },
-  {
-    "id": 10224,
-    "problem_id": 9945,
-    "problem": "<image>In right triangle ABC as shown, with \u2220ACB = 90\u00b0 and AB = 13, the sum of the areas of square ADEC and square BCFG is ().. A, B, C, D choices are ['25', '144', '150', '169'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9945.jpg"
-  },
-  {
-    "id": 10225,
-    "problem_id": 9946,
-    "problem": "<image>In triangle ABC, points E and F are on sides AB and AC respectively, and EF is parallel to BC. If the area of quadrilateral BCFE is 8 and the area of triangle AEF is 1, and AF is 3, then what is the length of CF?. A, B, C, D choices are ['6', '8', '9', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9946.jpg"
-  },
-  {
-    "id": 10226,
-    "problem_id": 9947,
-    "problem": "<image>In triangle ABC, points E and F are on sides AB and AC respectively, and EF is parallel to BC. If the area of quadrilateral BCFE is 8 and the area of triangle AEF is 1, and AF is 3, then what is the length of CF?. A, B, C, D choices are ['6', '8', '9', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9947.jpg"
-  },
-  {
-    "id": 10227,
-    "problem_id": 9948,
-    "problem": "<image>In triangle ABC, points E and F are on sides AB and AC respectively, and EF is parallel to BC. If the area of quadrilateral BCFE is 8 and the area of triangle AEF is 1, and AF is 3, then what is the length of CF?. A, B, C, D choices are ['6', '8', '9', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9948.jpg"
-  },
-  {
-    "id": 10228,
-    "problem_id": 9949,
-    "problem": "<image>In triangle ABC, points E and F are on sides AB and AC respectively, and EF is parallel to BC. If the area of quadrilateral BCFE is 8 and the area of triangle AEF is 1, and AF is 3, then what is the length of CF?. A, B, C, D choices are ['6', '8', '9', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9949.jpg"
-  },
-  {
-    "id": 10229,
-    "problem_id": 9950,
-    "problem": "<image>In triangle ABC, points E and F are on sides AB and AC respectively, and EF is parallel to BC. If the area of quadrilateral BCFE is 8 and the area of triangle AEF is 1, and AF is 3, then what is the length of CF?. A, B, C, D choices are ['6', '8', '9', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9950.jpg"
-  },
-  {
-    "id": 10230,
-    "problem_id": 9951,
-    "problem": "<image>As shown in the figure, it is known that AB is parallel to CD, \u2220A = 45\u00b0, \u2220C = \u2220E. What is the degree of \u2220C?. A, B, C, D choices are ['20\u00b0', '22.5\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9951.jpg"
-  },
-  {
-    "id": 10231,
-    "problem_id": 9952,
-    "problem": "<image>As shown in the figure, it is known that AB is parallel to CD, \u2220A = 45\u00b0, \u2220C = \u2220E. What is the degree of \u2220C?. A, B, C, D choices are ['20\u00b0', '22.5\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9952.jpg"
-  },
-  {
-    "id": 10232,
-    "problem_id": 9953,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9953.jpg"
-  },
-  {
-    "id": 10233,
-    "problem_id": 9954,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9954.jpg"
-  },
-  {
-    "id": 10234,
-    "problem_id": 9955,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9955.jpg"
-  },
-  {
-    "id": 10235,
-    "problem_id": 9956,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9956.jpg"
-  },
-  {
-    "id": 10236,
-    "problem_id": 9957,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9957.jpg"
-  },
-  {
-    "id": 10237,
-    "problem_id": 9958,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9958.jpg"
-  },
-  {
-    "id": 10238,
-    "problem_id": 9959,
-    "problem": "<image>In triangle ABC, where angle A = angle B = 45\u00b0 and AB = 4, the shaded shape with AC as one of its sides is a square. What is the area of this square?. A, B, C, D choices are ['2', '4', '8', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9959.jpg"
-  },
-  {
-    "id": 10239,
-    "problem_id": 9960,
-    "problem": "<image>As shown in the figure, D is a point on the BC side of triangle ABC, and AB=AC=BD. If \u22202=24\u00b0, then \u22201=().. A, B, C, D choices are ['44\u00b0', '68\u00b0', '64\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9960.jpg"
-  },
-  {
-    "id": 10240,
-    "problem_id": 9961,
-    "problem": "<image>As shown in the figure, if the regular pentagon ABCDE is inscribed in circle O, what is the degree measure of angle ABD? (). A, B, C, D choices are ['60\u00b0', '72\u00b0', '78\u00b0', '144\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9961.jpg"
-  },
-  {
-    "id": 10241,
-    "problem_id": 9962,
-    "problem": "<image>As shown in the figure, if the regular pentagon ABCDE is inscribed in circle O, what is the degree measure of angle ABD? (). A, B, C, D choices are ['60\u00b0', '72\u00b0', '78\u00b0', '144\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9962.jpg"
-  },
-  {
-    "id": 10242,
-    "problem_id": 9963,
-    "problem": "<image>As shown in the figure, if the regular pentagon ABCDE is inscribed in circle O, what is the degree measure of angle ABD? (). A, B, C, D choices are ['60\u00b0', '72\u00b0', '78\u00b0', '144\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9963.jpg"
-  },
-  {
-    "id": 10243,
-    "problem_id": 9964,
-    "problem": "<image>In rectangle ABCD, diagonal AC and BD intersect at point O. A perpendicular line from point A intersects BD at point E. If CD = 2 and \u2220BOC = 120\u00b0, what is the length of AE?. A, B, C, D choices are ['\u221a{2}', '\u221a{3}', '2', '\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9964.jpg"
-  },
-  {
-    "id": 10244,
-    "problem_id": 9965,
-    "problem": "<image>In rectangle ABCD, diagonal AC and BD intersect at point O. A perpendicular line from point A intersects BD at point E. If CD = 2 and \u2220BOC = 120\u00b0, what is the length of AE?. A, B, C, D choices are ['\u221a{2}', '\u221a{3}', '2', '\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9965.jpg"
-  },
-  {
-    "id": 10245,
-    "problem_id": 9966,
-    "problem": "<image>In rectangle ABCD, diagonal AC and BD intersect at point O. A perpendicular line from point A intersects BD at point E. If CD = 2 and \u2220BOC = 120\u00b0, what is the length of AE?. A, B, C, D choices are ['\u221a{2}', '\u221a{3}', '2', '\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9966.jpg"
-  },
-  {
-    "id": 10247,
-    "problem_id": 9967,
-    "problem": "<image>As shown in the figure, AB\u2225CD, AC intersects BD at point O. If \u2220A\uff1d25\u00b0 and \u2220D\uff1d45\u00b0, what is the size of \u2220AOB?. A, B, C, D choices are ['90\u00b0', '110\u00b0', '120\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n\n**Conclusion:**\nThe measure of \u2220AOB is 110\u00b0, which corresponds to option B. This was determined by using the properties of parallel lines and the angle sum property of triangles, and confirmed by considering vertically opposite angles.</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9967.jpg"
-  },
-  {
-    "id": 10248,
-    "problem_id": 9968,
-    "problem": "<image>In right triangle ABC shown in the diagram, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with its sides as their edges. Let S1, S2, S3 be the areas of these three squares. If S1\uff1d3 and S2\uff1d11, then S3\uff1d().. A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9968.jpg"
-  },
-  {
-    "id": 10249,
-    "problem_id": 9969,
-    "problem": "<image>In right triangle ABC shown in the diagram, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with its sides as their edges. Let S1, S2, S3 be the areas of these three squares. If S1\uff1d3 and S2\uff1d11, then S3\uff1d().. A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9969.jpg"
-  },
-  {
-    "id": 10250,
-    "problem_id": 9970,
-    "problem": "<image>In right triangle ABC shown in the diagram, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with its sides as their edges. Let S1, S2, S3 be the areas of these three squares. If S1\uff1d3 and S2\uff1d11, then S3\uff1d().. A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9970.jpg"
-  },
-  {
-    "id": 10251,
-    "problem_id": 9971,
-    "problem": "<image>In right triangle ABC shown in the diagram, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with its sides as their edges. Let S1, S2, S3 be the areas of these three squares. If S1\uff1d3 and S2\uff1d11, then S3\uff1d().. A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9971.jpg"
-  },
-  {
-    "id": 10252,
-    "problem_id": 9972,
-    "problem": "<image>In right triangle ABC shown in the diagram, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with its sides as their edges. Let S1, S2, S3 be the areas of these three squares. If S1\uff1d3 and S2\uff1d11, then S3\uff1d().. A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9972.jpg"
-  },
-  {
-    "id": 10253,
-    "problem_id": 9973,
-    "problem": "<image>In right triangle ABC shown in the diagram, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with its sides as their edges. Let S1, S2, S3 be the areas of these three squares. If S1\uff1d3 and S2\uff1d11, then S3\uff1d().. A, B, C, D choices are ['5', '8', '14', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9973.jpg"
-  },
-  {
-    "id": 10254,
-    "problem_id": 9974,
-    "problem": "<image>As shown in the figure, in triangle ABC, points D, E, and F are known to be the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 square centimeters. The area of triangle DEF is ().\n\n(Note: The input is already in English, so no need to translate the English parts.). A, B, C, D choices are ['2cm2', '1cm2', '0.5cm2', '0.25cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9974.jpg"
-  },
-  {
-    "id": 10255,
-    "problem_id": 9975,
-    "problem": "<image>As shown in the figure, in triangle ABC, points D, E, and F are known to be the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 square centimeters. The area of triangle DEF is ().\n\n(Note: The input is already in English, so no need to translate the English parts.). A, B, C, D choices are ['2cm2', '1cm2', '0.5cm2', '0.25cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9975.jpg"
-  },
-  {
-    "id": 10256,
-    "problem_id": 9976,
-    "problem": "<image>As shown in the figure, in triangle ABC, points D, E, and F are known to be the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 square centimeters. The area of triangle DEF is ().\n\n(Note: The input is already in English, so no need to translate the English parts.). A, B, C, D choices are ['2cm2', '1cm2', '0.5cm2', '0.25cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9976.jpg"
-  },
-  {
-    "id": 10257,
-    "problem_id": 9977,
-    "problem": "<image>As shown in the figure, in triangle ABC, points D, E, and F are known to be the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 square centimeters. The area of triangle DEF is ().\n\n(Note: The input is already in English, so no need to translate the English parts.). A, B, C, D choices are ['2cm2', '1cm2', '0.5cm2', '0.25cm2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9977.jpg"
-  },
-  {
-    "id": 10258,
-    "problem_id": 9978,
-    "problem": "<image>As shown in the figure, it is known that line a is parallel to line b, and c is the transverse line. If \u22201 = 60\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['30\u00b0', '60\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9978.jpg"
-  },
-  {
-    "id": 10259,
-    "problem_id": 9979,
-    "problem": "<image>In the right triangle ABC shown in the figure, \u2220ACB\uff1d90\u00b0, CD\u22a5AB and D is the foot of the perpendicular. If AD\uff1d8 and DB\uff1d2, what is the length of CB?. A, B, C, D choices are ['2\u221a{5}', '4', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9979.jpg"
-  },
-  {
-    "id": 10260,
-    "problem_id": 9980,
-    "problem": "<image>In the right triangle ABC shown in the figure, \u2220ACB\uff1d90\u00b0, CD\u22a5AB and D is the foot of the perpendicular. If AD\uff1d8 and DB\uff1d2, what is the length of CB?. A, B, C, D choices are ['2\u221a{5}', '4', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9980.jpg"
-  },
-  {
-    "id": 10261,
-    "problem_id": 9981,
-    "problem": "<image>In the right triangle ABC shown in the figure, \u2220ACB\uff1d90\u00b0, CD\u22a5AB and D is the foot of the perpendicular. If AD\uff1d8 and DB\uff1d2, what is the length of CB?. A, B, C, D choices are ['2\u221a{5}', '4', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9981.jpg"
-  },
-  {
-    "id": 10262,
-    "problem_id": 9982,
-    "problem": "<image>In the right triangle ABC shown in the figure, \u2220ACB\uff1d90\u00b0, CD\u22a5AB and D is the foot of the perpendicular. If AD\uff1d8 and DB\uff1d2, what is the length of CB?. A, B, C, D choices are ['2\u221a{5}', '4', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9982.jpg"
-  },
-  {
-    "id": 10263,
-    "problem_id": 9983,
-    "problem": "<image>In rectangle ABCD, an arc is drawn with point B as the center and AB as the radius, intersecting BC at point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at point Q. If AB = 15 and AD = 17, what is the length of PQ?. A, B, C, D choices are ['2', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9983.jpg"
-  },
-  {
-    "id": 10264,
-    "problem_id": 9984,
-    "problem": "<image>In rectangle ABCD, an arc is drawn with point B as the center and AB as the radius, intersecting BC at point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at point Q. If AB = 15 and AD = 17, what is the length of PQ?. A, B, C, D choices are ['2', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9984.jpg"
-  },
-  {
-    "id": 10265,
-    "problem_id": 9985,
-    "problem": "<image>In rectangle ABCD, an arc is drawn with point B as the center and AB as the radius, intersecting BC at point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at point Q. If AB = 15 and AD = 17, what is the length of PQ?. A, B, C, D choices are ['2', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9985.jpg"
-  },
-  {
-    "id": 10266,
-    "problem_id": 9986,
-    "problem": "<image>In rectangle ABCD, an arc is drawn with point B as the center and AB as the radius, intersecting BC at point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at point Q. If AB = 15 and AD = 17, what is the length of PQ?. A, B, C, D choices are ['2', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9986.jpg"
-  },
-  {
-    "id": 10267,
-    "problem_id": 9987,
-    "problem": "<image>In rectangle ABCD, an arc is drawn with point B as the center and AB as the radius, intersecting BC at point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at point Q. If AB = 15 and AD = 17, what is the length of PQ?. A, B, C, D choices are ['2', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9987.jpg"
-  },
-  {
-    "id": 10268,
-    "problem_id": 9988,
-    "problem": "<image>In rectangle ABCD, an arc is drawn with point B as the center and AB as the radius, intersecting BC at point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at point Q. If AB = 15 and AD = 17, what is the length of PQ?. A, B, C, D choices are ['2', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9988.jpg"
-  },
-  {
-    "id": 10269,
-    "problem_id": 9989,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9989.jpg"
-  },
-  {
-    "id": 10270,
-    "problem_id": 9990,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9990.jpg"
-  },
-  {
-    "id": 10271,
-    "problem_id": 9991,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9991.jpg"
-  },
-  {
-    "id": 10272,
-    "problem_id": 9992,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9992.jpg"
-  },
-  {
-    "id": 10273,
-    "problem_id": 9993,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9993.jpg"
-  },
-  {
-    "id": 10274,
-    "problem_id": 9994,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9994.jpg"
-  },
-  {
-    "id": 10275,
-    "problem_id": 9995,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9995.jpg"
-  },
-  {
-    "id": 10276,
-    "problem_id": 9996,
-    "problem": "<image>As shown in the diagram, if \u22201 is 140\u00b0 and \u22202 is 120\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '140\u00b0', '260\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9996.jpg"
-  },
-  {
-    "id": 10278,
-    "problem_id": 9997,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, BC\u2225DE. If \u2220CDE\uff1d140\u00b0, what is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '140\u00b0', '160\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9997.jpg"
-  },
-  {
-    "id": 10279,
-    "problem_id": 9998,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond with a side length of 5cm. Diagonal BD intersects with AC at point O, and BD = 6cm. What is the length of diagonal AC?. A, B, C, D choices are ['8cm', '4cm', '3cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9998.jpg"
-  },
-  {
-    "id": 10280,
-    "problem_id": 9999,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond with a side length of 5cm. Diagonal BD intersects with AC at point O, and BD = 6cm. What is the length of diagonal AC?. A, B, C, D choices are ['8cm', '4cm', '3cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/9999.jpg"
-  },
-  {
-    "id": 10281,
-    "problem_id": 10000,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond with a side length of 5cm. Diagonal BD intersects with AC at point O, and BD = 6cm. What is the length of diagonal AC?. A, B, C, D choices are ['8cm', '4cm', '3cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10000.jpg"
-  },
-  {
-    "id": 10282,
-    "problem_id": 10001,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond with a side length of 5cm. Diagonal BD intersects with AC at point O, and BD = 6cm. What is the length of diagonal AC?. A, B, C, D choices are ['8cm', '4cm', '3cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10001.jpg"
-  },
-  {
-    "id": 10283,
-    "problem_id": 10002,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a diamond with a side length of 5cm. Diagonal BD intersects with AC at point O, and BD = 6cm. What is the length of diagonal AC?. A, B, C, D choices are ['8cm', '4cm', '3cm', '6cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10002.jpg"
-  },
-  {
-    "id": 10284,
-    "problem_id": 10003,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to the circle O at points A and B respectively, point C is on circle O, and AC and BC are connected. If \u2220P = 80\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10003.jpg"
-  },
-  {
-    "id": 10285,
-    "problem_id": 10004,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to the circle O at points A and B respectively, point C is on circle O, and AC and BC are connected. If \u2220P = 80\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10004.jpg"
-  },
-  {
-    "id": 10286,
-    "problem_id": 10005,
-    "problem": "<image>As shown in the figure, PA and PB are tangent to the circle O at points A and B respectively, point C is on circle O, and AC and BC are connected. If \u2220P = 80\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10005.jpg"
-  },
-  {
-    "id": 10287,
-    "problem_id": 10006,
-    "problem": "<image>As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O, BE is the diameter of circle O, and AE is connected. If \u2220BCD\uff1d2\u2220BAD, then the degree of \u2220DAE is ().. A, B, C, D choices are ['30\u00b0', '35\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10006.jpg"
-  },
-  {
-    "id": 10288,
-    "problem_id": 10007,
-    "problem": "<image>In the figure, AE bisects \u2220DAB and intersects CD at point E in quadrilateral ABCD. If AB = 6 and CE = 2, what is the perimeter of ABCD?. A, B, C, D choices are ['14', '16', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10007.jpg"
-  },
-  {
-    "id": 10289,
-    "problem_id": 10008,
-    "problem": "<image>As shown in the figure, \"Zhaoshuang Xian's diagram\" is a large square composed of four congruent right-angled triangles and a small square. If the two legs of the right-angled triangle are 5 and 3 respectively, then what is the area of the small square?. A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10008.jpg"
-  },
-  {
-    "id": 10290,
-    "problem_id": 10009,
-    "problem": "<image>As shown in the figure, \"Zhaoshuang Xian's diagram\" is a large square composed of four congruent right-angled triangles and a small square. If the two legs of the right-angled triangle are 5 and 3 respectively, then what is the area of the small square?. A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10009.jpg"
-  },
-  {
-    "id": 10291,
-    "problem_id": 10010,
-    "problem": "<image>As shown in the figure, \"Zhaoshuang Xian's diagram\" is a large square composed of four congruent right-angled triangles and a small square. If the two legs of the right-angled triangle are 5 and 3 respectively, then what is the area of the small square?. A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10010.jpg"
-  },
-  {
-    "id": 10292,
-    "problem_id": 10011,
-    "problem": "<image>As shown in the figure, \"Zhaoshuang Xian's diagram\" is a large square composed of four congruent right-angled triangles and a small square. If the two legs of the right-angled triangle are 5 and 3 respectively, then what is the area of the small square?. A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10011.jpg"
-  },
-  {
-    "id": 10293,
-    "problem_id": 10012,
-    "problem": "<image>As shown in the figure, \"Zhaoshuang Xian's diagram\" is a large square composed of four congruent right-angled triangles and a small square. If the two legs of the right-angled triangle are 5 and 3 respectively, then what is the area of the small square?. A, B, C, D choices are ['4', '3', '2', '1'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10012.jpg"
-  },
-  {
-    "id": 10294,
-    "problem_id": 10013,
-    "problem": "<image>In triangle ABC, point D and E are the midpoints of sides AB and AC, respectively. Point F is a point on segment DE. AF and BF are connected, and \u2220AFB = 90\u00b0. If AB = 8 and BC = 14, then what is the length of EF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10013.jpg"
-  },
-  {
-    "id": 10295,
-    "problem_id": 10014,
-    "problem": "<image>In triangle ABC, point D and E are the midpoints of sides AB and AC, respectively. Point F is a point on segment DE. AF and BF are connected, and \u2220AFB = 90\u00b0. If AB = 8 and BC = 14, then what is the length of EF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10014.jpg"
-  },
-  {
-    "id": 10296,
-    "problem_id": 10015,
-    "problem": "<image>In triangle ABC, point D and E are the midpoints of sides AB and AC, respectively. Point F is a point on segment DE. AF and BF are connected, and \u2220AFB = 90\u00b0. If AB = 8 and BC = 14, then what is the length of EF?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10015.jpg"
-  },
-  {
-    "id": 10297,
-    "problem_id": 10016,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10016.jpg"
-  },
-  {
-    "id": 10298,
-    "problem_id": 10017,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10017.jpg"
-  },
-  {
-    "id": 10299,
-    "problem_id": 10018,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10018.jpg"
-  },
-  {
-    "id": 10300,
-    "problem_id": 10019,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10019.jpg"
-  },
-  {
-    "id": 10301,
-    "problem_id": 10020,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10020.jpg"
-  },
-  {
-    "id": 10302,
-    "problem_id": 10021,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10021.jpg"
-  },
-  {
-    "id": 10303,
-    "problem_id": 10022,
-    "problem": "<image>As shown in the figure, Xiaoliang starts from point P and walks forward 10 meters along a straight line before turning left 30 degrees. Then he walks forward 10 meters along another straight line and turns left 30 degrees again... He continues to walk in this way until he returns to the starting point P for the first time. How far did he walk in total?. A, B, C, D choices are ['100m', '120m', '140m', '300m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10022.jpg"
-  },
-  {
-    "id": 10304,
-    "problem_id": 10023,
-    "problem": "<image>In triangle ABC, angle B = 38\u00b0, angle C = 54\u00b0. AE is the altitude on side BC and AD is the angle bisector of angle BAC. What is the measure of angle DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10023.jpg"
-  },
-  {
-    "id": 10305,
-    "problem_id": 10024,
-    "problem": "<image>In triangle ABC, angle B = 38\u00b0, angle C = 54\u00b0. AE is the altitude on side BC and AD is the angle bisector of angle BAC. What is the measure of angle DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10024.jpg"
-  },
-  {
-    "id": 10306,
-    "problem_id": 10025,
-    "problem": "<image>In triangle ABC, angle B = 38\u00b0, angle C = 54\u00b0. AE is the altitude on side BC and AD is the angle bisector of angle BAC. What is the measure of angle DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10025.jpg"
-  },
-  {
-    "id": 10307,
-    "problem_id": 10026,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AC and AB, respectively. If the area of triangle ABC is 12, then the area of triangle BDE is ()?. A, B, C, D choices are ['12', '6', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10026.jpg"
-  },
-  {
-    "id": 10308,
-    "problem_id": 10027,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AC and AB, respectively. If the area of triangle ABC is 12, then the area of triangle BDE is ()?. A, B, C, D choices are ['12', '6', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10027.jpg"
-  },
-  {
-    "id": 10309,
-    "problem_id": 10028,
-    "problem": "<image>In triangle ABC, D and E are the midpoints of AC and AB, respectively. If the area of triangle ABC is 12, then the area of triangle BDE is ()?. A, B, C, D choices are ['12', '6', '3', '2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10028.jpg"
-  },
-  {
-    "id": 10310,
-    "problem_id": 10029,
-    "problem": "<image>In triangle ABC, with \u2220B = 38\u00b0 and \u2220C = 54\u00b0, AE is the altitude from side BC and AD is the angle bisector of \u2220BAC. What is the degree measurement of \u2220DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10029.jpg"
-  },
-  {
-    "id": 10311,
-    "problem_id": 10030,
-    "problem": "<image>In triangle ABC, with \u2220B = 38\u00b0 and \u2220C = 54\u00b0, AE is the altitude from side BC and AD is the angle bisector of \u2220BAC. What is the degree measurement of \u2220DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10030.jpg"
-  },
-  {
-    "id": 10312,
-    "problem_id": 10031,
-    "problem": "<image>In triangle ABC, with \u2220B = 38\u00b0 and \u2220C = 54\u00b0, AE is the altitude from side BC and AD is the angle bisector of \u2220BAC. What is the degree measurement of \u2220DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10031.jpg"
-  },
-  {
-    "id": 10313,
-    "problem_id": 10032,
-    "problem": "<image>In triangle ABC, with \u2220B = 38\u00b0 and \u2220C = 54\u00b0, AE is the altitude from side BC and AD is the angle bisector of \u2220BAC. What is the degree measurement of \u2220DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10032.jpg"
-  },
-  {
-    "id": 10314,
-    "problem_id": 10033,
-    "problem": "<image>In triangle ABC, with \u2220B = 38\u00b0 and \u2220C = 54\u00b0, AE is the altitude from side BC and AD is the angle bisector of \u2220BAC. What is the degree measurement of \u2220DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10033.jpg"
-  },
-  {
-    "id": 10315,
-    "problem_id": 10034,
-    "problem": "<image>In triangle ABC, with \u2220B = 38\u00b0 and \u2220C = 54\u00b0, AE is the altitude from side BC and AD is the angle bisector of \u2220BAC. What is the degree measurement of \u2220DAE?. A, B, C, D choices are ['8\u00b0', '10\u00b0', '12\u00b0', '14\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10034.jpg"
-  },
-  {
-    "id": 10316,
-    "problem_id": 10035,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220BAC = 33\u00b0, then the degree of \u2220D is equal to (). A, B, C, D choices are ['57\u00b0', '60\u00b0', '66\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10035.jpg"
-  },
-  {
-    "id": 10317,
-    "problem_id": 10036,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220BAC = 33\u00b0, then the degree of \u2220D is equal to (). A, B, C, D choices are ['57\u00b0', '60\u00b0', '66\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10036.jpg"
-  },
-  {
-    "id": 10318,
-    "problem_id": 10037,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220BAC = 33\u00b0, then the degree of \u2220D is equal to (). A, B, C, D choices are ['57\u00b0', '60\u00b0', '66\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10037.jpg"
-  },
-  {
-    "id": 10319,
-    "problem_id": 10038,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220BAC = 33\u00b0, then the degree of \u2220D is equal to (). A, B, C, D choices are ['57\u00b0', '60\u00b0', '66\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10038.jpg"
-  },
-  {
-    "id": 10320,
-    "problem_id": 10039,
-    "problem": "<image>As shown in the figure, line m is parallel to line n. Vertex A of right triangle ABC (\u2220C=90\u00b0) is on line n. If \u2220\u03b2=43\u00b0, what is the degree measure of \u2220\u03b1?. A, B, C, D choices are ['47\u00b0', '43\u00b0', '57\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10039.jpg"
-  },
-  {
-    "id": 10321,
-    "problem_id": 10040,
-    "problem": "<image>As shown in the figure, line m is parallel to line n. Vertex A of right triangle ABC (\u2220C=90\u00b0) is on line n. If \u2220\u03b2=43\u00b0, what is the degree measure of \u2220\u03b1?. A, B, C, D choices are ['47\u00b0', '43\u00b0', '57\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10040.jpg"
-  },
-  {
-    "id": 10322,
-    "problem_id": 10041,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10041.jpg"
-  },
-  {
-    "id": 10323,
-    "problem_id": 10042,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10042.jpg"
-  },
-  {
-    "id": 10324,
-    "problem_id": 10043,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10043.jpg"
-  },
-  {
-    "id": 10325,
-    "problem_id": 10044,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10044.jpg"
-  },
-  {
-    "id": 10326,
-    "problem_id": 10045,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10045.jpg"
-  },
-  {
-    "id": 10327,
-    "problem_id": 10046,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10046.jpg"
-  },
-  {
-    "id": 10328,
-    "problem_id": 10047,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10047.jpg"
-  },
-  {
-    "id": 10329,
-    "problem_id": 10048,
-    "problem": "<image>In the comprehensive practical activity class, Xiao Ming made a cone-shaped funnel model out of cardboard. As shown in the figure, its base radius is 6 and height is 8. What is the lateral area of this cone-shaped funnel? (). A, B, C, D choices are ['48\u03c0', '30\u03c0', '60\u03c0', '120\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10048.jpg"
-  },
-  {
-    "id": 10330,
-    "problem_id": 10049,
-    "problem": "<image>As shown in the figure, if one diagonal of a rhombus is 7 and its area is 28, then the length of the other diagonal of the rhombus is ().. A, B, C, D choices are ['8', '10', '12', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10049.jpg"
-  },
-  {
-    "id": 10331,
-    "problem_id": 10050,
-    "problem": "<image>As shown in the figure, if one diagonal of a rhombus is 7 and its area is 28, then the length of the other diagonal of the rhombus is ().. A, B, C, D choices are ['8', '10', '12', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10050.jpg"
-  },
-  {
-    "id": 10332,
-    "problem_id": 10051,
-    "problem": "<image>As shown in the figure, if one diagonal of a rhombus is 7 and its area is 28, then the length of the other diagonal of the rhombus is ().. A, B, C, D choices are ['8', '10', '12', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10051.jpg"
-  },
-  {
-    "id": 10333,
-    "problem_id": 10052,
-    "problem": "<image>As shown in the figure, if one diagonal of a rhombus is 7 and its area is 28, then the length of the other diagonal of the rhombus is ().. A, B, C, D choices are ['8', '10', '12', '14'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10052.jpg"
-  },
-  {
-    "id": 10335,
-    "problem_id": 10053,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, and ray OE bisects \u2220COB. If \u2220BOD=40\u00b0, then \u2220AOE is equal to ().. A, B, C, D choices are ['40\u00b0', '100\u00b0', '110\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10053.jpg"
-  },
-  {
-    "id": 10336,
-    "problem_id": 10054,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, and ray OE bisects \u2220COB. If \u2220BOD=40\u00b0, then \u2220AOE is equal to ().. A, B, C, D choices are ['40\u00b0', '100\u00b0', '110\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10054.jpg"
-  },
-  {
-    "id": 10337,
-    "problem_id": 10055,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, and ray OE bisects \u2220COB. If \u2220BOD=40\u00b0, then \u2220AOE is equal to ().. A, B, C, D choices are ['40\u00b0', '100\u00b0', '110\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10055.jpg"
-  },
-  {
-    "id": 10338,
-    "problem_id": 10056,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, and ray OE bisects \u2220COB. If \u2220BOD=40\u00b0, then \u2220AOE is equal to ().. A, B, C, D choices are ['40\u00b0', '100\u00b0', '110\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10056.jpg"
-  },
-  {
-    "id": 10339,
-    "problem_id": 10057,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, and ray OE bisects \u2220COB. If \u2220BOD=40\u00b0, then \u2220AOE is equal to ().. A, B, C, D choices are ['40\u00b0', '100\u00b0', '110\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10057.jpg"
-  },
-  {
-    "id": 10340,
-    "problem_id": 10058,
-    "problem": "<image>In triangle ABC, where \u2220C = 90\u00b0 and AB = 10, AD bisects \u2220BAC. If CD = 3, what is the area of triangle ABD?. A, B, C, D choices are ['15', '24', '30', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10058.jpg"
-  },
-  {
-    "id": 10342,
-    "problem_id": 10059,
-    "problem": "<image>In triangle ABC, where \u2220C = 90\u00b0 and AB = 10, AD bisects \u2220BAC. If CD = 3, what is the area of triangle ABD?. A, B, C, D choices are ['15', '24', '30', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10059.jpg"
-  },
-  {
-    "id": 10343,
-    "problem_id": 10060,
-    "problem": "<image>In triangle ABC, where \u2220C = 90\u00b0 and AB = 10, AD bisects \u2220BAC. If CD = 3, what is the area of triangle ABD?. A, B, C, D choices are ['15', '24', '30', '48'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10060.jpg"
-  },
-  {
-    "id": 10344,
-    "problem_id": 10061,
-    "problem": "<image>In triangle ABC, DE is parallel to BC, and AD/BD=2/3. If DE=4, then BC is equal to ().. A, B, C, D choices are ['6', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10061.jpg"
-  },
-  {
-    "id": 10345,
-    "problem_id": 10062,
-    "problem": "<image>In triangle ABC, DE is parallel to BC, and AD/BD=2/3. If DE=4, then BC is equal to ().. A, B, C, D choices are ['6', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10062.jpg"
-  },
-  {
-    "id": 10346,
-    "problem_id": 10063,
-    "problem": "<image>In triangle ABC, DE is parallel to BC, and AD/BD=2/3. If DE=4, then BC is equal to ().. A, B, C, D choices are ['6', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10063.jpg"
-  },
-  {
-    "id": 10347,
-    "problem_id": 10064,
-    "problem": "<image>In triangle ABC, DE is parallel to BC, and AD/BD=2/3. If DE=4, then BC is equal to ().. A, B, C, D choices are ['6', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10064.jpg"
-  },
-  {
-    "id": 10348,
-    "problem_id": 10065,
-    "problem": "<image>In triangle ABC, DE is parallel to BC, and AD/BD=2/3. If DE=4, then BC is equal to ().. A, B, C, D choices are ['6', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10065.jpg"
-  },
-  {
-    "id": 10349,
-    "problem_id": 10066,
-    "problem": "<image>In triangle ABC, DE is parallel to BC, and AD/BD=2/3. If DE=4, then BC is equal to ().. A, B, C, D choices are ['6', '8', '9', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10066.jpg"
-  },
-  {
-    "id": 10350,
-    "problem_id": 10067,
-    "problem": "<image>As shown in the figure, if \u22201 = 110\u00b0 and a is parallel to b, what is the size of \u22202?. A, B, C, D choices are ['60\u00b0', '80\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10067.jpg"
-  },
-  {
-    "id": 10351,
-    "problem_id": 10068,
-    "problem": "<image>As shown in the figure, if \u22201 = 110\u00b0 and a is parallel to b, what is the size of \u22202?. A, B, C, D choices are ['60\u00b0', '80\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10068.jpg"
-  },
-  {
-    "id": 10352,
-    "problem_id": 10069,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10069.jpg"
-  },
-  {
-    "id": 10353,
-    "problem_id": 10070,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10070.jpg"
-  },
-  {
-    "id": 10354,
-    "problem_id": 10071,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10071.jpg"
-  },
-  {
-    "id": 10355,
-    "problem_id": 10072,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10072.jpg"
-  },
-  {
-    "id": 10356,
-    "problem_id": 10073,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10073.jpg"
-  },
-  {
-    "id": 10357,
-    "problem_id": 10074,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10074.jpg"
-  },
-  {
-    "id": 10358,
-    "problem_id": 10075,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O. \u2220ACB = 38\u00b0, then \u2220AOB is equal to ().. A, B, C, D choices are ['52\u00b0', '68\u00b0', '76\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10075.jpg"
-  },
-  {
-    "id": 10359,
-    "problem_id": 10076,
-    "problem": "<image>As shown in the figure, PA is a tangent to circle O, and OP and OA are connected. If \u2220A = 50\u00b0, then what is the degree of \u2220POA? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10076.jpg"
-  },
-  {
-    "id": 10360,
-    "problem_id": 10077,
-    "problem": "<image>As shown in the figure, PA is a tangent to circle O, and OP and OA are connected. If \u2220A = 50\u00b0, then what is the degree of \u2220POA? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10077.jpg"
-  },
-  {
-    "id": 10361,
-    "problem_id": 10078,
-    "problem": "<image>As shown in the figure, PA is a tangent to circle O, and OP and OA are connected. If \u2220A = 50\u00b0, then what is the degree of \u2220POA? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10078.jpg"
-  },
-  {
-    "id": 10362,
-    "problem_id": 10079,
-    "problem": "<image>In the figure, CE bisects \u2220DCB in rectangle ABCD. If AE = 2 and DC = 6, what is the perimeter of ABCD?. A, B, C, D choices are ['16', '18', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10079.jpg"
-  },
-  {
-    "id": 10363,
-    "problem_id": 10080,
-    "problem": "<image>In the figure, CE bisects \u2220DCB in rectangle ABCD. If AE = 2 and DC = 6, what is the perimeter of ABCD?. A, B, C, D choices are ['16', '18', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10080.jpg"
-  },
-  {
-    "id": 10364,
-    "problem_id": 10081,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10081.jpg"
-  },
-  {
-    "id": 10365,
-    "problem_id": 10082,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10082.jpg"
-  },
-  {
-    "id": 10366,
-    "problem_id": 10083,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10083.jpg"
-  },
-  {
-    "id": 10367,
-    "problem_id": 10084,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10084.jpg"
-  },
-  {
-    "id": 10368,
-    "problem_id": 10085,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10085.jpg"
-  },
-  {
-    "id": 10369,
-    "problem_id": 10086,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10086.jpg"
-  },
-  {
-    "id": 10370,
-    "problem_id": 10087,
-    "problem": "<image>As shown in the figure, AD is the median of \u25b3ABC, CE is the median of \u25b3ACD, DF is the median of \u25b3CDE. If the area of \u25b3DEF is 2, then the area of \u25b3ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10087.jpg"
-  },
-  {
-    "id": 10371,
-    "problem_id": 10088,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and CA, respectively. If AB = 8cm and AC = 10cm, what is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['14', '18', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10088.jpg"
-  },
-  {
-    "id": 10372,
-    "problem_id": 10089,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and CA, respectively. If AB = 8cm and AC = 10cm, what is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['14', '18', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10089.jpg"
-  },
-  {
-    "id": 10373,
-    "problem_id": 10090,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and CA, respectively. If AB = 8cm and AC = 10cm, what is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['14', '18', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10090.jpg"
-  },
-  {
-    "id": 10374,
-    "problem_id": 10091,
-    "problem": "<image>In triangle ABC, D, E, and F are the midpoints of sides AB, BC, and CA, respectively. If AB = 8cm and AC = 10cm, what is the perimeter of quadrilateral ADEF?. A, B, C, D choices are ['14', '18', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10091.jpg"
-  },
-  {
-    "id": 10375,
-    "problem_id": 10092,
-    "problem": "<image>As shown in the diagram, PA and PB are tangent to circle O at points A and B respectively. PA = 4. CD is tangent to circle O at point E, intersecting PA and PB at points C and D. What is the perimeter of triangle PCD?. A, B, C, D choices are ['4', '8', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10092.jpg"
-  },
-  {
-    "id": 10376,
-    "problem_id": 10093,
-    "problem": "<image>As shown in the diagram, PA and PB are tangent to circle O at points A and B respectively. PA = 4. CD is tangent to circle O at point E, intersecting PA and PB at points C and D. What is the perimeter of triangle PCD?. A, B, C, D choices are ['4', '8', '12', '16'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10093.jpg"
-  },
-  {
-    "id": 10377,
-    "problem_id": 10094,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10094.jpg"
-  },
-  {
-    "id": 10378,
-    "problem_id": 10095,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10095.jpg"
-  },
-  {
-    "id": 10379,
-    "problem_id": 10096,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10096.jpg"
-  },
-  {
-    "id": 10380,
-    "problem_id": 10097,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10097.jpg"
-  },
-  {
-    "id": 10381,
-    "problem_id": 10098,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10098.jpg"
-  },
-  {
-    "id": 10382,
-    "problem_id": 10099,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10099.jpg"
-  },
-  {
-    "id": 10383,
-    "problem_id": 10100,
-    "problem": "<image>As shown in the figure, \u25b3ABC is an equilateral triangle, DE\u2225BC. If AB\uff1d7 and BD\uff1d3, what is the perimeter of \u25b3ADE?. A, B, C, D choices are ['4', '9', '12', '21'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10100.jpg"
-  },
-  {
-    "id": 10384,
-    "problem_id": 10101,
-    "problem": "<image>As shown in the diagram, regular hexagon ABCDEF is inscribed in circle O. BD is connected. What is the degree measure of angle CDB? (). A, B, C, D choices are ['90\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10101.jpg"
-  },
-  {
-    "id": 10385,
-    "problem_id": 10102,
-    "problem": "<image>As shown in the figure, in triangle ABC, it is known that D, E, and F are the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 cm\u00b2. The area of triangle DEF is () .. A, B, C, D choices are ['2cm2', '1cm2', '0.5cm22', '0.25cm22'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10102.jpg"
-  },
-  {
-    "id": 10386,
-    "problem_id": 10103,
-    "problem": "<image>As shown in the figure, in triangle ABC, it is known that D, E, and F are the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 cm\u00b2. The area of triangle DEF is () .. A, B, C, D choices are ['2cm2', '1cm2', '0.5cm22', '0.25cm22'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10103.jpg"
-  },
-  {
-    "id": 10387,
-    "problem_id": 10104,
-    "problem": "<image>As shown in the figure, in triangle ABC, it is known that D, E, and F are the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 cm\u00b2. The area of triangle DEF is () .. A, B, C, D choices are ['2cm2', '1cm2', '0.5cm22', '0.25cm22'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10104.jpg"
-  },
-  {
-    "id": 10388,
-    "problem_id": 10105,
-    "problem": "<image>As shown in the figure, in triangle ABC, it is known that D, E, and F are the midpoints of sides BC, AD, and CE, respectively, and the area of triangle ABC is 4 cm\u00b2. The area of triangle DEF is () .. A, B, C, D choices are ['2cm2', '1cm2', '0.5cm22', '0.25cm22'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10105.jpg"
-  },
-  {
-    "id": 10389,
-    "problem_id": 10106,
-    "problem": "<image>As shown in the diagram, \u25b3ABC is congruent to \u25b3AED. If \u2220B = 31\u00b0 and \u2220C = 60\u00b0, what is the degree measure of \u2220DAE?. A, B, C, D choices are ['85\u00b0', '87\u00b0', '89\u00b0', '91\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10106.jpg"
-  },
-  {
-    "id": 10390,
-    "problem_id": 10107,
-    "problem": "<image>As shown in the diagram, \u25b3ABC is congruent to \u25b3AED. If \u2220B = 31\u00b0 and \u2220C = 60\u00b0, what is the degree measure of \u2220DAE?. A, B, C, D choices are ['85\u00b0', '87\u00b0', '89\u00b0', '91\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10107.jpg"
-  },
-  {
-    "id": 10391,
-    "problem_id": 10108,
-    "problem": "<image>As shown in the diagram, \u25b3ABC is congruent to \u25b3AED. If \u2220B = 31\u00b0 and \u2220C = 60\u00b0, what is the degree measure of \u2220DAE?. A, B, C, D choices are ['85\u00b0', '87\u00b0', '89\u00b0', '91\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10108.jpg"
-  },
-  {
-    "id": 10392,
-    "problem_id": 10109,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, and point D is on circle O. If \u2220AOC=130\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['70\u00b0', '50\u00b0', '25\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10109.jpg"
-  },
-  {
-    "id": 10393,
-    "problem_id": 10110,
-    "problem": "<image>A right-angled triangle board with an angle of 30 degrees and a ruler are placed as shown in the figure. If \u22201 = 146\u00b033\u2032, what is the degree of \u22202? (). A, B, C, D choices are ['64\u00b027\u2032', '63\u00b027\u2032', '64\u00b033\u2032', '63\u00b033\u2032'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10110.jpg"
-  },
-  {
-    "id": 10394,
-    "problem_id": 10111,
-    "problem": "<image>A right-angled triangle board with an angle of 30 degrees and a ruler are placed as shown in the figure. If \u22201 = 146\u00b033\u2032, what is the degree of \u22202? (). A, B, C, D choices are ['64\u00b027\u2032', '63\u00b027\u2032', '64\u00b033\u2032', '63\u00b033\u2032'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10111.jpg"
-  },
-  {
-    "id": 10395,
-    "problem_id": 10112,
-    "problem": "<image>A right-angled triangle board with an angle of 30 degrees and a ruler are placed as shown in the figure. If \u22201 = 146\u00b033\u2032, what is the degree of \u22202? (). A, B, C, D choices are ['64\u00b027\u2032', '63\u00b027\u2032', '64\u00b033\u2032', '63\u00b033\u2032'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10112.jpg"
-  },
-  {
-    "id": 10396,
-    "problem_id": 10113,
-    "problem": "<image>A right-angled triangle board with an angle of 30 degrees and a ruler are placed as shown in the figure. If \u22201 = 146\u00b033\u2032, what is the degree of \u22202? (). A, B, C, D choices are ['64\u00b027\u2032', '63\u00b027\u2032', '64\u00b033\u2032', '63\u00b033\u2032'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10113.jpg"
-  },
-  {
-    "id": 10397,
-    "problem_id": 10114,
-    "problem": "<image>A right-angled triangle board with an angle of 30 degrees and a ruler are placed as shown in the figure. If \u22201 = 146\u00b033\u2032, what is the degree of \u22202? (). A, B, C, D choices are ['64\u00b027\u2032', '63\u00b027\u2032', '64\u00b033\u2032', '63\u00b033\u2032'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10114.jpg"
-  },
-  {
-    "id": 10398,
-    "problem_id": 10115,
-    "problem": "<image>In triangle ABC, D is a point on side AC, and \u2220DBC = \u2220A. If BC = \u221a6 and AC = 3, then AD = ().. A, B, C, D choices are ['2', '1', '1.5', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10115.jpg"
-  },
-  {
-    "id": 10399,
-    "problem_id": 10116,
-    "problem": "<image>In triangle ABC, AB=AC and \u2220BAC=100\u00b0. AD is the median of BC, and CE bisects \u2220BCA and intersects AB at point E. AD and CE intersect at point F. What is the measure of \u2220CFA?. A, B, C, D choices are ['100\u00b0', '105\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10116.jpg"
-  },
-  {
-    "id": 10400,
-    "problem_id": 10117,
-    "problem": "<image>In triangle ABC, AB=AC and \u2220BAC=100\u00b0. AD is the median of BC, and CE bisects \u2220BCA and intersects AB at point E. AD and CE intersect at point F. What is the measure of \u2220CFA?. A, B, C, D choices are ['100\u00b0', '105\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10117.jpg"
-  },
-  {
-    "id": 10401,
-    "problem_id": 10118,
-    "problem": "<image>As shown in the diagram, it is known that the regular pentagon ABCDE is inscribed in circle O. Connecting BD and CE intersect at point F. What is the degree measure of angle BFC? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '72\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10118.jpg"
-  },
-  {
-    "id": 10402,
-    "problem_id": 10119,
-    "problem": "<image>As shown in the diagram, it is known that the regular pentagon ABCDE is inscribed in circle O. Connecting BD and CE intersect at point F. What is the degree measure of angle BFC? (). A, B, C, D choices are ['60\u00b0', '70\u00b0', '72\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10119.jpg"
-  },
-  {
-    "id": 10403,
-    "problem_id": 10120,
-    "problem": "<image>In triangle ABC, D is a point on AB, with AD = AC. AE is perpendicular to CD, with E as the foot of the perpendicular. F is the midpoint of BC. If BD = 16, then the length of EF is () .. A, B, C, D choices are ['32', '16', '8', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10120.jpg"
-  },
-  {
-    "id": 10404,
-    "problem_id": 10121,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10121.jpg"
-  },
-  {
-    "id": 10405,
-    "problem_id": 10122,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10122.jpg"
-  },
-  {
-    "id": 10406,
-    "problem_id": 10123,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10123.jpg"
-  },
-  {
-    "id": 10407,
-    "problem_id": 10124,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10124.jpg"
-  },
-  {
-    "id": 10408,
-    "problem_id": 10125,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10125.jpg"
-  },
-  {
-    "id": 10409,
-    "problem_id": 10126,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10126.jpg"
-  },
-  {
-    "id": 10410,
-    "problem_id": 10127,
-    "problem": "<image>As shown in the figure, D and E are the midpoints of sides AB and AC of triangle ABC. If the perimeter of triangle ADE is 6, then the perimeter of triangle ABC is (). A, B, C, D choices are ['6', '12', '18', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10127.jpg"
-  },
-  {
-    "id": 10411,
-    "problem_id": 10128,
-    "problem": "<image>In the figure, ABCD, E is the midpoint of BC, DE \u22a5 AE, F is the midpoint of AD, and EF is connected. If AE = 6, DE = 8, what is the length of AB?. A, B, C, D choices are ['3', '4', '5', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10128.jpg"
-  },
-  {
-    "id": 10412,
-    "problem_id": 10129,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with the sides of triangle ABC as their respective edges. S1, S2, S3 represent the areas of these three squares. If S1\uff1d3 and S2\uff1d10, then S3\uff1d(). A, B, C, D choices are ['5', '7', '13', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10129.jpg"
-  },
-  {
-    "id": 10413,
-    "problem_id": 10130,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with the sides of triangle ABC as their respective edges. S1, S2, S3 represent the areas of these three squares. If S1\uff1d3 and S2\uff1d10, then S3\uff1d(). A, B, C, D choices are ['5', '7', '13', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10130.jpg"
-  },
-  {
-    "id": 10414,
-    "problem_id": 10131,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with the sides of triangle ABC as their respective edges. S1, S2, S3 represent the areas of these three squares. If S1\uff1d3 and S2\uff1d10, then S3\uff1d(). A, B, C, D choices are ['5', '7', '13', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10131.jpg"
-  },
-  {
-    "id": 10415,
-    "problem_id": 10132,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with the sides of triangle ABC as their respective edges. S1, S2, S3 represent the areas of these three squares. If S1\uff1d3 and S2\uff1d10, then S3\uff1d(). A, B, C, D choices are ['5', '7', '13', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10132.jpg"
-  },
-  {
-    "id": 10416,
-    "problem_id": 10133,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with the sides of triangle ABC as their respective edges. S1, S2, S3 represent the areas of these three squares. If S1\uff1d3 and S2\uff1d10, then S3\uff1d(). A, B, C, D choices are ['5', '7', '13', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10133.jpg"
-  },
-  {
-    "id": 10417,
-    "problem_id": 10134,
-    "problem": "<image>In right triangle ABC as shown in the figure, \u2220ACB\uff1d90\u00b0. Three squares are constructed outside triangle ABC with the sides of triangle ABC as their respective edges. S1, S2, S3 represent the areas of these three squares. If S1\uff1d3 and S2\uff1d10, then S3\uff1d(). A, B, C, D choices are ['5', '7', '13', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10134.jpg"
-  },
-  {
-    "id": 10418,
-    "problem_id": 10135,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is circumscribed around circle O, with DA = DC. If \u2220CBE = 45\u00b0, what is the degree measure of \u2220DAC? (). A, B, C, D choices are ['70\u00b0', '67.5\u00b0', '62.5\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10135.jpg"
-  },
-  {
-    "id": 10419,
-    "problem_id": 10136,
-    "problem": "<image>As shown in the figure, in the circle O with radius r = 10 and chord AB = 12, M is a moving point on the chord AB. What is the minimum length of segment OM? (). A, B, C, D choices are ['10', '16', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10136.jpg"
-  },
-  {
-    "id": 10420,
-    "problem_id": 10137,
-    "problem": "<image>As shown in the figure, in the circle O with radius r = 10 and chord AB = 12, M is a moving point on the chord AB. What is the minimum length of segment OM? (). A, B, C, D choices are ['10', '16', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10137.jpg"
-  },
-  {
-    "id": 10421,
-    "problem_id": 10138,
-    "problem": "<image>As shown in the figure, in the circle O with radius r = 10 and chord AB = 12, M is a moving point on the chord AB. What is the minimum length of segment OM? (). A, B, C, D choices are ['10', '16', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10138.jpg"
-  },
-  {
-    "id": 10422,
-    "problem_id": 10139,
-    "problem": "<image>As shown in the figure, in the circle O with radius r = 10 and chord AB = 12, M is a moving point on the chord AB. What is the minimum length of segment OM? (). A, B, C, D choices are ['10', '16', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10139.jpg"
-  },
-  {
-    "id": 10423,
-    "problem_id": 10140,
-    "problem": "<image>As shown in the figure, in the circle O with radius r = 10 and chord AB = 12, M is a moving point on the chord AB. What is the minimum length of segment OM? (). A, B, C, D choices are ['10', '16', '6', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10140.jpg"
-  },
-  {
-    "id": 10424,
-    "problem_id": 10141,
-    "problem": "<image>In triangle ABC, where angle C is 90 degrees, point D is on AC and DE is parallel to AB. If angle CDE is 160 degrees, what is the degree measure of angle B?. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10141.jpg"
-  },
-  {
-    "id": 10425,
-    "problem_id": 10142,
-    "problem": "<image>In right triangle ABC as shown, with \u2220B = 90\u00b0, AB = 3, BC = 4, point D is on BC. Among all the ADCE with AC as diagonal, what is the minimum value of DE?. A, B, C, D choices are ['2', '3', '4', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10142.jpg"
-  },
-  {
-    "id": 10426,
-    "problem_id": 10143,
-    "problem": "<image>As shown in the figure, points E and F are the midpoints of BD and CE respectively. If the area of triangle AEF is 3, what is the area of triangle ABC?. A, B, C, D choices are ['9', '10', '11', '12'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10143.jpg"
-  },
-  {
-    "id": 10427,
-    "problem_id": 10144,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 3, what is the area of rectangle ABCD? (). A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10144.jpg"
-  },
-  {
-    "id": 10428,
-    "problem_id": 10145,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 3, what is the area of rectangle ABCD? (). A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10145.jpg"
-  },
-  {
-    "id": 10429,
-    "problem_id": 10146,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 3, what is the area of rectangle ABCD? (). A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10146.jpg"
-  },
-  {
-    "id": 10430,
-    "problem_id": 10147,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 3, what is the area of rectangle ABCD? (). A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10147.jpg"
-  },
-  {
-    "id": 10431,
-    "problem_id": 10148,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 3, what is the area of rectangle ABCD? (). A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10148.jpg"
-  },
-  {
-    "id": 10432,
-    "problem_id": 10149,
-    "problem": "<image>In the rectangle ABCD shown in the figure, AC and BD intersect at point O. If the area of triangle AOB is 3, what is the area of rectangle ABCD? (). A, B, C, D choices are ['6', '9', '12', '15'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10149.jpg"
-  },
-  {
-    "id": 10433,
-    "problem_id": 10150,
-    "problem": "<image>In the right triangle ABC shown below, angle B is 90 degrees, AB is 8, BC is 5, E is a point on AB, and AC is the diagonal of parallelogram AECF. What is the minimum value of EF?. A, B, C, D choices are ['5', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10150.jpg"
-  },
-  {
-    "id": 10434,
-    "problem_id": 10151,
-    "problem": "<image>In the right triangle ABC shown below, angle B is 90 degrees, AB is 8, BC is 5, E is a point on AB, and AC is the diagonal of parallelogram AECF. What is the minimum value of EF?. A, B, C, D choices are ['5', '6', '8', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10151.jpg"
-  },
-  {
-    "id": 10435,
-    "problem_id": 10152,
-    "problem": "<image>As shown in the diagram, points A, B, and C are three points on the circle O. If \u2220AOC = 90\u00b0 and \u2220BAC = 30\u00b0, what is the size of \u2220AOB?. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10152.jpg"
-  },
-  {
-    "id": 10436,
-    "problem_id": 10153,
-    "problem": "<image>In triangle ABC, point D is the midpoint of BC. Connect AD, point E is the midpoint of AD, connect CE, and point F is the midpoint of CE. If the area of triangle DEF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10153.jpg"
-  },
-  {
-    "id": 10437,
-    "problem_id": 10154,
-    "problem": "<image>In triangle ABC, point D is the midpoint of BC. Connect AD, point E is the midpoint of AD, connect CE, and point F is the midpoint of CE. If the area of triangle DEF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10154.jpg"
-  },
-  {
-    "id": 10438,
-    "problem_id": 10155,
-    "problem": "<image>In triangle ABC, point D is the midpoint of BC. Connect AD, point E is the midpoint of AD, connect CE, and point F is the midpoint of CE. If the area of triangle DEF is 2, then the area of triangle ABC is (). A, B, C, D choices are ['16', '14', '12', '10'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10155.jpg"
-  },
-  {
-    "id": 10439,
-    "problem_id": 10156,
-    "problem": "<image>In the rhombus ABCD as shown in the figure, diagonals AC and BD intersect at point O, E is the midpoint of CD, and OE = 3. Find the length of AB.. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10156.jpg"
-  },
-  {
-    "id": 10440,
-    "problem_id": 10157,
-    "problem": "<image>In the rhombus ABCD as shown in the figure, diagonals AC and BD intersect at point O, E is the midpoint of CD, and OE = 3. Find the length of AB.. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10157.jpg"
-  },
-  {
-    "id": 10441,
-    "problem_id": 10158,
-    "problem": "<image>In the rhombus ABCD as shown in the figure, diagonals AC and BD intersect at point O, E is the midpoint of CD, and OE = 3. Find the length of AB.. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10158.jpg"
-  },
-  {
-    "id": 10442,
-    "problem_id": 10159,
-    "problem": "<image>In the rhombus ABCD as shown in the figure, diagonals AC and BD intersect at point O, E is the midpoint of CD, and OE = 3. Find the length of AB.. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10159.jpg"
-  },
-  {
-    "id": 10443,
-    "problem_id": 10160,
-    "problem": "<image>In the rhombus ABCD as shown in the figure, diagonals AC and BD intersect at point O, E is the midpoint of CD, and OE = 3. Find the length of AB.. A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10160.jpg"
-  },
-  {
-    "id": 10444,
-    "problem_id": 10161,
-    "problem": "<image>As shown in the figure, the straight lines AB and CD intersect at point O. OE bisects angle BOC. If angle AOD is 68\u00b0, what is the degree measure of angle COE?. A, B, C, D choices are ['32\u00b0', '34\u00b0', '36\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10161.jpg"
-  },
-  {
-    "id": 10445,
-    "problem_id": 10162,
-    "problem": "<image>As shown in the figure, the straight lines AB and CD intersect at point O. OE bisects angle BOC. If angle AOD is 68\u00b0, what is the degree measure of angle COE?. A, B, C, D choices are ['32\u00b0', '34\u00b0', '36\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10162.jpg"
-  },
-  {
-    "id": 10446,
-    "problem_id": 10163,
-    "problem": "<image>As shown in the figure, the straight lines AB and CD intersect at point O. OE bisects angle BOC. If angle AOD is 68\u00b0, what is the degree measure of angle COE?. A, B, C, D choices are ['32\u00b0', '34\u00b0', '36\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10163.jpg"
-  },
-  {
-    "id": 10447,
-    "problem_id": 10164,
-    "problem": "<image>As shown in the figure, the straight lines AB and CD intersect at point O. OE bisects angle BOC. If angle AOD is 68\u00b0, what is the degree measure of angle COE?. A, B, C, D choices are ['32\u00b0', '34\u00b0', '36\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10164.jpg"
-  },
-  {
-    "id": 10448,
-    "problem_id": 10165,
-    "problem": "<image>In the figure, in diamond ABCD, BC = 5, diagonal AC is equal to 8, and DE \u22a5 AB. What is the length of DE?. A, B, C, D choices are ['5', '6', '9.6', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10165.jpg"
-  },
-  {
-    "id": 10449,
-    "problem_id": 10166,
-    "problem": "<image>In the figure, in diamond ABCD, BC = 5, diagonal AC is equal to 8, and DE \u22a5 AB. What is the length of DE?. A, B, C, D choices are ['5', '6', '9.6', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10166.jpg"
-  },
-  {
-    "id": 10450,
-    "problem_id": 10167,
-    "problem": "<image>In the figure, in diamond ABCD, BC = 5, diagonal AC is equal to 8, and DE \u22a5 AB. What is the length of DE?. A, B, C, D choices are ['5', '6', '9.6', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10167.jpg"
-  },
-  {
-    "id": 10451,
-    "problem_id": 10168,
-    "problem": "<image>In the figure, in diamond ABCD, BC = 5, diagonal AC is equal to 8, and DE \u22a5 AB. What is the length of DE?. A, B, C, D choices are ['5', '6', '9.6', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10168.jpg"
-  },
-  {
-    "id": 10452,
-    "problem_id": 10169,
-    "problem": "<image>In the figure, in diamond ABCD, BC = 5, diagonal AC is equal to 8, and DE \u22a5 AB. What is the length of DE?. A, B, C, D choices are ['5', '6', '9.6', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10169.jpg"
-  },
-  {
-    "id": 10453,
-    "problem_id": 10170,
-    "problem": "<image>In the figure, in diamond ABCD, BC = 5, diagonal AC is equal to 8, and DE \u22a5 AB. What is the length of DE?. A, B, C, D choices are ['5', '6', '9.6', '4.8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10170.jpg"
-  },
-  {
-    "id": 10455,
-    "problem_id": 10171,
-    "problem": "<image>In triangle ABC, AB = AC, \u2220B = 30\u00b0, AD \u22a5 AC, intersects BC at point D, and AD = 4. Find the length of BC.. A, B, C, D choices are ['8', '4', '12', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10171.jpg"
-  },
-  {
-    "id": 10456,
-    "problem_id": 10172,
-    "problem": "<image>In the figure, quadrilateral ABCD, where AD \u2225 BC, AD = 2, BC = 5, point E and F are the midpoints of diagonal AC and BD, respectively. What is the length of EF?. A, B, C, D choices are ['1', '1.5', '2.5', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10172.jpg"
-  },
-  {
-    "id": 10457,
-    "problem_id": 10173,
-    "problem": "<image>In the figure, quadrilateral ABCD, where AD \u2225 BC, AD = 2, BC = 5, point E and F are the midpoints of diagonal AC and BD, respectively. What is the length of EF?. A, B, C, D choices are ['1', '1.5', '2.5', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10173.jpg"
-  },
-  {
-    "id": 10458,
-    "problem_id": 10174,
-    "problem": "<image>In the figure, quadrilateral ABCD, where AD \u2225 BC, AD = 2, BC = 5, point E and F are the midpoints of diagonal AC and BD, respectively. What is the length of EF?. A, B, C, D choices are ['1', '1.5', '2.5', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10174.jpg"
-  },
-  {
-    "id": 10459,
-    "problem_id": 10175,
-    "problem": "<image>In the figure, quadrilateral ABCD, where AD \u2225 BC, AD = 2, BC = 5, point E and F are the midpoints of diagonal AC and BD, respectively. What is the length of EF?. A, B, C, D choices are ['1', '1.5', '2.5', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10175.jpg"
-  },
-  {
-    "id": 10460,
-    "problem_id": 10176,
-    "problem": "<image>In the figure, quadrilateral ABCD, where AD \u2225 BC, AD = 2, BC = 5, point E and F are the midpoints of diagonal AC and BD, respectively. What is the length of EF?. A, B, C, D choices are ['1', '1.5', '2.5', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10176.jpg"
-  },
-  {
-    "id": 10461,
-    "problem_id": 10177,
-    "problem": "<image>In the figure, quadrilateral ABCD, where AD \u2225 BC, AD = 2, BC = 5, point E and F are the midpoints of diagonal AC and BD, respectively. What is the length of EF?. A, B, C, D choices are ['1', '1.5', '2.5', '3.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10177.jpg"
-  },
-  {
-    "id": 10462,
-    "problem_id": 10178,
-    "problem": "<image>As shown in the figure, AB\u2225CD and EC bisects \u2220AEF. If \u2220EFD = 130\u00b0, what is the degree measure of \u2220ECF?. A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10178.jpg"
-  },
-  {
-    "id": 10463,
-    "problem_id": 10179,
-    "problem": "<image>In quadrilateral ABCD, \u2220C = 110\u00b0, and the exterior angles adjacent to \u2220BAD and \u2220ABC are both 110\u00b0. What is the degree measure of the exterior angle \u03b1 of \u2220ADC? (). A, B, C, D choices are ['90\u00b0', '85\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10179.jpg"
-  },
-  {
-    "id": 10464,
-    "problem_id": 10180,
-    "problem": "<image>In quadrilateral ABCD, \u2220C = 110\u00b0, and the exterior angles adjacent to \u2220BAD and \u2220ABC are both 110\u00b0. What is the degree measure of the exterior angle \u03b1 of \u2220ADC? (). A, B, C, D choices are ['90\u00b0', '85\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10180.jpg"
-  },
-  {
-    "id": 10465,
-    "problem_id": 10181,
-    "problem": "<image>In quadrilateral ABCD, \u2220C = 110\u00b0, and the exterior angles adjacent to \u2220BAD and \u2220ABC are both 110\u00b0. What is the degree measure of the exterior angle \u03b1 of \u2220ADC? (). A, B, C, D choices are ['90\u00b0', '85\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10181.jpg"
-  },
-  {
-    "id": 10466,
-    "problem_id": 10182,
-    "problem": "<image>In quadrilateral ABCD, \u2220C = 110\u00b0, and the exterior angles adjacent to \u2220BAD and \u2220ABC are both 110\u00b0. What is the degree measure of the exterior angle \u03b1 of \u2220ADC? (). A, B, C, D choices are ['90\u00b0', '85\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10182.jpg"
-  },
-  {
-    "id": 10467,
-    "problem_id": 10183,
-    "problem": "<image>In quadrilateral ABCD, \u2220C = 110\u00b0, and the exterior angles adjacent to \u2220BAD and \u2220ABC are both 110\u00b0. What is the degree measure of the exterior angle \u03b1 of \u2220ADC? (). A, B, C, D choices are ['90\u00b0', '85\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10183.jpg"
-  },
-  {
-    "id": 10468,
-    "problem_id": 10184,
-    "problem": "<image>In quadrilateral ABCD, \u2220C = 110\u00b0, and the exterior angles adjacent to \u2220BAD and \u2220ABC are both 110\u00b0. What is the degree measure of the exterior angle \u03b1 of \u2220ADC? (). A, B, C, D choices are ['90\u00b0', '85\u00b0', '80\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10184.jpg"
-  },
-  {
-    "id": 10469,
-    "problem_id": 10185,
-    "problem": "<image>As shown in the diagram, triangle BCD is inscribed in circle O, and \u2220D = 70\u00b0. OA is perpendicular to BC and intersects circle O at point A. Connecting AC, what is the degree measure of \u2220OAC?. A, B, C, D choices are ['40\u00b0', '55\u00b0', '70\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10185.jpg"
-  },
-  {
-    "id": 10470,
-    "problem_id": 10186,
-    "problem": "<image>As shown in the figure, OA is perpendicular to OD, \u2220AOC = 3\u2220COD, OC bisects \u2220BOD. What is the degree of \u2220AOB?. A, B, C, D choices are ['45\u00b0', '46\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10186.jpg"
-  },
-  {
-    "id": 10471,
-    "problem_id": 10187,
-    "problem": "<image>As shown in the figure, OA is perpendicular to OD, \u2220AOC = 3\u2220COD, OC bisects \u2220BOD. What is the degree of \u2220AOB?. A, B, C, D choices are ['45\u00b0', '46\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10187.jpg"
-  },
-  {
-    "id": 10472,
-    "problem_id": 10188,
-    "problem": "<image>The triangle ruler is a good helper for us to learn mathematics. Place a pair of right-angled triangle rulers as shown in the figure. Point C is on the extension line of FD, point B is on ED, AB\u2225CF, \u2220F=\u2220ACB=90\u00b0, \u2220E=45\u00b0, \u2220A=60\u00b0, then \u2220CBD = ().. A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10188.jpg"
-  },
-  {
-    "id": 10473,
-    "problem_id": 10189,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10189.jpg"
-  },
-  {
-    "id": 10474,
-    "problem_id": 10190,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10190.jpg"
-  },
-  {
-    "id": 10475,
-    "problem_id": 10191,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10191.jpg"
-  },
-  {
-    "id": 10476,
-    "problem_id": 10192,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10192.jpg"
-  },
-  {
-    "id": 10477,
-    "problem_id": 10193,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10193.jpg"
-  },
-  {
-    "id": 10478,
-    "problem_id": 10194,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10194.jpg"
-  },
-  {
-    "id": 10479,
-    "problem_id": 10195,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10195.jpg"
-  },
-  {
-    "id": 10480,
-    "problem_id": 10196,
-    "problem": "<image>As shown in the figure, square M and N are constructed with one leg and the hypotenuse of a right triangle as their sides. The areas of the squares are 9cm and 25cm, respectively. What is the area of the right triangle?. A, B, C, D choices are ['6', '12', '24', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10196.jpg"
-  },
-  {
-    "id": 10481,
-    "problem_id": 10197,
-    "problem": "<image>In the square ABCD, E is a point on the diagonal BD. Connect AE and CE. If \u2220BCE = 70\u00b0, what is \u2220EAD?. A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10197.jpg"
-  },
-  {
-    "id": 10482,
-    "problem_id": 10198,
-    "problem": "<image>In triangle ABC, \u2220ACB=90\u00b0, \u2220A=25\u00b0. Point D is on side AB. If we fold triangle ABC along CD so that point B lands on point B' on side AC, what is the degree measure of \u2220ADB'?. A, B, C, D choices are ['25\u00b0', '30\u00b0', '35\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10198.jpg"
-  },
-  {
-    "id": 10483,
-    "problem_id": 10199,
-    "problem": "<image>Given that AB\u2225CD, BC bisects \u2220ABE, and \u2220C = 33\u00b0, what is the degree measure of \u2220CEF?. A, B, C, D choices are ['66\u00b0', '49\u00b0', '33\u00b0', '16\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10199.jpg"
-  },
-  {
-    "id": 10484,
-    "problem_id": 10200,
-    "problem": "<image>Given that AB\u2225CD, BC bisects \u2220ABE, and \u2220C = 33\u00b0, what is the degree measure of \u2220CEF?. A, B, C, D choices are ['66\u00b0', '49\u00b0', '33\u00b0', '16\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10200.jpg"
-  },
-  {
-    "id": 10485,
-    "problem_id": 10201,
-    "problem": "<image>As shown in the figure, the length of the base BC of isosceles triangle ABC is 4cm, and the area is 12cm2. D is the midpoint of side BC. The perpendicular bisector of side AB intersects AD at point M and AC at point F. The value of BM + DM is () .. A, B, C, D choices are ['2cm', '10cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10201.jpg"
-  },
-  {
-    "id": 10486,
-    "problem_id": 10202,
-    "problem": "<image>As shown in the figure, the length of the base BC of isosceles triangle ABC is 4cm, and the area is 12cm2. D is the midpoint of side BC. The perpendicular bisector of side AB intersects AD at point M and AC at point F. The value of BM + DM is () .. A, B, C, D choices are ['2cm', '10cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10202.jpg"
-  },
-  {
-    "id": 10487,
-    "problem_id": 10203,
-    "problem": "<image>As shown in the figure, the length of the base BC of isosceles triangle ABC is 4cm, and the area is 12cm2. D is the midpoint of side BC. The perpendicular bisector of side AB intersects AD at point M and AC at point F. The value of BM + DM is () .. A, B, C, D choices are ['2cm', '10cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10203.jpg"
-  },
-  {
-    "id": 10488,
-    "problem_id": 10204,
-    "problem": "<image>As shown in the figure, the length of the base BC of isosceles triangle ABC is 4cm, and the area is 12cm2. D is the midpoint of side BC. The perpendicular bisector of side AB intersects AD at point M and AC at point F. The value of BM + DM is () .. A, B, C, D choices are ['2cm', '10cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10204.jpg"
-  },
-  {
-    "id": 10489,
-    "problem_id": 10205,
-    "problem": "<image>As shown in the figure, the length of the base BC of isosceles triangle ABC is 4cm, and the area is 12cm2. D is the midpoint of side BC. The perpendicular bisector of side AB intersects AD at point M and AC at point F. The value of BM + DM is () .. A, B, C, D choices are ['2cm', '10cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10205.jpg"
-  },
-  {
-    "id": 10490,
-    "problem_id": 10206,
-    "problem": "<image>As shown in the figure, the length of the base BC of isosceles triangle ABC is 4cm, and the area is 12cm2. D is the midpoint of side BC. The perpendicular bisector of side AB intersects AD at point M and AC at point F. The value of BM + DM is () .. A, B, C, D choices are ['2cm', '10cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10206.jpg"
-  },
-  {
-    "id": 10491,
-    "problem_id": 10207,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, point B is on line a, and AB is perpendicular to BC. If \u22201 = 35\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['35\u00b0', '50\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10207.jpg"
-  },
-  {
-    "id": 10492,
-    "problem_id": 10208,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, point B is on line a, and AB is perpendicular to BC. If \u22201 = 35\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['35\u00b0', '50\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10208.jpg"
-  },
-  {
-    "id": 10493,
-    "problem_id": 10209,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, point B is on line a, and AB is perpendicular to BC. If \u22201 = 35\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['35\u00b0', '50\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10209.jpg"
-  },
-  {
-    "id": 10494,
-    "problem_id": 10210,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10210.jpg"
-  },
-  {
-    "id": 10495,
-    "problem_id": 10211,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10211.jpg"
-  },
-  {
-    "id": 10496,
-    "problem_id": 10212,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10212.jpg"
-  },
-  {
-    "id": 10497,
-    "problem_id": 10213,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10213.jpg"
-  },
-  {
-    "id": 10498,
-    "problem_id": 10214,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10214.jpg"
-  },
-  {
-    "id": 10499,
-    "problem_id": 10215,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10215.jpg"
-  },
-  {
-    "id": 10500,
-    "problem_id": 10216,
-    "problem": "<image>As shown in the figure, if the right angle vertex of the triangle is placed on one side of the ruler and \u22201\uff1d65\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['15\u00b0', '30\u00b0', '25\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10216.jpg"
-  },
-  {
-    "id": 10501,
-    "problem_id": 10217,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, and points C, D are on circle O. If \u2220ABD = 15\u00b0, what is the size of \u2220BCD? (). A, B, C, D choices are ['100\u00b0', '105\u00b0', '110\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10217.jpg"
-  },
-  {
-    "id": 10502,
-    "problem_id": 10218,
-    "problem": "<image>Figure 1 shows a tall glass filled with liquid (data shown in the figure). After pouring out some of the liquid, it is placed on a horizontal table as shown in Figure 2. The height of the liquid level AB at this time is equal to () .. A, B, C, D choices are ['4cm', '3cm', '2cm', '1cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10218.jpg"
-  },
-  {
-    "id": 10503,
-    "problem_id": 10219,
-    "problem": "<image>Figure 1 shows a tall glass filled with liquid (data shown in the figure). After pouring out some of the liquid, it is placed on a horizontal table as shown in Figure 2. The height of the liquid level AB at this time is equal to () .. A, B, C, D choices are ['4cm', '3cm', '2cm', '1cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10219.jpg"
-  },
-  {
-    "id": 10504,
-    "problem_id": 10220,
-    "problem": "<image>Figure 1 shows a tall glass filled with liquid (data shown in the figure). After pouring out some of the liquid, it is placed on a horizontal table as shown in Figure 2. The height of the liquid level AB at this time is equal to () .. A, B, C, D choices are ['4cm', '3cm', '2cm', '1cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10220.jpg"
-  },
-  {
-    "id": 10505,
-    "problem_id": 10221,
-    "problem": "<image>Figure 1 shows a tall glass filled with liquid (data shown in the figure). After pouring out some of the liquid, it is placed on a horizontal table as shown in Figure 2. The height of the liquid level AB at this time is equal to () .. A, B, C, D choices are ['4cm', '3cm', '2cm', '1cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10221.jpg"
-  },
-  {
-    "id": 10506,
-    "problem_id": 10222,
-    "problem": "<image>Figure 1 shows a tall glass filled with liquid (data shown in the figure). After pouring out some of the liquid, it is placed on a horizontal table as shown in Figure 2. The height of the liquid level AB at this time is equal to () .. A, B, C, D choices are ['4cm', '3cm', '2cm', '1cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10222.jpg"
-  },
-  {
-    "id": 10507,
-    "problem_id": 10223,
-    "problem": "<image>Figure 1 shows a tall glass filled with liquid (data shown in the figure). After pouring out some of the liquid, it is placed on a horizontal table as shown in Figure 2. The height of the liquid level AB at this time is equal to () .. A, B, C, D choices are ['4cm', '3cm', '2cm', '1cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10223.jpg"
-  },
-  {
-    "id": 10508,
-    "problem_id": 10224,
-    "problem": "<image>As shown in the figure, a \"fish\" pattern is composed of four line segments, a, b, c, and d. If \u22201 = 45\u00b0, \u22202 = 45\u00b0, and \u22203 = 140\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10224.jpg"
-  },
-  {
-    "id": 10509,
-    "problem_id": 10225,
-    "problem": "<image>As shown in the figure, a \"fish\" pattern is composed of four line segments, a, b, c, and d. If \u22201 = 45\u00b0, \u22202 = 45\u00b0, and \u22203 = 140\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10225.jpg"
-  },
-  {
-    "id": 10510,
-    "problem_id": 10226,
-    "problem": "<image>As shown in the figure, a \"fish\" pattern is composed of four line segments, a, b, c, and d. If \u22201 = 45\u00b0, \u22202 = 45\u00b0, and \u22203 = 140\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10226.jpg"
-  },
-  {
-    "id": 10511,
-    "problem_id": 10227,
-    "problem": "<image>As shown in the figure, a \"fish\" pattern is composed of four line segments, a, b, c, and d. If \u22201 = 45\u00b0, \u22202 = 45\u00b0, and \u22203 = 140\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10227.jpg"
-  },
-  {
-    "id": 10513,
-    "problem_id": 10228,
-    "problem": "<image>Given points A, B, C, and D on circle O, with AB and CD intersecting at point E outside of circle O. If angle BCD is 25 degrees and angle E is 39 degrees, what is the degree measure of angle ADC?. A, B, C, D choices are ['64\u00b0', '65\u00b0', '51\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10228.jpg"
-  },
-  {
-    "id": 10514,
-    "problem_id": 10229,
-    "problem": "<image>Given points A, B, C, and D on circle O, with AB and CD intersecting at point E outside of circle O. If angle BCD is 25 degrees and angle E is 39 degrees, what is the degree measure of angle ADC?. A, B, C, D choices are ['64\u00b0', '65\u00b0', '51\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10229.jpg"
-  },
-  {
-    "id": 10515,
-    "problem_id": 10230,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10230.jpg"
-  },
-  {
-    "id": 10516,
-    "problem_id": 10231,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10231.jpg"
-  },
-  {
-    "id": 10517,
-    "problem_id": 10232,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10232.jpg"
-  },
-  {
-    "id": 10518,
-    "problem_id": 10233,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10233.jpg"
-  },
-  {
-    "id": 10519,
-    "problem_id": 10234,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10234.jpg"
-  },
-  {
-    "id": 10520,
-    "problem_id": 10235,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10235.jpg"
-  },
-  {
-    "id": 10521,
-    "problem_id": 10236,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10236.jpg"
-  },
-  {
-    "id": 10522,
-    "problem_id": 10237,
-    "problem": "<image>In right triangle ABC as shown, \u2220ACB = 90\u00b0, CD is the altitude from AB, CE is the median on AB, AD = 2, CE = 10, then CD = ().. A, B, C, D choices are ['2', '3', '4', '6'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10237.jpg"
-  },
-  {
-    "id": 10523,
-    "problem_id": 10238,
-    "problem": "<image>In triangle ABC, D is a point on the extension of BC. If angle B is 50 degrees and angle ACD is 130 degrees, what is the measure of angle A?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10238.jpg"
-  },
-  {
-    "id": 10524,
-    "problem_id": 10239,
-    "problem": "<image>In triangle ABC, D is a point on the extension of BC. If angle B is 50 degrees and angle ACD is 130 degrees, what is the measure of angle A?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10239.jpg"
-  },
-  {
-    "id": 10525,
-    "problem_id": 10240,
-    "problem": "<image>In triangle ABC, D is a point on the extension of BC. If angle B is 50 degrees and angle ACD is 130 degrees, what is the measure of angle A?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10240.jpg"
-  },
-  {
-    "id": 10526,
-    "problem_id": 10241,
-    "problem": "<image>In triangle ABC, D is a point on the extension of BC. If angle B is 50 degrees and angle ACD is 130 degrees, what is the measure of angle A?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10241.jpg"
-  },
-  {
-    "id": 10527,
-    "problem_id": 10242,
-    "problem": "<image>In triangle ABC, D is a point on the extension of BC. If angle B is 50 degrees and angle ACD is 130 degrees, what is the measure of angle A?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10242.jpg"
-  },
-  {
-    "id": 10528,
-    "problem_id": 10243,
-    "problem": "<image>In triangle ABC, D is a point on the extension of BC. If angle B is 50 degrees and angle ACD is 130 degrees, what is the measure of angle A?. A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10243.jpg"
-  },
-  {
-    "id": 10529,
-    "problem_id": 10244,
-    "problem": "<image>As shown in the figure, points A, D, B, F are on a straight line, and \u25b3ABC is congruent to \u25b3FDE. If AF = 10 and AD = 3.5, then the length of BD is ().. A, B, C, D choices are ['3', '3.5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10244.jpg"
-  },
-  {
-    "id": 10530,
-    "problem_id": 10245,
-    "problem": "<image>As shown in the figure, points A, D, B, F are on a straight line, and \u25b3ABC is congruent to \u25b3FDE. If AF = 10 and AD = 3.5, then the length of BD is ().. A, B, C, D choices are ['3', '3.5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10245.jpg"
-  },
-  {
-    "id": 10531,
-    "problem_id": 10246,
-    "problem": "<image>As shown in the figure, points A, D, B, F are on a straight line, and \u25b3ABC is congruent to \u25b3FDE. If AF = 10 and AD = 3.5, then the length of BD is ().. A, B, C, D choices are ['3', '3.5', '6', '7'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10246.jpg"
-  },
-  {
-    "id": 10532,
-    "problem_id": 10247,
-    "problem": "<image>As shown in the diagram, AB\u2225CD and BC bisects \u2220ABD. If \u22201 = 65\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['65\u00b0', '60\u00b0', '55\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10247.jpg"
-  },
-  {
-    "id": 10533,
-    "problem_id": 10248,
-    "problem": "<image>As shown in the diagram, AB\u2225CD and BC bisects \u2220ABD. If \u22201 = 65\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['65\u00b0', '60\u00b0', '55\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10248.jpg"
-  },
-  {
-    "id": 10534,
-    "problem_id": 10249,
-    "problem": "<image>In quadrilateral ABCD, AB=6, BC=10, \u2220A=130\u00b0, \u2220D=100\u00b0, and AD=CD. If E and F are the midpoints of sides AD and CD, respectively, what is the length of EF?. A, B, C, D choices are ['3', '4', '2', '\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10249.jpg"
-  },
-  {
-    "id": 10536,
-    "problem_id": 10250,
-    "problem": "<image>In the figure, DE bisects \u2220ADC in ABCD, AD = 9, BE = 3, what is the perimeter of ABCD? (). A, B, C, D choices are ['15', '24', '30', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10250.jpg"
-  },
-  {
-    "id": 10537,
-    "problem_id": 10251,
-    "problem": "<image>As shown in the diagram, DE is the median of triangle ABC, point F is on DE, and \u2220AFB = 90\u00b0. If AB = 6 and BC = 10, then the length of EF is ().. A, B, C, D choices are ['1', '2', '3', '5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10251.jpg"
-  },
-  {
-    "id": 10538,
-    "problem_id": 10252,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10252.jpg"
-  },
-  {
-    "id": 10539,
-    "problem_id": 10253,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10253.jpg"
-  },
-  {
-    "id": 10540,
-    "problem_id": 10254,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10254.jpg"
-  },
-  {
-    "id": 10541,
-    "problem_id": 10255,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10255.jpg"
-  },
-  {
-    "id": 10542,
-    "problem_id": 10256,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10256.jpg"
-  },
-  {
-    "id": 10543,
-    "problem_id": 10257,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10257.jpg"
-  },
-  {
-    "id": 10544,
-    "problem_id": 10258,
-    "problem": "<image>In triangle ABC, AB = 7, AC = 6, BC = 5, D and E are the midpoints of AB and AC respectively. What is the length of DE?. A, B, C, D choices are ['4', '3.5', '3', '2.5'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10258.jpg"
-  },
-  {
-    "id": 10545,
-    "problem_id": 10259,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles \u2220DCE = 115\u00b0, then what is the degree measure of the other exterior angle \u2220DAF?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10259.jpg"
-  },
-  {
-    "id": 10546,
-    "problem_id": 10260,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles \u2220DCE = 115\u00b0, then what is the degree measure of the other exterior angle \u2220DAF?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10260.jpg"
-  },
-  {
-    "id": 10547,
-    "problem_id": 10261,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles \u2220DCE = 115\u00b0, then what is the degree measure of the other exterior angle \u2220DAF?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10261.jpg"
-  },
-  {
-    "id": 10548,
-    "problem_id": 10262,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles \u2220DCE = 115\u00b0, then what is the degree measure of the other exterior angle \u2220DAF?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10262.jpg"
-  },
-  {
-    "id": 10549,
-    "problem_id": 10263,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles \u2220DCE = 115\u00b0, then what is the degree measure of the other exterior angle \u2220DAF?. A, B, C, D choices are ['75\u00b0', '65\u00b0', '55\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10263.jpg"
-  },
-  {
-    "id": 10550,
-    "problem_id": 10264,
-    "problem": "<image>As shown in the figure, in the quadrilateral ABCD inscribed in a circle, if \u2220C=80\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['120\u00b0', '100\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10264.jpg"
-  },
-  {
-    "id": 10551,
-    "problem_id": 10265,
-    "problem": "<image>As shown in the figure, in the quadrilateral ABCD inscribed in a circle, if \u2220C=80\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['120\u00b0', '100\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10265.jpg"
-  },
-  {
-    "id": 10552,
-    "problem_id": 10266,
-    "problem": "<image>As shown in the figure, in the quadrilateral ABCD inscribed in a circle, if \u2220C=80\u00b0, then \u2220A is equal to ().. A, B, C, D choices are ['120\u00b0', '100\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10266.jpg"
-  },
-  {
-    "id": 10553,
-    "problem_id": 10267,
-    "problem": "<image>In triangle ABC as shown, \u2220ABC = 50\u00b0, \u2220ACB = 80\u00b0, BP bisects \u2220ABC, and CP bisects \u2220ACB. What is the measure of \u2220BPC? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10267.jpg"
-  },
-  {
-    "id": 10554,
-    "problem_id": 10268,
-    "problem": "<image>In triangle ABC as shown, \u2220ABC = 50\u00b0, \u2220ACB = 80\u00b0, BP bisects \u2220ABC, and CP bisects \u2220ACB. What is the measure of \u2220BPC? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10268.jpg"
-  },
-  {
-    "id": 10555,
-    "problem_id": 10269,
-    "problem": "<image>In triangle ABC as shown, \u2220ABC = 50\u00b0, \u2220ACB = 80\u00b0, BP bisects \u2220ABC, and CP bisects \u2220ACB. What is the measure of \u2220BPC? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10269.jpg"
-  },
-  {
-    "id": 10556,
-    "problem_id": 10270,
-    "problem": "<image>In triangle ABC as shown, \u2220ABC = 50\u00b0, \u2220ACB = 80\u00b0, BP bisects \u2220ABC, and CP bisects \u2220ACB. What is the measure of \u2220BPC? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '115\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10270.jpg"
-  },
-  {
-    "id": 10557,
-    "problem_id": 10271,
-    "problem": "<image>As shown in the diagram, if the right angle vertex of the triangle is placed on one side of the ruler, and \u22201 = 65\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10271.jpg"
-  },
-  {
-    "id": 10558,
-    "problem_id": 10272,
-    "problem": "<image>As shown in the diagram, if the right angle vertex of the triangle is placed on one side of the ruler, and \u22201 = 65\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10272.jpg"
-  },
-  {
-    "id": 10559,
-    "problem_id": 10273,
-    "problem": "<image>As shown in the diagram, if the right angle vertex of the triangle is placed on one side of the ruler, and \u22201 = 65\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10273.jpg"
-  },
-  {
-    "id": 10560,
-    "problem_id": 10274,
-    "problem": "<image>As shown in the diagram, if the right angle vertex of the triangle is placed on one side of the ruler, and \u22201 = 65\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10274.jpg"
-  },
-  {
-    "id": 10561,
-    "problem_id": 10275,
-    "problem": "<image>As shown in the diagram, if the right angle vertex of the triangle is placed on one side of the ruler, and \u22201 = 65\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10275.jpg"
-  },
-  {
-    "id": 10562,
-    "problem_id": 10276,
-    "problem": "<image>As shown in the figure, BC is the diameter of the circle O, AD is perpendicular to BC, and if \u2220D = 36\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['72\u00b0', '54\u00b0', '45\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10276.jpg"
-  },
-  {
-    "id": 10563,
-    "problem_id": 10277,
-    "problem": "<image>As shown in the diagram, line AB is parallel to CD. If \u22201 = 70\u00b0, what is the degree measure of \u2220BOF? (). A, B, C, D choices are ['70\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10277.jpg"
-  },
-  {
-    "id": 10564,
-    "problem_id": 10278,
-    "problem": "<image>As shown in the diagram, line AB is parallel to CD. If \u22201 = 70\u00b0, what is the degree measure of \u2220BOF? (). A, B, C, D choices are ['70\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10278.jpg"
-  },
-  {
-    "id": 10565,
-    "problem_id": 10279,
-    "problem": "<image>As shown in the diagram, line AB is parallel to CD. If \u22201 = 70\u00b0, what is the degree measure of \u2220BOF? (). A, B, C, D choices are ['70\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10279.jpg"
-  },
-  {
-    "id": 10566,
-    "problem_id": 10280,
-    "problem": "<image>As shown in the diagram, line AB is parallel to CD. If \u22201 = 70\u00b0, what is the degree measure of \u2220BOF? (). A, B, C, D choices are ['70\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10280.jpg"
-  },
-  {
-    "id": 10567,
-    "problem_id": 10281,
-    "problem": "<image>As shown in the diagram, line AB is parallel to CD. If \u22201 = 70\u00b0, what is the degree measure of \u2220BOF? (). A, B, C, D choices are ['70\u00b0', '100\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10281.jpg"
-  },
-  {
-    "id": 10568,
-    "problem_id": 10282,
-    "problem": "<image>Given the diagram, where AB is the diameter of the circumcircle of triangle ABC and \u2220A = 35\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10282.jpg"
-  },
-  {
-    "id": 10569,
-    "problem_id": 10283,
-    "problem": "<image>Given the diagram, where AB is the diameter of the circumcircle of triangle ABC and \u2220A = 35\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10283.jpg"
-  },
-  {
-    "id": 10570,
-    "problem_id": 10284,
-    "problem": "<image>Given the diagram, where AB is the diameter of the circumcircle of triangle ABC and \u2220A = 35\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10284.jpg"
-  },
-  {
-    "id": 10571,
-    "problem_id": 10285,
-    "problem": "<image>Given the diagram, where AB is the diameter of the circumcircle of triangle ABC and \u2220A = 35\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10285.jpg"
-  },
-  {
-    "id": 10572,
-    "problem_id": 10286,
-    "problem": "<image>Given the diagram, where AB is the diameter of the circumcircle of triangle ABC and \u2220A = 35\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10286.jpg"
-  },
-  {
-    "id": 10573,
-    "problem_id": 10287,
-    "problem": "<image>Given the diagram, where AB is the diameter of the circumcircle of triangle ABC and \u2220A = 35\u00b0, what is the degree of \u2220B? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10287.jpg"
-  },
-  {
-    "id": 10574,
-    "problem_id": 10288,
-    "problem": "<image>As shown in the diagram, in triangle ABC, the angle bisector of angle ABC intersects with the exterior angle bisector of angle ACB at point D. If angle A is 50 degrees, then what is the measure of angle D?. A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10288.jpg"
-  },
-  {
-    "id": 10575,
-    "problem_id": 10289,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10289.jpg"
-  },
-  {
-    "id": 10576,
-    "problem_id": 10290,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10290.jpg"
-  },
-  {
-    "id": 10577,
-    "problem_id": 10291,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10291.jpg"
-  },
-  {
-    "id": 10578,
-    "problem_id": 10292,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10292.jpg"
-  },
-  {
-    "id": 10579,
-    "problem_id": 10293,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10293.jpg"
-  },
-  {
-    "id": 10580,
-    "problem_id": 10294,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10294.jpg"
-  },
-  {
-    "id": 10581,
-    "problem_id": 10295,
-    "problem": "<image>As shown, \u25b3ABC is congruent to \u25b3DCB, and points A and B correspond to points D and C, respectively. If AB = 7 cm, BC = 12 cm, and AC = 9 cm, then the length of BD is ().. A, B, C, D choices are ['7cm', '9cm', '12cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10295.jpg"
-  },
-  {
-    "id": 10582,
-    "problem_id": 10296,
-    "problem": "<image>In the figure, A, B, C, D, E, and F are six points on a plane. What is the sum of the degrees of \u2220A, \u2220B, \u2220C, \u2220D, \u2220E, and \u2220F? (). A, B, C, D choices are ['180\u00b0', '360\u00b0', '540\u00b0', '720\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10296.jpg"
-  },
-  {
-    "id": 10583,
-    "problem_id": 10297,
-    "problem": "<image>In the figure, A, B, C, D, E, and F are six points on a plane. What is the sum of the degrees of \u2220A, \u2220B, \u2220C, \u2220D, \u2220E, and \u2220F? (). A, B, C, D choices are ['180\u00b0', '360\u00b0', '540\u00b0', '720\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10297.jpg"
-  },
-  {
-    "id": 10584,
-    "problem_id": 10298,
-    "problem": "<image>In the figure, A, B, C, D, E, and F are six points on a plane. What is the sum of the degrees of \u2220A, \u2220B, \u2220C, \u2220D, \u2220E, and \u2220F? (). A, B, C, D choices are ['180\u00b0', '360\u00b0', '540\u00b0', '720\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10298.jpg"
-  },
-  {
-    "id": 10585,
-    "problem_id": 10299,
-    "problem": "<image>In the figure, A, B, C, D, E, and F are six points on a plane. What is the sum of the degrees of \u2220A, \u2220B, \u2220C, \u2220D, \u2220E, and \u2220F? (). A, B, C, D choices are ['180\u00b0', '360\u00b0', '540\u00b0', '720\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10299.jpg"
-  },
-  {
-    "id": 10586,
-    "problem_id": 10300,
-    "problem": "<image>In the figure, A, B, C, D, E, and F are six points on a plane. What is the sum of the degrees of \u2220A, \u2220B, \u2220C, \u2220D, \u2220E, and \u2220F? (). A, B, C, D choices are ['180\u00b0', '360\u00b0', '540\u00b0', '720\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10300.jpg"
-  },
-  {
-    "id": 10587,
-    "problem_id": 10301,
-    "problem": "<image>In the figure, A, B, C, D, E, and F are six points on a plane. What is the sum of the degrees of \u2220A, \u2220B, \u2220C, \u2220D, \u2220E, and \u2220F? (). A, B, C, D choices are ['180\u00b0', '360\u00b0', '540\u00b0', '720\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10301.jpg"
-  },
-  {
-    "id": 10588,
-    "problem_id": 10302,
-    "problem": "<image>As shown in the figure, it is known that AF bisects \u2220BAC, and FD is perpendicular to BC at point F. If \u2220B is 20 degrees larger than \u2220C, then what is the degree measure of \u2220F? (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10302.jpg"
-  },
-  {
-    "id": 10589,
-    "problem_id": 10303,
-    "problem": "<image>As shown in the figure, it is known that AF bisects \u2220BAC, and FD is perpendicular to BC at point F. If \u2220B is 20 degrees larger than \u2220C, then what is the degree measure of \u2220F? (). A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10303.jpg"
-  },
-  {
-    "id": 10590,
-    "problem_id": 10304,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10304.jpg"
-  },
-  {
-    "id": 10591,
-    "problem_id": 10305,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10305.jpg"
-  },
-  {
-    "id": 10592,
-    "problem_id": 10306,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10306.jpg"
-  },
-  {
-    "id": 10593,
-    "problem_id": 10307,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10307.jpg"
-  },
-  {
-    "id": 10594,
-    "problem_id": 10308,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10308.jpg"
-  },
-  {
-    "id": 10595,
-    "problem_id": 10309,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10309.jpg"
-  },
-  {
-    "id": 10596,
-    "problem_id": 10310,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10310.jpg"
-  },
-  {
-    "id": 10597,
-    "problem_id": 10311,
-    "problem": "<image>As shown in the figure, \u25b3ABC is congruent to \u25b3BAD, with corresponding points A and B, and C and D. If AB=6cm, BD=5cm, and AD=4cm, what is the length of BC? (). A, B, C, D choices are ['6cm', '5cm', '4cm', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10311.jpg"
-  },
-  {
-    "id": 10599,
-    "problem_id": 10312,
-    "problem": "<image>In the diagram, BD is the diameter of circle O, and \u2220A=30\u00b0, then what is the degree of \u2220CBD? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10312.jpg"
-  },
-  {
-    "id": 10600,
-    "problem_id": 10313,
-    "problem": "<image>As shown in the figure, an ant crawls from point A to point B on the surface of a rectangular paper box with dimensions of 3cm by 3cm by 8cm. What is the length of the shortest path it travels? (). A, B, C, D choices are ['(3+8)cm', '10cm', '14cm', '.\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10313.jpg"
-  },
-  {
-    "id": 10601,
-    "problem_id": 10314,
-    "problem": "<image>As shown in the figure, an ant crawls from point A to point B on the surface of a rectangular paper box with dimensions of 3cm by 3cm by 8cm. What is the length of the shortest path it travels? (). A, B, C, D choices are ['(3+8)cm', '10cm', '14cm', '.\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10314.jpg"
-  },
-  {
-    "id": 10602,
-    "problem_id": 10315,
-    "problem": "<image>As shown in the figure, point O lies on the straight line AB and OC is perpendicular to OD. If \u2220COA = 36\u00b0, then what is the size of \u2220DOB? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10315.jpg"
-  },
-  {
-    "id": 10603,
-    "problem_id": 10316,
-    "problem": "<image>As shown in the figure, point O lies on the straight line AB and OC is perpendicular to OD. If \u2220COA = 36\u00b0, then what is the size of \u2220DOB? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10316.jpg"
-  },
-  {
-    "id": 10604,
-    "problem_id": 10317,
-    "problem": "<image>As shown in the figure, point O lies on the straight line AB and OC is perpendicular to OD. If \u2220COA = 36\u00b0, then what is the size of \u2220DOB? (). A, B, C, D choices are ['36\u00b0', '54\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10317.jpg"
-  },
-  {
-    "id": 10605,
-    "problem_id": 10318,
-    "problem": "<image>As shown in the figure, the angle bisectors BO and CO of triangle ABC intersect at point O, and \u2220A = 120\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10318.jpg"
-  },
-  {
-    "id": 10606,
-    "problem_id": 10319,
-    "problem": "<image>As shown in the figure, the angle bisectors BO and CO of triangle ABC intersect at point O, and \u2220A = 120\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10319.jpg"
-  },
-  {
-    "id": 10607,
-    "problem_id": 10320,
-    "problem": "<image>As shown in the figure, the angle bisectors BO and CO of triangle ABC intersect at point O, and \u2220A = 120\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10320.jpg"
-  },
-  {
-    "id": 10608,
-    "problem_id": 10321,
-    "problem": "<image>As shown in the figure, the angle bisectors BO and CO of triangle ABC intersect at point O, and \u2220A = 120\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10321.jpg"
-  },
-  {
-    "id": 10609,
-    "problem_id": 10322,
-    "problem": "<image>As shown in the figure, the angle bisectors BO and CO of triangle ABC intersect at point O, and \u2220A = 120\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10322.jpg"
-  },
-  {
-    "id": 10610,
-    "problem_id": 10323,
-    "problem": "<image>As shown in the figure, the angle bisectors BO and CO of triangle ABC intersect at point O, and \u2220A = 120\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['150\u00b0', '140\u00b0', '130\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10323.jpg"
-  },
-  {
-    "id": 10611,
-    "problem_id": 10324,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10324.jpg"
-  },
-  {
-    "id": 10612,
-    "problem_id": 10325,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10325.jpg"
-  },
-  {
-    "id": 10613,
-    "problem_id": 10326,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10326.jpg"
-  },
-  {
-    "id": 10614,
-    "problem_id": 10327,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10327.jpg"
-  },
-  {
-    "id": 10615,
-    "problem_id": 10328,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10328.jpg"
-  },
-  {
-    "id": 10616,
-    "problem_id": 10329,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10329.jpg"
-  },
-  {
-    "id": 10617,
-    "problem_id": 10330,
-    "problem": "<image>As shown in the diagram, points A, B, and C are all on circle O, and \u2220ACB = 35\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10330.jpg"
-  },
-  {
-    "id": 10618,
-    "problem_id": 10331,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u2220A+\u2220B=200\u00b0, the bisectors of \u2220ADC and \u2220DCB intersect at point O. What is the degree measure of \u2220COD? (). A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10331.jpg"
-  },
-  {
-    "id": 10619,
-    "problem_id": 10332,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u2220A+\u2220B=200\u00b0, the bisectors of \u2220ADC and \u2220DCB intersect at point O. What is the degree measure of \u2220COD? (). A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10332.jpg"
-  },
-  {
-    "id": 10620,
-    "problem_id": 10333,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u2220A+\u2220B=200\u00b0, the bisectors of \u2220ADC and \u2220DCB intersect at point O. What is the degree measure of \u2220COD? (). A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10333.jpg"
-  },
-  {
-    "id": 10621,
-    "problem_id": 10334,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u2220A+\u2220B=200\u00b0, the bisectors of \u2220ADC and \u2220DCB intersect at point O. What is the degree measure of \u2220COD? (). A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10334.jpg"
-  },
-  {
-    "id": 10622,
-    "problem_id": 10335,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u2220A+\u2220B=200\u00b0, the bisectors of \u2220ADC and \u2220DCB intersect at point O. What is the degree measure of \u2220COD? (). A, B, C, D choices are ['80\u00b0', '90\u00b0', '100\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10335.jpg"
-  },
-  {
-    "id": 10623,
-    "problem_id": 10336,
-    "problem": "<image>Given the triangle ABC as shown in the figure, where AD is the angle bisector of triangle ABC and BE is the altitude of triangle ABC. If \u2220C = 70\u00b0 and \u2220ABC = 48\u00b0, then what is the value of \u22203?. A, B, C, D choices are ['59\u00b0', '60\u00b0', '56\u00b0', '22\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10336.jpg"
-  },
-  {
-    "id": 10624,
-    "problem_id": 10337,
-    "problem": "<image>As shown in the diagram, DE is the perpendicular bisector of side AC in triangle ABC. If BC = 18cm and AB = 10cm, what is the perimeter of triangle ABD?. A, B, C, D choices are ['16cm', '18cm', '26cm', '28cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]\n\n**Reasoning:**\n\nSince DE is the perpendicular bisector of AC, D is the midpoint of AC, so DA = DC.\n\nGiven that BC = BD + DC = BD + DA = 18 cm.\n\nTherefore, the perimeter of triangle ABD is AB + BD + DA = 10 cm + 18 cm = 28 cm.</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10337.jpg"
-  },
-  {
-    "id": 10625,
-    "problem_id": 10338,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O, E is a point on the extension of CD. If \u2220ADE = 120\u00b0, then what is the measure of \u2220B?. A, B, C, D choices are ['130\u00b0', '120\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10338.jpg"
-  },
-  {
-    "id": 10626,
-    "problem_id": 10339,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O, E is a point on the extension of CD. If \u2220ADE = 120\u00b0, then what is the measure of \u2220B?. A, B, C, D choices are ['130\u00b0', '120\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10339.jpg"
-  },
-  {
-    "id": 10627,
-    "problem_id": 10340,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O, E is a point on the extension of CD. If \u2220ADE = 120\u00b0, then what is the measure of \u2220B?. A, B, C, D choices are ['130\u00b0', '120\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10340.jpg"
-  },
-  {
-    "id": 10628,
-    "problem_id": 10341,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is inscribed in circle O, E is a point on the extension of CD. If \u2220ADE = 120\u00b0, then what is the measure of \u2220B?. A, B, C, D choices are ['130\u00b0', '120\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10341.jpg"
-  },
-  {
-    "id": 10629,
-    "problem_id": 10342,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10342.jpg"
-  },
-  {
-    "id": 10630,
-    "problem_id": 10343,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10343.jpg"
-  },
-  {
-    "id": 10631,
-    "problem_id": 10344,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10344.jpg"
-  },
-  {
-    "id": 10632,
-    "problem_id": 10345,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10345.jpg"
-  },
-  {
-    "id": 10633,
-    "problem_id": 10346,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10346.jpg"
-  },
-  {
-    "id": 10634,
-    "problem_id": 10347,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10347.jpg"
-  },
-  {
-    "id": 10635,
-    "problem_id": 10348,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10348.jpg"
-  },
-  {
-    "id": 10636,
-    "problem_id": 10349,
-    "problem": "<image>In triangle ABC, BE and CF are the angle bisectors of angles ABC and ACB, respectively. If angle A measures 50 degrees, what is the measure of angle BDC? (). A, B, C, D choices are ['105\u00b0', '115\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10349.jpg"
-  },
-  {
-    "id": 10637,
-    "problem_id": 10350,
-    "problem": "<image>In triangle ABC, as shown in the figure, \u2220C=90\u00b0. Point D is on side BC, and DE\u2225AB. If \u2220CDE=150\u00b0, what is the degree measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '60\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10350.jpg"
-  },
-  {
-    "id": 10638,
-    "problem_id": 10351,
-    "problem": "<image>As shown in the figure, line m is parallel to line n, AB is perpendicular to line m, and \u2220ABC = 130\u00b0. Then, what is the value of \u2220\u0251? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10351.jpg"
-  },
-  {
-    "id": 10639,
-    "problem_id": 10352,
-    "problem": "<image>As shown in the figure, line m is parallel to line n, AB is perpendicular to line m, and \u2220ABC = 130\u00b0. Then, what is the value of \u2220\u0251? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10352.jpg"
-  },
-  {
-    "id": 10640,
-    "problem_id": 10353,
-    "problem": "<image>As shown in the figure, line m is parallel to line n, AB is perpendicular to line m, and \u2220ABC = 130\u00b0. Then, what is the value of \u2220\u0251? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10353.jpg"
-  },
-  {
-    "id": 10641,
-    "problem_id": 10354,
-    "problem": "<image>As shown in the figure, line m is parallel to line n, AB is perpendicular to line m, and \u2220ABC = 130\u00b0. Then, what is the value of \u2220\u0251? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10354.jpg"
-  },
-  {
-    "id": 10642,
-    "problem_id": 10355,
-    "problem": "<image>As shown in the figure, line m is parallel to line n, AB is perpendicular to line m, and \u2220ABC = 130\u00b0. Then, what is the value of \u2220\u0251? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10355.jpg"
-  },
-  {
-    "id": 10643,
-    "problem_id": 10356,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and a right triangle is placed as shown. If \u2220DCB=90\u00b0 and \u22202+\u2220B=70\u00b0, what is the degree measure of \u22201?. A, B, C, D choices are ['40\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10356.jpg"
-  },
-  {
-    "id": 10644,
-    "problem_id": 10357,
-    "problem": "<image>As shown in the figure, line segment AB is the diameter of circle O, chord CD is parallel to AB, and \u2220CAB=25\u00b0. Then, what is the measure of \u2220AOD? (). A, B, C, D choices are ['155\u00b0', '140\u00b0', '130\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10357.jpg"
-  },
-  {
-    "id": 10645,
-    "problem_id": 10358,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220OAB = 40\u00b0, then what is the measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10358.jpg"
-  },
-  {
-    "id": 10646,
-    "problem_id": 10359,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220OAB = 40\u00b0, then what is the measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10359.jpg"
-  },
-  {
-    "id": 10647,
-    "problem_id": 10360,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220OAB = 40\u00b0, then what is the measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10360.jpg"
-  },
-  {
-    "id": 10648,
-    "problem_id": 10361,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220OAB = 40\u00b0, then what is the measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10361.jpg"
-  },
-  {
-    "id": 10649,
-    "problem_id": 10362,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220OAB = 40\u00b0, then what is the measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10362.jpg"
-  },
-  {
-    "id": 10650,
-    "problem_id": 10363,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220OAB = 40\u00b0, then what is the measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10363.jpg"
-  },
-  {
-    "id": 10651,
-    "problem_id": 10364,
-    "problem": "<image>Line a is parallel to line b as shown in the figure. Ray DC intersects line a at point C. A line is drawn through point D perpendicular to line b at point E. It is known that \u22201=25\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['115\u00b0', '125\u00b0', '155\u00b0', '165\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10364.jpg"
-  },
-  {
-    "id": 10652,
-    "problem_id": 10365,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and \u22201 = 75\u00b0, \u22202 = 35\u00b0, what is the degree of \u22203? (). A, B, C, D choices are ['75\u00b0', '55\u00b0', '40\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10365.jpg"
-  },
-  {
-    "id": 10653,
-    "problem_id": 10366,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and \u22201 = 75\u00b0, \u22202 = 35\u00b0, what is the degree of \u22203? (). A, B, C, D choices are ['75\u00b0', '55\u00b0', '40\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10366.jpg"
-  },
-  {
-    "id": 10654,
-    "problem_id": 10367,
-    "problem": "<image>As shown in the figure, point P is outside the circle O. PA and PB are tangent to circle O at points A and B respectively, and \u2220P = 50\u00b0. Then, what is the measure of \u2220AOB? (). A, B, C, D choices are ['150\u00b0', '130\u00b0', '155\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10367.jpg"
-  },
-  {
-    "id": 10655,
-    "problem_id": 10368,
-    "problem": "<image>As shown in the figure, point P is outside the circle O. PA and PB are tangent to circle O at points A and B respectively, and \u2220P = 50\u00b0. Then, what is the measure of \u2220AOB? (). A, B, C, D choices are ['150\u00b0', '130\u00b0', '155\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10368.jpg"
-  },
-  {
-    "id": 10656,
-    "problem_id": 10369,
-    "problem": "<image>As shown in the figure, point P is outside the circle O. PA and PB are tangent to circle O at points A and B respectively, and \u2220P = 50\u00b0. Then, what is the measure of \u2220AOB? (). A, B, C, D choices are ['150\u00b0', '130\u00b0', '155\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10369.jpg"
-  },
-  {
-    "id": 10657,
-    "problem_id": 10370,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10370.jpg"
-  },
-  {
-    "id": 10658,
-    "problem_id": 10371,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10371.jpg"
-  },
-  {
-    "id": 10659,
-    "problem_id": 10372,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10372.jpg"
-  },
-  {
-    "id": 10660,
-    "problem_id": 10373,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10373.jpg"
-  },
-  {
-    "id": 10661,
-    "problem_id": 10374,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10374.jpg"
-  },
-  {
-    "id": 10662,
-    "problem_id": 10375,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10375.jpg"
-  },
-  {
-    "id": 10663,
-    "problem_id": 10376,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10376.jpg"
-  },
-  {
-    "id": 10664,
-    "problem_id": 10377,
-    "problem": "<image>As shown in the figure, points A and B are located at opposite ends of a pond. Xiao Cong wants to measure the distance between A and B with a rope, but the rope is not long enough. A classmate came up with an idea to help him: first, choose a point C on the ground that can directly reach A and B, then find the midpoints D and E of AC and BC, and measure the length of DE as 10m. The distance between A and B is () meters.. A, B, C, D choices are ['15m', '25m', '30m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10377.jpg"
-  },
-  {
-    "id": 10665,
-    "problem_id": 10378,
-    "problem": "<image>As shown in the diagram, the short arm OA of the railway crossing gate is 1m long, and the long arm OB is 8m long. When the outer end A of the short arm drops by 0.5m, how much does the outer end B of the long arm rise?. A, B, C, D choices are ['2m', '4m', '4.5m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10378.jpg"
-  },
-  {
-    "id": 10666,
-    "problem_id": 10379,
-    "problem": "<image>As shown in the diagram, the short arm OA of the railway crossing gate is 1m long, and the long arm OB is 8m long. When the outer end A of the short arm drops by 0.5m, how much does the outer end B of the long arm rise?. A, B, C, D choices are ['2m', '4m', '4.5m', '8m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10379.jpg"
-  },
-  {
-    "id": 10667,
-    "problem_id": 10380,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220ABC=70\u00b0, then what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10380.jpg"
-  },
-  {
-    "id": 10669,
-    "problem_id": 10381,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, and C and D are two points on circle O. If \u2220ABC=70\u00b0, then what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10381.jpg"
-  },
-  {
-    "id": 10670,
-    "problem_id": 10382,
-    "problem": "<image>In triangle ABC shown below, D and E are the midpoints of AB and AC respectively, and \u2220B = 30\u00b0. If triangle ADE is folded along DE and point A lands on point A' in the same plane as the triangle, what is the degree measurement of \u2220BDA'?. A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10382.jpg"
-  },
-  {
-    "id": 10671,
-    "problem_id": 10383,
-    "problem": "<image>In triangle ABC as shown in the figure, AB=AD=DC, \u2220B=70\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['35\u00b0', '40\u00b0', '45\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10383.jpg"
-  },
-  {
-    "id": 10672,
-    "problem_id": 10384,
-    "problem": "<image>As shown in the figure, the two vertices of a right triangle board with a 30\u00b0 angle are placed on a pair of opposite sides of a rectangular ruler. If \u22202 = 60\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['22.5\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10384.jpg"
-  },
-  {
-    "id": 10673,
-    "problem_id": 10385,
-    "problem": "<image>If a right isosceles triangle and a ruler are placed as shown in the figure, and \u22201 = 60\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['85\u00b0', '75\u00b0', '60\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10385.jpg"
-  },
-  {
-    "id": 10674,
-    "problem_id": 10386,
-    "problem": "<image>If a right isosceles triangle and a ruler are placed as shown in the figure, and \u22201 = 60\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['85\u00b0', '75\u00b0', '60\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10386.jpg"
-  },
-  {
-    "id": 10676,
-    "problem_id": 10387,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201=60\u00b0, \u22202=40\u00b0, then \u22203 is equal to (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10387.jpg"
-  },
-  {
-    "id": 10677,
-    "problem_id": 10388,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201=60\u00b0, \u22202=40\u00b0, then \u22203 is equal to (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10388.jpg"
-  },
-  {
-    "id": 10678,
-    "problem_id": 10389,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201=60\u00b0, \u22202=40\u00b0, then \u22203 is equal to (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10389.jpg"
-  },
-  {
-    "id": 10679,
-    "problem_id": 10390,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201=60\u00b0, \u22202=40\u00b0, then \u22203 is equal to (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10390.jpg"
-  },
-  {
-    "id": 10680,
-    "problem_id": 10391,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201=60\u00b0, \u22202=40\u00b0, then \u22203 is equal to (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10391.jpg"
-  },
-  {
-    "id": 10681,
-    "problem_id": 10392,
-    "problem": "<image>As shown in the figure, PA and PB are tangents of circle O, and points A and B are the points of tangency. AC is the diameter of circle O. Given that \u2220P=40\u00b0, what is the measure of \u2220ACB?. A, B, C, D choices are ['60\u00b0', '65\u00b0', '70\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10392.jpg"
-  },
-  {
-    "id": 10683,
-    "problem_id": 10393,
-    "problem": "<image>As shown in the figure, AB and CD are both chords of circle O, and AB is perpendicular to CD. If \u2220CDB = 62\u00b0, what is the measure of \u2220ACD? (). A, B, C, D choices are ['28\u00b0', '31\u00b0', '38\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10393.jpg"
-  },
-  {
-    "id": 10684,
-    "problem_id": 10394,
-    "problem": "<image>In triangle ABC, where angle A is 90\u00b0, point D is on side AC, and DE is parallel to BC. If angle 1 is 155\u00b0, what is the degree of angle B?. A, B, C, D choices are ['45\u00b0', '55\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10394.jpg"
-  },
-  {
-    "id": 10685,
-    "problem_id": 10395,
-    "problem": "<image>In triangle ABC, where angle A is 90\u00b0, point D is on side AC, and DE is parallel to BC. If angle 1 is 155\u00b0, what is the degree of angle B?. A, B, C, D choices are ['45\u00b0', '55\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10395.jpg"
-  },
-  {
-    "id": 10686,
-    "problem_id": 10396,
-    "problem": "<image>As shown in the figure, AB is parallel to CD. The line EF intersects AB and CD at points E and F, respectively. If \u2220AEF = 40\u00b0, then what is the measure of \u2220EFD? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10396.jpg"
-  },
-  {
-    "id": 10687,
-    "problem_id": 10397,
-    "problem": "<image>As shown in the figure, AB is parallel to CD. The line EF intersects AB and CD at points E and F, respectively. If \u2220AEF = 40\u00b0, then what is the measure of \u2220EFD? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10397.jpg"
-  },
-  {
-    "id": 10688,
-    "problem_id": 10398,
-    "problem": "<image>As shown in the figure, AB is parallel to CD. The line EF intersects AB and CD at points E and F, respectively. If \u2220AEF = 40\u00b0, then what is the measure of \u2220EFD? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10398.jpg"
-  },
-  {
-    "id": 10689,
-    "problem_id": 10399,
-    "problem": "<image>As shown in the diagram, AB is a chord of circle O. If C is a point on circle O and \u2220C=60\u00b0, then \u2220OBA is equal to (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10399.jpg"
-  },
-  {
-    "id": 10690,
-    "problem_id": 10400,
-    "problem": "<image>As shown in the diagram, AB is a chord of circle O. If C is a point on circle O and \u2220C=60\u00b0, then \u2220OBA is equal to (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10400.jpg"
-  },
-  {
-    "id": 10691,
-    "problem_id": 10401,
-    "problem": "<image>As shown in the diagram, AB is a chord of circle O. If C is a point on circle O and \u2220C=60\u00b0, then \u2220OBA is equal to (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10401.jpg"
-  },
-  {
-    "id": 10692,
-    "problem_id": 10402,
-    "problem": "<image>As shown in the diagram, AB is a chord of circle O. If C is a point on circle O and \u2220C=60\u00b0, then \u2220OBA is equal to (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10402.jpg"
-  },
-  {
-    "id": 10693,
-    "problem_id": 10403,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10403.jpg"
-  },
-  {
-    "id": 10694,
-    "problem_id": 10404,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10404.jpg"
-  },
-  {
-    "id": 10695,
-    "problem_id": 10405,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10405.jpg"
-  },
-  {
-    "id": 10696,
-    "problem_id": 10406,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10406.jpg"
-  },
-  {
-    "id": 10697,
-    "problem_id": 10407,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10407.jpg"
-  },
-  {
-    "id": 10698,
-    "problem_id": 10408,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10408.jpg"
-  },
-  {
-    "id": 10699,
-    "problem_id": 10409,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10409.jpg"
-  },
-  {
-    "id": 10700,
-    "problem_id": 10410,
-    "problem": "<image>As shown in the figure, the length of the generatrix of a cone-shaped mold is 10, and the radius of its base is 5. What is the lateral area of this cone-shaped mold? (). A, B, C, D choices are ['10\u03c0', '50\u03c0', '100\u03c0', '150\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10410.jpg"
-  },
-  {
-    "id": 10701,
-    "problem_id": 10411,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, and the line EF intersects AB and CD at points E and F respectively. EG bisects \u2220BEF and intersects CD at point G. If \u22201=50\u00b0, what is the degree of \u22202?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '60\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10411.jpg"
-  },
-  {
-    "id": 10702,
-    "problem_id": 10412,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, and the line EF intersects AB and CD at points E and F respectively. EG bisects \u2220BEF and intersects CD at point G. If \u22201=50\u00b0, what is the degree of \u22202?. A, B, C, D choices are ['50\u00b0', '65\u00b0', '60\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10412.jpg"
-  },
-  {
-    "id": 10704,
-    "problem_id": 10413,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10413.jpg"
-  },
-  {
-    "id": 10705,
-    "problem_id": 10414,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10414.jpg"
-  },
-  {
-    "id": 10706,
-    "problem_id": 10415,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10415.jpg"
-  },
-  {
-    "id": 10707,
-    "problem_id": 10416,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10416.jpg"
-  },
-  {
-    "id": 10708,
-    "problem_id": 10417,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10417.jpg"
-  },
-  {
-    "id": 10709,
-    "problem_id": 10418,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10418.jpg"
-  },
-  {
-    "id": 10710,
-    "problem_id": 10419,
-    "problem": "<image>In triangle ABC as shown, with \u2220B=40\u00b0 and \u2220C=30\u00b0, extend BA to point D. What is the measure of \u2220CAD? (). A, B, C, D choices are ['110\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10419.jpg"
-  },
-  {
-    "id": 10711,
-    "problem_id": 10420,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10420.jpg"
-  },
-  {
-    "id": 10712,
-    "problem_id": 10421,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10421.jpg"
-  },
-  {
-    "id": 10713,
-    "problem_id": 10422,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10422.jpg"
-  },
-  {
-    "id": 10714,
-    "problem_id": 10423,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10423.jpg"
-  },
-  {
-    "id": 10715,
-    "problem_id": 10424,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10424.jpg"
-  },
-  {
-    "id": 10716,
-    "problem_id": 10425,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10425.jpg"
-  },
-  {
-    "id": 10717,
-    "problem_id": 10426,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10426.jpg"
-  },
-  {
-    "id": 10718,
-    "problem_id": 10427,
-    "problem": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB? (). A, B, C, D choices are ['3cm', '4cm', '6cm', '8cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10427.jpg"
-  },
-  {
-    "id": 10720,
-    "problem_id": 10428,
-    "problem": "<image>As shown in the figure, BC is perpendicular to AE at point C, CD is parallel to AB, \u2220B = 40\u00b0, then the degree measure of \u2220ECD is ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10428.jpg"
-  },
-  {
-    "id": 10721,
-    "problem_id": 10429,
-    "problem": "<image>As shown in the figure, BC is perpendicular to AE at point C, CD is parallel to AB, \u2220B = 40\u00b0, then the degree measure of \u2220ECD is ().. A, B, C, D choices are ['70\u00b0', '60\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10429.jpg"
-  },
-  {
-    "id": 10722,
-    "problem_id": 10430,
-    "problem": "<image>(3 points) As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220A=70\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10430.jpg"
-  },
-  {
-    "id": 10723,
-    "problem_id": 10431,
-    "problem": "<image>(3 points) As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220A=70\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10431.jpg"
-  },
-  {
-    "id": 10724,
-    "problem_id": 10432,
-    "problem": "<image>(3 points) As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220A=70\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10432.jpg"
-  },
-  {
-    "id": 10725,
-    "problem_id": 10433,
-    "problem": "<image>(3 points) As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220A=70\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10433.jpg"
-  },
-  {
-    "id": 10726,
-    "problem_id": 10434,
-    "problem": "<image>(3 points) As shown in the diagram, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220A=70\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['100\u00b0', '110\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10434.jpg"
-  },
-  {
-    "id": 10727,
-    "problem_id": 10435,
-    "problem": "<image>In triangle ABC as shown, AB=AC, BD bisects angle ABC and intersects AC at point D, AE is parallel to BD and intersects the extension of CB at point E. If angle E is 35 degrees, what is the degree measure of angle BAC? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10435.jpg"
-  },
-  {
-    "id": 10728,
-    "problem_id": 10436,
-    "problem": "<image>In triangle ABC as shown, AB=AC, BD bisects angle ABC and intersects AC at point D, AE is parallel to BD and intersects the extension of CB at point E. If angle E is 35 degrees, what is the degree measure of angle BAC? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10436.jpg"
-  },
-  {
-    "id": 10729,
-    "problem_id": 10437,
-    "problem": "<image>In triangle ABC as shown, AB=AC, BD bisects angle ABC and intersects AC at point D, AE is parallel to BD and intersects the extension of CB at point E. If angle E is 35 degrees, what is the degree measure of angle BAC? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10437.jpg"
-  },
-  {
-    "id": 10730,
-    "problem_id": 10438,
-    "problem": "<image>In triangle ABC as shown, AB=AC, BD bisects angle ABC and intersects AC at point D, AE is parallel to BD and intersects the extension of CB at point E. If angle E is 35 degrees, what is the degree measure of angle BAC? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10438.jpg"
-  },
-  {
-    "id": 10731,
-    "problem_id": 10439,
-    "problem": "<image>In triangle ABC as shown, AB=AC, BD bisects angle ABC and intersects AC at point D, AE is parallel to BD and intersects the extension of CB at point E. If angle E is 35 degrees, what is the degree measure of angle BAC? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10439.jpg"
-  },
-  {
-    "id": 10733,
-    "problem_id": 10440,
-    "problem": "<image>As shown in the figure, square OABC is rotated counterclockwise around point O by 40 degrees to obtain square ODEF. If AF is connected, what is the degree of angle OFA? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10440.jpg"
-  },
-  {
-    "id": 10734,
-    "problem_id": 10441,
-    "problem": "<image>As shown in the figure, square OABC is rotated counterclockwise around point O by 40 degrees to obtain square ODEF. If AF is connected, what is the degree of angle OFA? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10441.jpg"
-  },
-  {
-    "id": 10735,
-    "problem_id": 10442,
-    "problem": "<image>As shown in the diagram, OA is the radius of circle O, chord BC is perpendicular to OA, and D is a point on circle O. If \u2220ADC = 26\u00b0, what is the degree measure of \u2220AOB? (). A, B, C, D choices are ['13\u00b0', '26\u00b0', '52\u00b0', '78\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10442.jpg"
-  },
-  {
-    "id": 10736,
-    "problem_id": 10443,
-    "problem": "<image>Given a quadrilateral ABCD as shown in the figure, with midpoints E, F, G, and H on its sides. If the lengths of the diagonals AC and BD are both 20 cm, what is the perimeter of quadrilateral EFGH?. A, B, C, D choices are ['80cm', '40cm', '20cm', '10cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10443.jpg"
-  },
-  {
-    "id": 10740,
-    "problem_id": 10444,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10444.jpg"
-  },
-  {
-    "id": 10741,
-    "problem_id": 10445,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10445.jpg"
-  },
-  {
-    "id": 10742,
-    "problem_id": 10446,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10446.jpg"
-  },
-  {
-    "id": 10743,
-    "problem_id": 10447,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10447.jpg"
-  },
-  {
-    "id": 10744,
-    "problem_id": 10448,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10448.jpg"
-  },
-  {
-    "id": 10745,
-    "problem_id": 10449,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10449.jpg"
-  },
-  {
-    "id": 10746,
-    "problem_id": 10450,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10450.jpg"
-  },
-  {
-    "id": 10747,
-    "problem_id": 10451,
-    "problem": "<image>In triangle ABC as shown in the figure, angle A is 40\u00b0. Point D is a point on the extension of side BC, and angle CBD is 120\u00b0. What is the measure of angle C?. A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10451.jpg"
-  },
-  {
-    "id": 10748,
-    "problem_id": 10452,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10452.jpg"
-  },
-  {
-    "id": 10749,
-    "problem_id": 10453,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10453.jpg"
-  },
-  {
-    "id": 10750,
-    "problem_id": 10454,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10454.jpg"
-  },
-  {
-    "id": 10751,
-    "problem_id": 10455,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10455.jpg"
-  },
-  {
-    "id": 10752,
-    "problem_id": 10456,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10456.jpg"
-  },
-  {
-    "id": 10753,
-    "problem_id": 10457,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10457.jpg"
-  },
-  {
-    "id": 10754,
-    "problem_id": 10458,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10458.jpg"
-  },
-  {
-    "id": 10755,
-    "problem_id": 10459,
-    "problem": "<image>As shown in the figure, \u22201 + \u2220B = 180\u00b0, \u22202 = 45\u00b0, what is the degree of \u2220D?. A, B, C, D choices are ['25\u00b0', '45\u00b0', '50\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10459.jpg"
-  },
-  {
-    "id": 10756,
-    "problem_id": 10460,
-    "problem": "<image>As shown in the figure, it is known that line AB is parallel to CD, and line EF intersects AB and CD at points M and N respectively. NH is the angle bisector of \u2220MND. If \u2220AMN=56\u00b0, then the degree measure of \u2220MNH is (). A, B, C, D choices are ['28\u00b0', '30\u00b0', '34\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10460.jpg"
-  },
-  {
-    "id": 10757,
-    "problem_id": 10461,
-    "problem": "<image>As shown in the figure, it is known that line AB is parallel to CD, and line EF intersects AB and CD at points M and N respectively. NH is the angle bisector of \u2220MND. If \u2220AMN=56\u00b0, then the degree measure of \u2220MNH is (). A, B, C, D choices are ['28\u00b0', '30\u00b0', '34\u00b0', '56\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10461.jpg"
-  },
-  {
-    "id": 10758,
-    "problem_id": 10462,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and \u2220A=50\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['50\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10462.jpg"
-  },
-  {
-    "id": 10759,
-    "problem_id": 10463,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and \u2220A=50\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['50\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10463.jpg"
-  },
-  {
-    "id": 10760,
-    "problem_id": 10464,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and \u2220A=50\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['50\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10464.jpg"
-  },
-  {
-    "id": 10761,
-    "problem_id": 10465,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, and \u2220A=50\u00b0, then what is the size of \u22201? (). A, B, C, D choices are ['50\u00b0', '120\u00b0', '130\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{A}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10465.jpg"
-  },
-  {
-    "id": 10764,
-    "problem_id": 10466,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10466.jpg"
-  },
-  {
-    "id": 10765,
-    "problem_id": 10467,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10467.jpg"
-  },
-  {
-    "id": 10766,
-    "problem_id": 10468,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10468.jpg"
-  },
-  {
-    "id": 10767,
-    "problem_id": 10469,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10469.jpg"
-  },
-  {
-    "id": 10768,
-    "problem_id": 10470,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10470.jpg"
-  },
-  {
-    "id": 10769,
-    "problem_id": 10471,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10471.jpg"
-  },
-  {
-    "id": 10770,
-    "problem_id": 10472,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10472.jpg"
-  },
-  {
-    "id": 10771,
-    "problem_id": 10473,
-    "problem": "<image>As shown in the figure, there is a wooden box with dimensions of length, width, and height of 12cm, 4cm, and 3cm respectively. A thin wooden stick (the thickness of the stick is negligible) is placed inside the box, and it is required that the stick cannot protrude from the box. Please calculate the maximum length of the thin wooden stick that can be placed inside the box.. A, B, C, D choices are ['13cm', '14cm', '15cm', '16cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10473.jpg"
-  },
-  {
-    "id": 10772,
-    "problem_id": 10474,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10474.jpg"
-  },
-  {
-    "id": 10773,
-    "problem_id": 10475,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10475.jpg"
-  },
-  {
-    "id": 10774,
-    "problem_id": 10476,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10476.jpg"
-  },
-  {
-    "id": 10775,
-    "problem_id": 10477,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10477.jpg"
-  },
-  {
-    "id": 10776,
-    "problem_id": 10478,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10478.jpg"
-  },
-  {
-    "id": 10777,
-    "problem_id": 10479,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10479.jpg"
-  },
-  {
-    "id": 10778,
-    "problem_id": 10480,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220OBC = 42\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['42\u00b0', '48\u00b0', '52\u00b0', '58\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10480.jpg"
-  },
-  {
-    "id": 10779,
-    "problem_id": 10481,
-    "problem": "<image>Given the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If angle B is 70 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['110\u00b0', '90\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10481.jpg"
-  },
-  {
-    "id": 10780,
-    "problem_id": 10482,
-    "problem": "<image>Given the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If angle B is 70 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['110\u00b0', '90\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10482.jpg"
-  },
-  {
-    "id": 10781,
-    "problem_id": 10483,
-    "problem": "<image>Given the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If angle B is 70 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['110\u00b0', '90\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10483.jpg"
-  },
-  {
-    "id": 10782,
-    "problem_id": 10484,
-    "problem": "<image>Given the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If angle B is 70 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['110\u00b0', '90\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10484.jpg"
-  },
-  {
-    "id": 10783,
-    "problem_id": 10485,
-    "problem": "<image>Given the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If angle B is 70 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['110\u00b0', '90\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10485.jpg"
-  },
-  {
-    "id": 10784,
-    "problem_id": 10486,
-    "problem": "<image>Given the diagram, AB is the diameter of circle O, arc BC is equal to arc BD, and \u2220A = 25\u00b0. What is the degree measure of \u2220BOD? (). A, B, C, D choices are ['25\u00b0', '50\u00b0', '12.5\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10486.jpg"
-  },
-  {
-    "id": 10785,
-    "problem_id": 10487,
-    "problem": "<image>Given the diagram, AB is the diameter of circle O, arc BC is equal to arc BD, and \u2220A = 25\u00b0. What is the degree measure of \u2220BOD? (). A, B, C, D choices are ['25\u00b0', '50\u00b0', '12.5\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10487.jpg"
-  },
-  {
-    "id": 10786,
-    "problem_id": 10488,
-    "problem": "<image>As shown in the diagram, line a and b intersect with line c and d. It is known that \u22201 = \u22202 and \u22203 = 110\u00b0. Find the degree measure of \u22204.. A, B, C, D choices are ['70\u00b0', '80\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10488.jpg"
-  },
-  {
-    "id": 10787,
-    "problem_id": 10489,
-    "problem": "<image>As shown in the diagram, line a and b intersect with line c and d. It is known that \u22201 = \u22202 and \u22203 = 110\u00b0. Find the degree measure of \u22204.. A, B, C, D choices are ['70\u00b0', '80\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10489.jpg"
-  },
-  {
-    "id": 10788,
-    "problem_id": 10490,
-    "problem": "<image>As shown in the diagram, line a and b intersect with line c and d. It is known that \u22201 = \u22202 and \u22203 = 110\u00b0. Find the degree measure of \u22204.. A, B, C, D choices are ['70\u00b0', '80\u00b0', '110\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10490.jpg"
-  },
-  {
-    "id": 10789,
-    "problem_id": 10491,
-    "problem": "<image>As shown in the figure, the three vertices of triangle ABD are on circle O, AB is the diameter, point C is on circle O, and \u2220ABD=52\u00b0. Then, \u2220BCD is equal to (). A, B, C, D choices are ['32\u00b0', '38\u00b0', '52\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10491.jpg"
-  },
-  {
-    "id": 10790,
-    "problem_id": 10492,
-    "problem": "<image>As shown in the figure, line AB is parallel to CD. A right triangle board EFG (\u2220E=60\u00b0) with a 60\u00b0 angle and a right vertex F is on line AB, and the hypotenuse EG intersects AB at point H, and CD intersects FG at point M. If \u2220AHG=50\u00b0, then \u2220FMD is equal to ().. A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10492.jpg"
-  },
-  {
-    "id": 10791,
-    "problem_id": 10493,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220A = 72\u00b0. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['15\u00b0', '18\u00b0', '20\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10493.jpg"
-  },
-  {
-    "id": 10792,
-    "problem_id": 10494,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220A = 72\u00b0. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['15\u00b0', '18\u00b0', '20\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10494.jpg"
-  },
-  {
-    "id": 10793,
-    "problem_id": 10495,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220A = 72\u00b0. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['15\u00b0', '18\u00b0', '20\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10495.jpg"
-  },
-  {
-    "id": 10794,
-    "problem_id": 10496,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220A = 72\u00b0. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['15\u00b0', '18\u00b0', '20\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10496.jpg"
-  },
-  {
-    "id": 10795,
-    "problem_id": 10497,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220A = 72\u00b0. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['15\u00b0', '18\u00b0', '20\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10497.jpg"
-  },
-  {
-    "id": 10796,
-    "problem_id": 10498,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220A = 72\u00b0. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['15\u00b0', '18\u00b0', '20\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10498.jpg"
-  },
-  {
-    "id": 10797,
-    "problem_id": 10499,
-    "problem": "<image>In triangle ABC shown in the diagram, AB = AC, BD bisects angle ABC, angle A = 36 degrees, then the degree measure of angle 1 is (). A, B, C, D choices are ['36\u00b0', '60\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10499.jpg"
-  },
-  {
-    "id": 10798,
-    "problem_id": 10500,
-    "problem": "<image>In triangle ABC shown in the diagram, AB = AC, BD bisects angle ABC, angle A = 36 degrees, then the degree measure of angle 1 is (). A, B, C, D choices are ['36\u00b0', '60\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10500.jpg"
-  },
-  {
-    "id": 10799,
-    "problem_id": 10501,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The vertex B of the right triangle ABC lies on line a and angle C measures 90 degrees. If angle beta measures 55 degrees, what is the degree measure of angle alpha? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '35\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10501.jpg"
-  },
-  {
-    "id": 10800,
-    "problem_id": 10502,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The vertex B of the right triangle ABC lies on line a and angle C measures 90 degrees. If angle beta measures 55 degrees, what is the degree measure of angle alpha? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '35\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10502.jpg"
-  },
-  {
-    "id": 10801,
-    "problem_id": 10503,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The vertex B of the right triangle ABC lies on line a and angle C measures 90 degrees. If angle beta measures 55 degrees, what is the degree measure of angle alpha? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '35\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10503.jpg"
-  },
-  {
-    "id": 10802,
-    "problem_id": 10504,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. The vertex B of the right triangle ABC lies on line a and angle C measures 90 degrees. If angle beta measures 55 degrees, what is the degree measure of angle alpha? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '35\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10504.jpg"
-  },
-  {
-    "id": 10803,
-    "problem_id": 10505,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10505.jpg"
-  },
-  {
-    "id": 10804,
-    "problem_id": 10506,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10506.jpg"
-  },
-  {
-    "id": 10805,
-    "problem_id": 10507,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10507.jpg"
-  },
-  {
-    "id": 10806,
-    "problem_id": 10508,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10508.jpg"
-  },
-  {
-    "id": 10807,
-    "problem_id": 10509,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10509.jpg"
-  },
-  {
-    "id": 10808,
-    "problem_id": 10510,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10510.jpg"
-  },
-  {
-    "id": 10809,
-    "problem_id": 10511,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10511.jpg"
-  },
-  {
-    "id": 10811,
-    "problem_id": 10512,
-    "problem": "<image>Given that AB\u2225CD, \u2220A=46\u00b0, and \u2220C=27\u00b0, what is the measure of \u2220AEC?. A, B, C, D choices are ['19\u00b0', '29\u00b0', '63\u00b0', '73\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10512.jpg"
-  },
-  {
-    "id": 10812,
-    "problem_id": 10513,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point E is on segment BC, if \u22201=40\u00b0, \u22202=30\u00b0, then what is the degree measure of \u22203? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '55\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10513.jpg"
-  },
-  {
-    "id": 10813,
-    "problem_id": 10514,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, point E is on segment BC, if \u22201=40\u00b0, \u22202=30\u00b0, then what is the degree measure of \u22203? (). A, B, C, D choices are ['70\u00b0', '60\u00b0', '55\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10514.jpg"
-  },
-  {
-    "id": 10814,
-    "problem_id": 10515,
-    "problem": "<image>Given AB\u2225CD in the diagram, if \u2220A=25\u00b0 and \u2220E=40\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '65\u00b0', '115\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10515.jpg"
-  },
-  {
-    "id": 10815,
-    "problem_id": 10516,
-    "problem": "<image>Given AB\u2225CD in the diagram, if \u2220A=25\u00b0 and \u2220E=40\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '65\u00b0', '115\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10516.jpg"
-  },
-  {
-    "id": 10816,
-    "problem_id": 10517,
-    "problem": "<image>Given AB\u2225CD in the diagram, if \u2220A=25\u00b0 and \u2220E=40\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '65\u00b0', '115\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10517.jpg"
-  },
-  {
-    "id": 10817,
-    "problem_id": 10518,
-    "problem": "<image>Given AB\u2225CD in the diagram, if \u2220A=25\u00b0 and \u2220E=40\u00b0, what is the measure of \u2220C? (). A, B, C, D choices are ['40\u00b0', '65\u00b0', '115\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10518.jpg"
-  },
-  {
-    "id": 10818,
-    "problem_id": 10519,
-    "problem": "<image>(3 points) As shown in the figure, it is known that the line AB is parallel to CD, and the line EF intersects AB and CD at points N and M. Line MG bisects angle EMD. If angle BNE is 30 degrees, then what is the measure of angle EMG?. A, B, C, D choices are ['15\u00b0', '30\u00b0', '75\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10519.jpg"
-  },
-  {
-    "id": 10819,
-    "problem_id": 10520,
-    "problem": "<image>(3 points) As shown in the figure, it is known that the line AB is parallel to CD, and the line EF intersects AB and CD at points N and M. Line MG bisects angle EMD. If angle BNE is 30 degrees, then what is the measure of angle EMG?. A, B, C, D choices are ['15\u00b0', '30\u00b0', '75\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10520.jpg"
-  },
-  {
-    "id": 10820,
-    "problem_id": 10521,
-    "problem": "<image>(3 points) As shown in the figure, it is known that the line AB is parallel to CD, and the line EF intersects AB and CD at points N and M. Line MG bisects angle EMD. If angle BNE is 30 degrees, then what is the measure of angle EMG?. A, B, C, D choices are ['15\u00b0', '30\u00b0', '75\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10521.jpg"
-  },
-  {
-    "id": 10821,
-    "problem_id": 10522,
-    "problem": "<image>(3 points) As shown in the figure, it is known that the line AB is parallel to CD, and the line EF intersects AB and CD at points N and M. Line MG bisects angle EMD. If angle BNE is 30 degrees, then what is the measure of angle EMG?. A, B, C, D choices are ['15\u00b0', '30\u00b0', '75\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10522.jpg"
-  },
-  {
-    "id": 10822,
-    "problem_id": 10523,
-    "problem": "<image>In triangle ABC as shown in the figure, D is a point on the extension of BC, \u2220B=40\u00b0, \u2220ACD=120\u00b0, then the measure of \u2220A is (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10523.jpg"
-  },
-  {
-    "id": 10823,
-    "problem_id": 10524,
-    "problem": "<image>In triangle ABC as shown in the figure, D is a point on the extension of BC, \u2220B=40\u00b0, \u2220ACD=120\u00b0, then the measure of \u2220A is (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10524.jpg"
-  },
-  {
-    "id": 10824,
-    "problem_id": 10525,
-    "problem": "<image>In triangle ABC as shown in the figure, D is a point on the extension of BC, \u2220B=40\u00b0, \u2220ACD=120\u00b0, then the measure of \u2220A is (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10525.jpg"
-  },
-  {
-    "id": 10825,
-    "problem_id": 10526,
-    "problem": "<image>In triangle ABC as shown in the figure, D is a point on the extension of BC, \u2220B=40\u00b0, \u2220ACD=120\u00b0, then the measure of \u2220A is (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10526.jpg"
-  },
-  {
-    "id": 10826,
-    "problem_id": 10527,
-    "problem": "<image>In triangle ABC as shown in the figure, D is a point on the extension of BC, \u2220B=40\u00b0, \u2220ACD=120\u00b0, then the measure of \u2220A is (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10527.jpg"
-  },
-  {
-    "id": 10827,
-    "problem_id": 10528,
-    "problem": "<image>In triangle ABC as shown in the figure, D is a point on the extension of BC, \u2220B=40\u00b0, \u2220ACD=120\u00b0, then the measure of \u2220A is (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '70\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10528.jpg"
-  },
-  {
-    "id": 10828,
-    "problem_id": 10529,
-    "problem": "<image>As shown in the figure, if \u2220AOB = 100\u00b0, then the sum of \u2220A and \u2220B is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10529.jpg"
-  },
-  {
-    "id": 10829,
-    "problem_id": 10530,
-    "problem": "<image>As shown in the figure, if \u2220AOB = 100\u00b0, then the sum of \u2220A and \u2220B is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10530.jpg"
-  },
-  {
-    "id": 10831,
-    "problem_id": 10531,
-    "problem": "<image>As shown in the figure, if \u2220AOB = 100\u00b0, then the sum of \u2220A and \u2220B is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10531.jpg"
-  },
-  {
-    "id": 10832,
-    "problem_id": 10532,
-    "problem": "<image>As shown in the figure, if \u2220AOB = 100\u00b0, then the sum of \u2220A and \u2220B is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10532.jpg"
-  },
-  {
-    "id": 10833,
-    "problem_id": 10533,
-    "problem": "<image>As shown in the figure, if \u2220AOB = 100\u00b0, then the sum of \u2220A and \u2220B is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10533.jpg"
-  },
-  {
-    "id": 10834,
-    "problem_id": 10534,
-    "problem": "<image>As shown in the figure, if \u2220AOB = 100\u00b0, then the sum of \u2220A and \u2220B is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10534.jpg"
-  },
-  {
-    "id": 10835,
-    "problem_id": 10535,
-    "problem": "<image>In the diagram, in \u2299O, if \u2220AOB=45\u00b0, then \u2220C is (). A, B, C, D choices are ['22.5\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10535.jpg"
-  },
-  {
-    "id": 10836,
-    "problem_id": 10536,
-    "problem": "<image>In the diagram, in \u2299O, if \u2220AOB=45\u00b0, then \u2220C is (). A, B, C, D choices are ['22.5\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10536.jpg"
-  },
-  {
-    "id": 10837,
-    "problem_id": 10537,
-    "problem": "<image>In the diagram, in \u2299O, if \u2220AOB=45\u00b0, then \u2220C is (). A, B, C, D choices are ['22.5\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10537.jpg"
-  },
-  {
-    "id": 10838,
-    "problem_id": 10538,
-    "problem": "<image>In the diagram, in \u2299O, if \u2220AOB=45\u00b0, then \u2220C is (). A, B, C, D choices are ['22.5\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10538.jpg"
-  },
-  {
-    "id": 10839,
-    "problem_id": 10539,
-    "problem": "<image>In the diagram, in \u2299O, if \u2220AOB=45\u00b0, then \u2220C is (). A, B, C, D choices are ['22.5\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10539.jpg"
-  },
-  {
-    "id": 10840,
-    "problem_id": 10540,
-    "problem": "<image>In the diagram, in \u2299O, if \u2220AOB=45\u00b0, then \u2220C is (). A, B, C, D choices are ['22.5\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10540.jpg"
-  },
-  {
-    "id": 10841,
-    "problem_id": 10541,
-    "problem": "<image>As shown in the figure, it is known that line AB is parallel to CD, and the bisector EF of angle BEG intersects CD at point F. If \u22201 is 42\u00b0, then the measure of \u22202 is (). A, B, C, D choices are ['159\u00b0', '148\u00b0', '142\u00b0', '138\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10541.jpg"
-  },
-  {
-    "id": 10842,
-    "problem_id": 10542,
-    "problem": "<image>As shown in the figure, line AB is parallel to line CD, and line EF intersects AB and CD at points E and F, respectively. If \u2220AEF = 50\u00b0, then what is the size of \u2220EFC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10542.jpg"
-  },
-  {
-    "id": 10843,
-    "problem_id": 10543,
-    "problem": "<image>As shown in the figure, line AB is parallel to line CD, and line EF intersects AB and CD at points E and F, respectively. If \u2220AEF = 50\u00b0, then what is the size of \u2220EFC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10543.jpg"
-  },
-  {
-    "id": 10844,
-    "problem_id": 10544,
-    "problem": "<image>As shown in the figure, line AB is parallel to line CD, and line EF intersects AB and CD at points E and F, respectively. If \u2220AEF = 50\u00b0, then what is the size of \u2220EFC? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '120\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10544.jpg"
-  },
-  {
-    "id": 10845,
-    "problem_id": 10545,
-    "problem": "<image>As shown in the figure, line m is parallel to line n. One acute vertex C of triangle ABC with a 45\u00b0 angle is placed on line n. Then, the sum of \u22201 and \u22202 is (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10545.jpg"
-  },
-  {
-    "id": 10846,
-    "problem_id": 10546,
-    "problem": "<image>As shown in the figure, line m is parallel to line n. One acute vertex C of triangle ABC with a 45\u00b0 angle is placed on line n. Then, the sum of \u22201 and \u22202 is (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10546.jpg"
-  },
-  {
-    "id": 10847,
-    "problem_id": 10547,
-    "problem": "<image>Given that l\u2225m and an equilateral triangle ABC, where vertex B is on line m and \u22201 = 20\u00b0, what is the degree measure of \u22202?. A, B, C, D choices are ['60\u00b0', '45\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10547.jpg"
-  },
-  {
-    "id": 10848,
-    "problem_id": 10548,
-    "problem": "<image>As shown in the figure, OA = OB = 6cm. Segment OB rotates counterclockwise 120\u00b0 from its position coinciding with OA. During the rotation, the midpoint of AB is denoted as P (when OA coincides with OB, point P coincides with point A). The length of the path that point P moves along is ().. A, B, C, D choices are ['6cm', '4\u03c0cm', '2\u03c0cm', '3cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10548.jpg"
-  },
-  {
-    "id": 10849,
-    "problem_id": 10549,
-    "problem": "<image>As shown in the figure, OA = OB = 6cm. Segment OB rotates counterclockwise 120\u00b0 from its position coinciding with OA. During the rotation, the midpoint of AB is denoted as P (when OA coincides with OB, point P coincides with point A). The length of the path that point P moves along is ().. A, B, C, D choices are ['6cm', '4\u03c0cm', '2\u03c0cm', '3cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10549.jpg"
-  },
-  {
-    "id": 10850,
-    "problem_id": 10550,
-    "problem": "<image>As shown in the figure, OA = OB = 6cm. Segment OB rotates counterclockwise 120\u00b0 from its position coinciding with OA. During the rotation, the midpoint of AB is denoted as P (when OA coincides with OB, point P coincides with point A). The length of the path that point P moves along is ().. A, B, C, D choices are ['6cm', '4\u03c0cm', '2\u03c0cm', '3cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10550.jpg"
-  },
-  {
-    "id": 10851,
-    "problem_id": 10551,
-    "problem": "<image>As shown in the diagram, in triangle ABC, AB = 1 and AC = 2. Now, triangle ABC is rotated clockwise 90 degrees around point C to obtain triangle A'B'C'. AB' is then connected and it is known that AB' = 3. What is the degree measurement of angle A'?. A, B, C, D choices are ['125\u00b0', '130\u00b0', '135\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10551.jpg"
-  },
-  {
-    "id": 10852,
-    "problem_id": 10552,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O, AD is the diameter of circle O, and \u2220ABC = 25\u00b0. What is the degree measure of \u2220CAD? (). A, B, C, D choices are ['25\u00b0', '50\u00b0', '65\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10552.jpg"
-  },
-  {
-    "id": 10853,
-    "problem_id": 10553,
-    "problem": "<image>As shown in the diagram, it is known that AB\u2225CD, EF bisects \u2220CEG, \u22201 = 80\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10553.jpg"
-  },
-  {
-    "id": 10854,
-    "problem_id": 10554,
-    "problem": "<image>As shown in the figure, after folding a rectangular paper with a length of 10cm and a width of 8cm twice, cut along the dashed line connecting the midpoints of the two adjacent sides of the resulting rectangle, and then open it up. What is the area of the diamond obtained? (). A, B, C, D choices are ['10cm', '20cm', '40cm', '80cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10554.jpg"
-  },
-  {
-    "id": 10855,
-    "problem_id": 10555,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O, with points of tangency A and B, respectively. \u2220APB = 50\u00b0, and C is a point on circle O. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10555.jpg"
-  },
-  {
-    "id": 10856,
-    "problem_id": 10556,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O, with points of tangency A and B, respectively. \u2220APB = 50\u00b0, and C is a point on circle O. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10556.jpg"
-  },
-  {
-    "id": 10857,
-    "problem_id": 10557,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O, with points of tangency A and B, respectively. \u2220APB = 50\u00b0, and C is a point on circle O. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10557.jpg"
-  },
-  {
-    "id": 10858,
-    "problem_id": 10558,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O, with points of tangency A and B, respectively. \u2220APB = 50\u00b0, and C is a point on circle O. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10558.jpg"
-  },
-  {
-    "id": 10859,
-    "problem_id": 10559,
-    "problem": "<image>In the diagram, point O is an interior point of triangle ABC. \u2220A = 80\u00b0, \u22201 = 15\u00b0, \u22202 = 40\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['95\u00b0', '120\u00b0', '135\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10559.jpg"
-  },
-  {
-    "id": 10860,
-    "problem_id": 10560,
-    "problem": "<image>In the diagram, point O is an interior point of triangle ABC. \u2220A = 80\u00b0, \u22201 = 15\u00b0, \u22202 = 40\u00b0. What is the measure of \u2220BOC? (). A, B, C, D choices are ['95\u00b0', '120\u00b0', '135\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10560.jpg"
-  },
-  {
-    "id": 10861,
-    "problem_id": 10561,
-    "problem": "<image>In triangle ABC, as shown in the figure, AB=AC and \u2220A=40\u00b0. If P is a point inside the triangle and \u2220PBC=\u2220PCA, then what is the measure of \u2220BPC? (). A, B, C, D choices are ['110\u00b0', '125\u00b0', '130\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10561.jpg"
-  },
-  {
-    "id": 10862,
-    "problem_id": 10562,
-    "problem": "<image>In triangle ABC, as shown in the figure, AB=AC and \u2220A=40\u00b0. If P is a point inside the triangle and \u2220PBC=\u2220PCA, then what is the measure of \u2220BPC? (). A, B, C, D choices are ['110\u00b0', '125\u00b0', '130\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10562.jpg"
-  },
-  {
-    "id": 10863,
-    "problem_id": 10563,
-    "problem": "<image>In triangle ABC, as shown in the figure, AB=AC and \u2220A=40\u00b0. If P is a point inside the triangle and \u2220PBC=\u2220PCA, then what is the measure of \u2220BPC? (). A, B, C, D choices are ['110\u00b0', '125\u00b0', '130\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10563.jpg"
-  },
-  {
-    "id": 10864,
-    "problem_id": 10564,
-    "problem": "<image>As shown in the figure, squares are constructed outside of a right triangle with each side as one side of the square. The areas of two of the small squares are 9 and 25 respectively. What is the area of square A?. A, B, C, D choices are ['16', '32', '34', '64'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10564.jpg"
-  },
-  {
-    "id": 10865,
-    "problem_id": 10565,
-    "problem": "<image>As shown in the figure, squares are constructed outside of a right triangle with each side as one side of the square. The areas of two of the small squares are 9 and 25 respectively. What is the area of square A?. A, B, C, D choices are ['16', '32', '34', '64'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10565.jpg"
-  },
-  {
-    "id": 10866,
-    "problem_id": 10566,
-    "problem": "<image>As shown in the figure, squares are constructed outside of a right triangle with each side as one side of the square. The areas of two of the small squares are 9 and 25 respectively. What is the area of square A?. A, B, C, D choices are ['16', '32', '34', '64'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10566.jpg"
-  },
-  {
-    "id": 10868,
-    "problem_id": 10567,
-    "problem": "<image>Given triangle ABC \u224c triangle ADC, angle B = 30\u00b0, angle DAC = 25\u00b0, find angle ACB.. A, B, C, D choices are ['55\u00b0', '60\u00b0', '120\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10567.jpg"
-  },
-  {
-    "id": 10869,
-    "problem_id": 10568,
-    "problem": "<image>Given triangle ABC \u224c triangle ADC, angle B = 30\u00b0, angle DAC = 25\u00b0, find angle ACB.. A, B, C, D choices are ['55\u00b0', '60\u00b0', '120\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10568.jpg"
-  },
-  {
-    "id": 10871,
-    "problem_id": 10569,
-    "problem": "<image>Given triangle ABC \u224c triangle ADC, angle B = 30\u00b0, angle DAC = 25\u00b0, find angle ACB.. A, B, C, D choices are ['55\u00b0', '60\u00b0', '120\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10569.jpg"
-  },
-  {
-    "id": 10872,
-    "problem_id": 10570,
-    "problem": "<image>If a strip of paper with two parallel sides is folded as shown in the figure and \u22201 is 62\u00b0, what is the measure of \u22202? (). A, B, C, D choices are ['62\u00b0', '56\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10570.jpg"
-  },
-  {
-    "id": 10873,
-    "problem_id": 10571,
-    "problem": "<image>If a strip of paper with two parallel sides is folded as shown in the figure and \u22201 is 62\u00b0, what is the measure of \u22202? (). A, B, C, D choices are ['62\u00b0', '56\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10571.jpg"
-  },
-  {
-    "id": 10874,
-    "problem_id": 10572,
-    "problem": "<image>If a strip of paper with two parallel sides is folded as shown in the figure and \u22201 is 62\u00b0, what is the measure of \u22202? (). A, B, C, D choices are ['62\u00b0', '56\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10572.jpg"
-  },
-  {
-    "id": 10875,
-    "problem_id": 10573,
-    "problem": "<image>As shown in the figure, if AD=AE, BE=CD, \u22201=\u22202=110\u00b0, and \u2220BAC=80\u00b0, what is the degree measure of \u2220CAE? (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10573.jpg"
-  },
-  {
-    "id": 10876,
-    "problem_id": 10574,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10574.jpg"
-  },
-  {
-    "id": 10877,
-    "problem_id": 10575,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10575.jpg"
-  },
-  {
-    "id": 10878,
-    "problem_id": 10576,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10576.jpg"
-  },
-  {
-    "id": 10879,
-    "problem_id": 10577,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10577.jpg"
-  },
-  {
-    "id": 10880,
-    "problem_id": 10578,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10578.jpg"
-  },
-  {
-    "id": 10881,
-    "problem_id": 10579,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10579.jpg"
-  },
-  {
-    "id": 10882,
-    "problem_id": 10580,
-    "problem": "<image>As shown in the picture, in order to measure the height of a tree, Xiaogang used a bamboo pole with a length of 2 meters as a measuring tool. He moved the bamboo pole until the shadow of the bamboo pole and the top of the tree fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point was 6 meters, and the distance between the bamboo pole and the tree was 15 meters. What is the height of this tree? (). A, B, C, D choices are ['5m', '7m', '7.5m', '21m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10580.jpg"
-  },
-  {
-    "id": 10883,
-    "problem_id": 10581,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10581.jpg"
-  },
-  {
-    "id": 10884,
-    "problem_id": 10582,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10582.jpg"
-  },
-  {
-    "id": 10885,
-    "problem_id": 10583,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10583.jpg"
-  },
-  {
-    "id": 10886,
-    "problem_id": 10584,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10584.jpg"
-  },
-  {
-    "id": 10887,
-    "problem_id": 10585,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10585.jpg"
-  },
-  {
-    "id": 10888,
-    "problem_id": 10586,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10586.jpg"
-  },
-  {
-    "id": 10889,
-    "problem_id": 10587,
-    "problem": "<image>In triangle ABC as shown in the figure, D and E are points on AB and AC respectively, and DE is parallel to BC. If AD = 2 cm, DB = 1 cm, and AE = 1.8 cm, then EC = (). A, B, C, D choices are ['0.9cm', '1cm', '3.6cm', '0.2cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10587.jpg"
-  },
-  {
-    "id": 10890,
-    "problem_id": 10588,
-    "problem": "<image>As shown in the diagram, in triangle ABC, angle B is 48\u00b0. The bisectors of the exterior angles DAC and ACF intersect at point E. The measure of angle AEC is () .. A, B, C, D choices are ['56\u00b0', '66\u00b0', '76\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10588.jpg"
-  },
-  {
-    "id": 10891,
-    "problem_id": 10589,
-    "problem": "<image>As shown in the diagram, in triangle ABC, angle B is 48\u00b0. The bisectors of the exterior angles DAC and ACF intersect at point E. The measure of angle AEC is () .. A, B, C, D choices are ['56\u00b0', '66\u00b0', '76\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10589.jpg"
-  },
-  {
-    "id": 10892,
-    "problem_id": 10590,
-    "problem": "<image>As shown in the diagram, in triangle ABC, angle B is 48\u00b0. The bisectors of the exterior angles DAC and ACF intersect at point E. The measure of angle AEC is () .. A, B, C, D choices are ['56\u00b0', '66\u00b0', '76\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10590.jpg"
-  },
-  {
-    "id": 10893,
-    "problem_id": 10591,
-    "problem": "<image>As shown in the diagram, in triangle ABC, angle B is 48\u00b0. The bisectors of the exterior angles DAC and ACF intersect at point E. The measure of angle AEC is () .. A, B, C, D choices are ['56\u00b0', '66\u00b0', '76\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10591.jpg"
-  },
-  {
-    "id": 10894,
-    "problem_id": 10592,
-    "problem": "<image>As shown in the diagram, in triangle ABC, angle B is 48\u00b0. The bisectors of the exterior angles DAC and ACF intersect at point E. The measure of angle AEC is () .. A, B, C, D choices are ['56\u00b0', '66\u00b0', '76\u00b0', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10592.jpg"
-  },
-  {
-    "id": 10895,
-    "problem_id": 10593,
-    "problem": "<image>Given that AB is parallel to CD, DE is perpendicular to AC with E as the foot of the perpendicular, and angle A is 130 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10593.jpg"
-  },
-  {
-    "id": 10896,
-    "problem_id": 10594,
-    "problem": "<image>Given that AB is parallel to CD, DE is perpendicular to AC with E as the foot of the perpendicular, and angle A is 130 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10594.jpg"
-  },
-  {
-    "id": 10897,
-    "problem_id": 10595,
-    "problem": "<image>Given that AB is parallel to CD, DE is perpendicular to AC with E as the foot of the perpendicular, and angle A is 130 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10595.jpg"
-  },
-  {
-    "id": 10898,
-    "problem_id": 10596,
-    "problem": "<image>Given that AB is parallel to CD, DE is perpendicular to AC with E as the foot of the perpendicular, and angle A is 130 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10596.jpg"
-  },
-  {
-    "id": 10899,
-    "problem_id": 10597,
-    "problem": "<image>Given that AB is parallel to CD, DE is perpendicular to AC with E as the foot of the perpendicular, and angle A is 130 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10597.jpg"
-  },
-  {
-    "id": 10900,
-    "problem_id": 10598,
-    "problem": "<image>Given that AB is parallel to CD, DE is perpendicular to AC with E as the foot of the perpendicular, and angle A is 130 degrees, what is the degree measure of angle D?. A, B, C, D choices are ['20\u00b0', '40\u00b0', '50\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10598.jpg"
-  },
-  {
-    "id": 10901,
-    "problem_id": 10599,
-    "problem": "<image>In the figure, in circle O, ABDC is an inscribed quadrilateral with \u2220BOC = 110\u00b0. What is the degree measure of \u2220BDC? (). A, B, C, D choices are ['110\u00b0', '70\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10599.jpg"
-  },
-  {
-    "id": 10902,
-    "problem_id": 10600,
-    "problem": "<image>In the figure, in circle O, ABDC is an inscribed quadrilateral with \u2220BOC = 110\u00b0. What is the degree measure of \u2220BDC? (). A, B, C, D choices are ['110\u00b0', '70\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10600.jpg"
-  },
-  {
-    "id": 10903,
-    "problem_id": 10601,
-    "problem": "<image>In the figure, in circle O, ABDC is an inscribed quadrilateral with \u2220BOC = 110\u00b0. What is the degree measure of \u2220BDC? (). A, B, C, D choices are ['110\u00b0', '70\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10601.jpg"
-  },
-  {
-    "id": 10904,
-    "problem_id": 10602,
-    "problem": "<image>In the figure, in circle O, ABDC is an inscribed quadrilateral with \u2220BOC = 110\u00b0. What is the degree measure of \u2220BDC? (). A, B, C, D choices are ['110\u00b0', '70\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10602.jpg"
-  },
-  {
-    "id": 10905,
-    "problem_id": 10603,
-    "problem": "<image>The diagram shows a schematic diagram designed by Xiao Ming to measure the height of a certain ancient city wall using a flashlight. A horizontal plane mirror is placed at point P, and the light travels from point A and reflects off the mirror to shine exactly on the top of the ancient city wall CD at point C. It is known that AB is perpendicular to BD, CD is perpendicular to BD, and AB = 1.2 meters, BP = 1.8 meters, PD = 12 meters. What is the height of the ancient city wall? (). A, B, C, D choices are ['6\u7c73', '8\u7c73', '18\u7c73', '24\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10603.jpg"
-  },
-  {
-    "id": 10906,
-    "problem_id": 10604,
-    "problem": "<image>The diagram shows a schematic diagram designed by Xiao Ming to measure the height of a certain ancient city wall using a flashlight. A horizontal plane mirror is placed at point P, and the light travels from point A and reflects off the mirror to shine exactly on the top of the ancient city wall CD at point C. It is known that AB is perpendicular to BD, CD is perpendicular to BD, and AB = 1.2 meters, BP = 1.8 meters, PD = 12 meters. What is the height of the ancient city wall? (). A, B, C, D choices are ['6\u7c73', '8\u7c73', '18\u7c73', '24\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10604.jpg"
-  },
-  {
-    "id": 10907,
-    "problem_id": 10605,
-    "problem": "<image>The diagram shows a schematic diagram designed by Xiao Ming to measure the height of a certain ancient city wall using a flashlight. A horizontal plane mirror is placed at point P, and the light travels from point A and reflects off the mirror to shine exactly on the top of the ancient city wall CD at point C. It is known that AB is perpendicular to BD, CD is perpendicular to BD, and AB = 1.2 meters, BP = 1.8 meters, PD = 12 meters. What is the height of the ancient city wall? (). A, B, C, D choices are ['6\u7c73', '8\u7c73', '18\u7c73', '24\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10605.jpg"
-  },
-  {
-    "id": 10908,
-    "problem_id": 10606,
-    "problem": "<image>In the figure, in quadrilateral ABCD, CB=CD, \u2220ABC=\u2220ADC=90\u00b0, and \u2220BAC=35\u00b0. Find the degree measure of \u2220BCD.. A, B, C, D choices are ['145\u00b0', '130\u00b0', '110\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10606.jpg"
-  },
-  {
-    "id": 10909,
-    "problem_id": 10607,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10607.jpg"
-  },
-  {
-    "id": 10910,
-    "problem_id": 10608,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10608.jpg"
-  },
-  {
-    "id": 10911,
-    "problem_id": 10609,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10609.jpg"
-  },
-  {
-    "id": 10912,
-    "problem_id": 10610,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10610.jpg"
-  },
-  {
-    "id": 10913,
-    "problem_id": 10611,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10611.jpg"
-  },
-  {
-    "id": 10914,
-    "problem_id": 10612,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10612.jpg"
-  },
-  {
-    "id": 10915,
-    "problem_id": 10613,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10613.jpg"
-  },
-  {
-    "id": 10916,
-    "problem_id": 10614,
-    "problem": "<image>As shown in the figure, place the ruler and the right-angled triangle board as shown in the figure. It is known that \u22201 = 35\u00b0, then the size of \u22202 is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10614.jpg"
-  },
-  {
-    "id": 10917,
-    "problem_id": 10615,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10615.jpg"
-  },
-  {
-    "id": 10918,
-    "problem_id": 10616,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10616.jpg"
-  },
-  {
-    "id": 10919,
-    "problem_id": 10617,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10617.jpg"
-  },
-  {
-    "id": 10920,
-    "problem_id": 10618,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10618.jpg"
-  },
-  {
-    "id": 10921,
-    "problem_id": 10619,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10619.jpg"
-  },
-  {
-    "id": 10922,
-    "problem_id": 10620,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10620.jpg"
-  },
-  {
-    "id": 10923,
-    "problem_id": 10621,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10621.jpg"
-  },
-  {
-    "id": 10924,
-    "problem_id": 10622,
-    "problem": "<image>As shown in the diagram, to measure the distance between two points A and B on the edge of a pond, Xiaoming selected a point O on one side of the pond and measured that the midpoint of OA and OB are points D and E respectively, and DE = 14 meters. What is the distance between A and B? (). A, B, C, D choices are ['18\u7c73', '24\u7c73', '30\u7c73', '28\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10622.jpg"
-  },
-  {
-    "id": 10925,
-    "problem_id": 10623,
-    "problem": "<image>In triangle ABC as shown, \u2220ACB=90\u00b0, CD\u2225AB, and \u2220ACD=40\u00b0. What is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10623.jpg"
-  },
-  {
-    "id": 10926,
-    "problem_id": 10624,
-    "problem": "<image>In triangle ABC as shown, \u2220ACB=90\u00b0, CD\u2225AB, and \u2220ACD=40\u00b0. What is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10624.jpg"
-  },
-  {
-    "id": 10927,
-    "problem_id": 10625,
-    "problem": "<image>In triangle ABC as shown, \u2220ACB=90\u00b0, CD\u2225AB, and \u2220ACD=40\u00b0. What is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10625.jpg"
-  },
-  {
-    "id": 10928,
-    "problem_id": 10626,
-    "problem": "<image>In triangle ABC as shown, \u2220ACB=90\u00b0, CD\u2225AB, and \u2220ACD=40\u00b0. What is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10626.jpg"
-  },
-  {
-    "id": 10929,
-    "problem_id": 10627,
-    "problem": "<image>In triangle ABC as shown, \u2220ACB=90\u00b0, CD\u2225AB, and \u2220ACD=40\u00b0. What is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10627.jpg"
-  },
-  {
-    "id": 10930,
-    "problem_id": 10628,
-    "problem": "<image>In triangle ABC as shown, \u2220ACB=90\u00b0, CD\u2225AB, and \u2220ACD=40\u00b0. What is the degree measure of \u2220B? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10628.jpg"
-  },
-  {
-    "id": 10931,
-    "problem_id": 10629,
-    "problem": "<image>As shown in the figure, lines a and b are intersected by line c, and a//b. If \u22201=55\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10629.jpg"
-  },
-  {
-    "id": 10932,
-    "problem_id": 10630,
-    "problem": "<image>As shown in the figure, lines a and b are intersected by line c, and a//b. If \u22201=55\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10630.jpg"
-  },
-  {
-    "id": 10933,
-    "problem_id": 10631,
-    "problem": "<image>In quadrilateral ABCD as shown, where \u2220B=120\u00b0 and \u2220D=50\u00b0, a triangle PRC' is folded inward from \u2220C such that C'P is parallel to AB and C'R is parallel to AD. What is the degree measure of \u2220C? (). A, B, C, D choices are ['80\u00b0', '85\u00b0', '95\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10631.jpg"
-  },
-  {
-    "id": 10934,
-    "problem_id": 10632,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD. If \u2220A=25\u00b0 and \u2220E=40\u00b0, then what is the size of \u2220C? (). A, B, C, D choices are ['25\u00b0', '40\u00b0', '65\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10632.jpg"
-  },
-  {
-    "id": 10935,
-    "problem_id": 10633,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD. If \u2220A=25\u00b0 and \u2220E=40\u00b0, then what is the size of \u2220C? (). A, B, C, D choices are ['25\u00b0', '40\u00b0', '65\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10633.jpg"
-  },
-  {
-    "id": 10936,
-    "problem_id": 10634,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD. If \u2220A=25\u00b0 and \u2220E=40\u00b0, then what is the size of \u2220C? (). A, B, C, D choices are ['25\u00b0', '40\u00b0', '65\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10634.jpg"
-  },
-  {
-    "id": 10937,
-    "problem_id": 10635,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD. If \u2220A=25\u00b0 and \u2220E=40\u00b0, then what is the size of \u2220C? (). A, B, C, D choices are ['25\u00b0', '40\u00b0', '65\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10635.jpg"
-  },
-  {
-    "id": 10938,
-    "problem_id": 10636,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD. If \u2220A=25\u00b0 and \u2220E=40\u00b0, then what is the size of \u2220C? (). A, B, C, D choices are ['25\u00b0', '40\u00b0', '65\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10636.jpg"
-  },
-  {
-    "id": 10939,
-    "problem_id": 10637,
-    "problem": "<image>As shown in the figure, AB is parallel to EF, CD is perpendicular to EF at point D. If \u2220ABC=40\u00b0, then \u2220BCD=(). A, B, C, D choices are ['140\u00b0', '130\u00b0', '120\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10637.jpg"
-  },
-  {
-    "id": 10940,
-    "problem_id": 10638,
-    "problem": "<image>As shown in the figure, AB is parallel to EF, CD is perpendicular to EF at point D. If \u2220ABC=40\u00b0, then \u2220BCD=(). A, B, C, D choices are ['140\u00b0', '130\u00b0', '120\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10638.jpg"
-  },
-  {
-    "id": 10941,
-    "problem_id": 10639,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and line c intersects lines a and b. If \u22201 = 56\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['24\u00b0', '34\u00b0', '56\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{C}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10639.jpg"
-  },
-  {
-    "id": 10942,
-    "problem_id": 10640,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, and line c intersects lines a and b. If \u22201 = 56\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['24\u00b0', '34\u00b0', '56\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10640.jpg"
-  },
-  {
-    "id": 10943,
-    "problem_id": 10641,
-    "problem": "<image>As shown in the figure, it is known that line AB is parallel to CD, the angle bisector of angle GEB intersects CD at point F, and angle 1 is 42\u00b0. Then angle 2 is equal to ().. A, B, C, D choices are ['138\u00b0', '142\u00b0', '148\u00b0', '159\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10641.jpg"
-  },
-  {
-    "id": 10944,
-    "problem_id": 10642,
-    "problem": "<image>As shown in the figure, it is known that line AB is parallel to CD, the angle bisector of angle GEB intersects CD at point F, and angle 1 is 42\u00b0. Then angle 2 is equal to ().. A, B, C, D choices are ['138\u00b0', '142\u00b0', '148\u00b0', '159\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10642.jpg"
-  },
-  {
-    "id": 10945,
-    "problem_id": 10643,
-    "problem": "<image>As shown in the diagram, the vertices A and C of rectangle ABCD are on lines a and b respectively, and a is parallel to b, and \u22201 = 60\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10643.jpg"
-  },
-  {
-    "id": 10946,
-    "problem_id": 10644,
-    "problem": "<image>As shown in the diagram, the vertices A and C of rectangle ABCD are on lines a and b respectively, and a is parallel to b, and \u22201 = 60\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10644.jpg"
-  },
-  {
-    "id": 10947,
-    "problem_id": 10645,
-    "problem": "<image>As shown in the diagram, the vertices A and C of rectangle ABCD are on lines a and b respectively, and a is parallel to b, and \u22201 = 60\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10645.jpg"
-  },
-  {
-    "id": 10948,
-    "problem_id": 10646,
-    "problem": "<image>As shown in the figure, the right angle vertex of a right triangle is placed on one side of a ruler. If \u22201 = 50\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10646.jpg"
-  },
-  {
-    "id": 10949,
-    "problem_id": 10647,
-    "problem": "<image>As shown in the figure, the right angle vertex of a right triangle is placed on one side of a ruler. If \u22201 = 50\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10647.jpg"
-  },
-  {
-    "id": 10950,
-    "problem_id": 10648,
-    "problem": "<image>As shown in the figure, the right angle vertex of a right triangle is placed on one side of a ruler. If \u22201 = 50\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10648.jpg"
-  },
-  {
-    "id": 10951,
-    "problem_id": 10649,
-    "problem": "<image>As shown in the figure, the right angle vertex of a right triangle is placed on one side of a ruler. If \u22201 = 50\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10649.jpg"
-  },
-  {
-    "id": 10952,
-    "problem_id": 10650,
-    "problem": "<image>As shown in the figure, the right angle vertex of a right triangle is placed on one side of a ruler. If \u22201 = 50\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10650.jpg"
-  },
-  {
-    "id": 10953,
-    "problem_id": 10651,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. Line l intersects lines a and b at points A and B, respectively. A line perpendicular to line l passes through point A and intersects line b at point C. If angle 1 is 58 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['58\u00b0', '42\u00b0', '32\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10651.jpg"
-  },
-  {
-    "id": 10954,
-    "problem_id": 10652,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. Line l intersects lines a and b at points A and B, respectively. A line perpendicular to line l passes through point A and intersects line b at point C. If angle 1 is 58 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['58\u00b0', '42\u00b0', '32\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10652.jpg"
-  },
-  {
-    "id": 10955,
-    "problem_id": 10653,
-    "problem": "<image>As shown in the diagram, line a is parallel to line b. Line l intersects lines a and b at points A and B, respectively. A line perpendicular to line l passes through point A and intersects line b at point C. If angle 1 is 58 degrees, what is the degree measure of angle 2?. A, B, C, D choices are ['58\u00b0', '42\u00b0', '32\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10653.jpg"
-  },
-  {
-    "id": 10956,
-    "problem_id": 10654,
-    "problem": "<image>As shown in the figure, line a and line b are intersected by line c. If a||b and \u22201=110\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['70\u00b0', '75\u00b0', '80\u00b0', '85\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10654.jpg"
-  },
-  {
-    "id": 10958,
-    "problem_id": 10655,
-    "problem": "<image>A ship departs from point A on the sea level and travels 40 nautical miles towards the direction of south-west 40\u00b0 to reach point B, then travels 40 nautical miles towards the direction of north-west 20\u00b0 from point B to reach point C, as shown in the figure. What is the distance between points A and C?. A, B, C, D choices are ['30\u6d77\u91cc', '40\u6d77\u91cc', '50\u6d77\u91cc', '60\u6d77\u91cc'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10655.jpg"
-  },
-  {
-    "id": 10959,
-    "problem_id": 10656,
-    "problem": "<image>A ship departs from point A on the sea level and travels 40 nautical miles towards the direction of south-west 40\u00b0 to reach point B, then travels 40 nautical miles towards the direction of north-west 20\u00b0 from point B to reach point C, as shown in the figure. What is the distance between points A and C?. A, B, C, D choices are ['30\u6d77\u91cc', '40\u6d77\u91cc', '50\u6d77\u91cc', '60\u6d77\u91cc'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10656.jpg"
-  },
-  {
-    "id": 10960,
-    "problem_id": 10657,
-    "problem": "<image>A ship departs from point A on the sea level and travels 40 nautical miles towards the direction of south-west 40\u00b0 to reach point B, then travels 40 nautical miles towards the direction of north-west 20\u00b0 from point B to reach point C, as shown in the figure. What is the distance between points A and C?. A, B, C, D choices are ['30\u6d77\u91cc', '40\u6d77\u91cc', '50\u6d77\u91cc', '60\u6d77\u91cc'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10657.jpg"
-  },
-  {
-    "id": 10961,
-    "problem_id": 10658,
-    "problem": "<image>A ship departs from point A on the sea level and travels 40 nautical miles towards the direction of south-west 40\u00b0 to reach point B, then travels 40 nautical miles towards the direction of north-west 20\u00b0 from point B to reach point C, as shown in the figure. What is the distance between points A and C?. A, B, C, D choices are ['30\u6d77\u91cc', '40\u6d77\u91cc', '50\u6d77\u91cc', '60\u6d77\u91cc'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10658.jpg"
-  },
-  {
-    "id": 10962,
-    "problem_id": 10659,
-    "problem": "<image>As shown in the figure, triangle OAB is rotated counterclockwise around point O by 80 degrees to obtain triangle OCD. If \u2220A = 110\u00b0 and \u2220D = 40\u00b0, what is the degree measure of \u2220\u03b1? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10659.jpg"
-  },
-  {
-    "id": 10963,
-    "problem_id": 10660,
-    "problem": "<image>As shown in the figure, triangle OAB is rotated counterclockwise around point O by 80 degrees to obtain triangle OCD. If \u2220A = 110\u00b0 and \u2220D = 40\u00b0, what is the degree measure of \u2220\u03b1? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10660.jpg"
-  },
-  {
-    "id": 10964,
-    "problem_id": 10661,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Connect OA and OB. Point C and O are on the same side of the chord AB. If \u2220ABO = 50\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10661.jpg"
-  },
-  {
-    "id": 10965,
-    "problem_id": 10662,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Connect OA and OB. Point C and O are on the same side of the chord AB. If \u2220ABO = 50\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10662.jpg"
-  },
-  {
-    "id": 10966,
-    "problem_id": 10663,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Connect OA and OB. Point C and O are on the same side of the chord AB. If \u2220ABO = 50\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10663.jpg"
-  },
-  {
-    "id": 10967,
-    "problem_id": 10664,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Connect OA and OB. Point C and O are on the same side of the chord AB. If \u2220ABO = 50\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10664.jpg"
-  },
-  {
-    "id": 10968,
-    "problem_id": 10665,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Connect OA and OB. Point C and O are on the same side of the chord AB. If \u2220ABO = 50\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10665.jpg"
-  },
-  {
-    "id": 10969,
-    "problem_id": 10666,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. Connect OA and OB. Point C and O are on the same side of the chord AB. If \u2220ABO = 50\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10666.jpg"
-  },
-  {
-    "id": 10970,
-    "problem_id": 10667,
-    "problem": "<image>As shown in the figure, AB and CD are chords of circle O, and AB is perpendicular to CD. If \u2220CDB = 50\u00b0, then what is the size of \u2220ACD? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10667.jpg"
-  },
-  {
-    "id": 10971,
-    "problem_id": 10668,
-    "problem": "<image>As shown in the figure, AB and CD are chords of circle O, and AB is perpendicular to CD. If \u2220CDB = 50\u00b0, then what is the size of \u2220ACD? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10668.jpg"
-  },
-  {
-    "id": 10972,
-    "problem_id": 10669,
-    "problem": "<image>In triangle ABC as shown, AB=AC, \u2220A=36\u00b0, BD is the altitude from vertex A to side AC. What is the degree measure of \u2220DBC?. A, B, C, D choices are ['18\u00b0', '24\u00b0', '30\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10669.jpg"
-  },
-  {
-    "id": 10973,
-    "problem_id": 10670,
-    "problem": "<image>In triangle ABC as shown, AB=AC, \u2220A=36\u00b0, BD is the altitude from vertex A to side AC. What is the degree measure of \u2220DBC?. A, B, C, D choices are ['18\u00b0', '24\u00b0', '30\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10670.jpg"
-  },
-  {
-    "id": 10974,
-    "problem_id": 10671,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, EC is perpendicular to CD at C, CF intersects AB at B. If angle 2 measures 29 degrees, what is the degree measure of angle 1? (). A, B, C, D choices are ['58\u00b0', '59\u00b0', '61\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10671.jpg"
-  },
-  {
-    "id": 10975,
-    "problem_id": 10672,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD, EC is perpendicular to CD at C, CF intersects AB at B. If angle 2 measures 29 degrees, what is the degree measure of angle 1? (). A, B, C, D choices are ['58\u00b0', '59\u00b0', '61\u00b0', '62\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10672.jpg"
-  },
-  {
-    "id": 10976,
-    "problem_id": 10673,
-    "problem": "<image>In the figure, a\u2225b, point B lies on line a, AB\u22a5BC, if \u22201=38\u00b0, what is the degree of \u22202? (). A, B, C, D choices are ['38\u00b0', '52\u00b0', '76\u00b0', '142\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10673.jpg"
-  },
-  {
-    "id": 10977,
-    "problem_id": 10674,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. If \u22201 = 40\u00b0 and \u22202 = 55\u00b0, then what is the measure of \u22203? (). A, B, C, D choices are ['85\u00b0', '95\u00b0', '105\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10674.jpg"
-  },
-  {
-    "id": 10978,
-    "problem_id": 10675,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. If \u22201 = 40\u00b0 and \u22202 = 55\u00b0, then what is the measure of \u22203? (). A, B, C, D choices are ['85\u00b0', '95\u00b0', '105\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10675.jpg"
-  },
-  {
-    "id": 10979,
-    "problem_id": 10676,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. If \u22201 = 40\u00b0 and \u22202 = 55\u00b0, then what is the measure of \u22203? (). A, B, C, D choices are ['85\u00b0', '95\u00b0', '105\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10676.jpg"
-  },
-  {
-    "id": 10980,
-    "problem_id": 10677,
-    "problem": "<image>As shown in the figure, line a is parallel to line b. If \u22201 = 40\u00b0 and \u22202 = 55\u00b0, then what is the measure of \u22203? (). A, B, C, D choices are ['85\u00b0', '95\u00b0', '105\u00b0', '115\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10677.jpg"
-  },
-  {
-    "id": 10981,
-    "problem_id": 10678,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, EO is perpendicular to CD at point O, and \u2220AOE=36\u00b0. What is the measure of \u2220BOD? (). A, B, C, D choices are ['36\u00b0', '44\u00b0', '50\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10678.jpg"
-  },
-  {
-    "id": 10982,
-    "problem_id": 10679,
-    "problem": "<image>As shown in the figure, line AB and CD intersect at point O, EO is perpendicular to CD at point O, and \u2220AOE=36\u00b0. What is the measure of \u2220BOD? (). A, B, C, D choices are ['36\u00b0', '44\u00b0', '50\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10679.jpg"
-  },
-  {
-    "id": 10983,
-    "problem_id": 10680,
-    "problem": "<image>As shown in the figure, place an isosceles right triangle board on a rectangular sheet of paper as shown. Where \u2220\u03b1 = 24\u00b0, the degree of \u2220\u03b2 is ().. A, B, C, D choices are ['24\u00b0', '21\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10680.jpg"
-  },
-  {
-    "id": 10984,
-    "problem_id": 10681,
-    "problem": "<image>As shown in the figure, place an isosceles right triangle board on a rectangular sheet of paper as shown. Where \u2220\u03b1 = 24\u00b0, the degree of \u2220\u03b2 is ().. A, B, C, D choices are ['24\u00b0', '21\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10681.jpg"
-  },
-  {
-    "id": 10985,
-    "problem_id": 10682,
-    "problem": "<image>As shown in the figure, place an isosceles right triangle board on a rectangular sheet of paper as shown. Where \u2220\u03b1 = 24\u00b0, the degree of \u2220\u03b2 is ().. A, B, C, D choices are ['24\u00b0', '21\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10682.jpg"
-  },
-  {
-    "id": 10986,
-    "problem_id": 10683,
-    "problem": "<image>As shown in the figure, place an isosceles right triangle board on a rectangular sheet of paper as shown. Where \u2220\u03b1 = 24\u00b0, the degree of \u2220\u03b2 is ().. A, B, C, D choices are ['24\u00b0', '21\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10683.jpg"
-  },
-  {
-    "id": 10987,
-    "problem_id": 10684,
-    "problem": "<image>As shown in the figure, place an isosceles right triangle board on a rectangular sheet of paper as shown. Where \u2220\u03b1 = 24\u00b0, the degree of \u2220\u03b2 is ().. A, B, C, D choices are ['24\u00b0', '21\u00b0', '30\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10684.jpg"
-  },
-  {
-    "id": 10988,
-    "problem_id": 10685,
-    "problem": "<image>On a rectangular lawn with a length of 12m and a width of 6m as shown in the figure, there is a curved asphalt path (the horizontal width of the path is 2m anywhere). What is the area of the lawn represented by the blank space? (). A, B, C, D choices are ['70', '60', '48', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10685.jpg"
-  },
-  {
-    "id": 10989,
-    "problem_id": 10686,
-    "problem": "<image>On a rectangular lawn with a length of 12m and a width of 6m as shown in the figure, there is a curved asphalt path (the horizontal width of the path is 2m anywhere). What is the area of the lawn represented by the blank space? (). A, B, C, D choices are ['70', '60', '48', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10686.jpg"
-  },
-  {
-    "id": 10990,
-    "problem_id": 10687,
-    "problem": "<image>On a rectangular lawn with a length of 12m and a width of 6m as shown in the figure, there is a curved asphalt path (the horizontal width of the path is 2m anywhere). What is the area of the lawn represented by the blank space? (). A, B, C, D choices are ['70', '60', '48', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10687.jpg"
-  },
-  {
-    "id": 10992,
-    "problem_id": 10688,
-    "problem": "<image>Given the clockwise rotation of triangle ABC around point C by 60 degrees to obtain triangle A'B'C as shown in the figure. If angle A measures 40 degrees and angle B measures 110 degrees, what is the degree measure of angle BCA'?. A, B, C, D choices are ['100\u00b0', '90\u00b0', '70\u00b0', '110\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10688.jpg"
-  },
-  {
-    "id": 10993,
-    "problem_id": 10689,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10689.jpg"
-  },
-  {
-    "id": 10994,
-    "problem_id": 10690,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10690.jpg"
-  },
-  {
-    "id": 10995,
-    "problem_id": 10691,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10691.jpg"
-  },
-  {
-    "id": 10996,
-    "problem_id": 10692,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10692.jpg"
-  },
-  {
-    "id": 10997,
-    "problem_id": 10693,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10693.jpg"
-  },
-  {
-    "id": 10998,
-    "problem_id": 10694,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10694.jpg"
-  },
-  {
-    "id": 10999,
-    "problem_id": 10695,
-    "problem": "<image>Given that the central angle \u2220BOC is 78\u00b0 as shown in the figure, what is the measure of the arc angle \u2220BAC? (). A, B, C, D choices are ['156\u00b0', '78\u00b0', '39\u00b0', '12\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10695.jpg"
-  },
-  {
-    "id": 11001,
-    "problem_id": 10696,
-    "problem": "<image>As shown in the figure, the diameter CD of circle O is perpendicular to chord AB. If \u2220AOC=40\u00b0, what is the degree of \u2220CDB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10696.jpg"
-  },
-  {
-    "id": 11002,
-    "problem_id": 10697,
-    "problem": "<image>Given AB\u2225CD as shown in the figure, with \u2220D=50\u00b0 and BC bisecting \u2220ABD, what is the measure of \u2220ABC? (). A, B, C, D choices are ['65\u00b0', '55\u00b0', '50\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10697.jpg"
-  },
-  {
-    "id": 11003,
-    "problem_id": 10698,
-    "problem": "<image>As shown in the figure, the vertices of triangle ABC are all on the circle O. If \u2220A=36\u00b0, what is the degree measure of \u2220BOC? (). A, B, C, D choices are ['18\u00b0', '36\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10698.jpg"
-  },
-  {
-    "id": 11004,
-    "problem_id": 10699,
-    "problem": "<image>As shown in the figure, the vertices of triangle ABC are all on the circle O. If \u2220A=36\u00b0, what is the degree measure of \u2220BOC? (). A, B, C, D choices are ['18\u00b0', '36\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10699.jpg"
-  },
-  {
-    "id": 11005,
-    "problem_id": 10700,
-    "problem": "<image>As shown in the figure, the vertices of triangle ABC are all on the circle O. If \u2220A=36\u00b0, what is the degree measure of \u2220BOC? (). A, B, C, D choices are ['18\u00b0', '36\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10700.jpg"
-  },
-  {
-    "id": 11006,
-    "problem_id": 10701,
-    "problem": "<image>As shown in the figure, the vertices of triangle ABC are all on the circle O. If \u2220A=36\u00b0, what is the degree measure of \u2220BOC? (). A, B, C, D choices are ['18\u00b0', '36\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10701.jpg"
-  },
-  {
-    "id": 11007,
-    "problem_id": 10702,
-    "problem": "<image>As shown in the figure, the vertices of triangle ABC are all on the circle O. If \u2220A=36\u00b0, what is the degree measure of \u2220BOC? (). A, B, C, D choices are ['18\u00b0', '36\u00b0', '60\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10702.jpg"
-  },
-  {
-    "id": 11008,
-    "problem_id": 10703,
-    "problem": "<image>As shown in the figure, AB is tangent to circle O at point B, and \u2220AOB=60\u00b0. Find the degree measure of \u2220A.. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10703.jpg"
-  },
-  {
-    "id": 11009,
-    "problem_id": 10704,
-    "problem": "<image>As shown in the figure, AB is tangent to circle O at point B, and \u2220AOB=60\u00b0. Find the degree measure of \u2220A.. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10704.jpg"
-  },
-  {
-    "id": 11010,
-    "problem_id": 10705,
-    "problem": "<image>As shown in the figure, AB is tangent to circle O at point B, and \u2220AOB=60\u00b0. Find the degree measure of \u2220A.. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10705.jpg"
-  },
-  {
-    "id": 11011,
-    "problem_id": 10706,
-    "problem": "<image>As shown in the figure, AB is tangent to circle O at point B, and \u2220AOB=60\u00b0. Find the degree measure of \u2220A.. A, B, C, D choices are ['15\u00b0', '30\u00b0', '45\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10706.jpg"
-  },
-  {
-    "id": 11012,
-    "problem_id": 10707,
-    "problem": "<image>As shown in the diagram, line a is perpendicular to line c, and line b is perpendicular to line c. If \u22201=70\u00b0, then \u22202=(). A, B, C, D choices are ['70\u00b0', '90\u00b0', '110\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10707.jpg"
-  },
-  {
-    "id": 11013,
-    "problem_id": 10708,
-    "problem": "<image>As shown in the diagram, line a is perpendicular to line c, and line b is perpendicular to line c. If \u22201=70\u00b0, then \u22202=(). A, B, C, D choices are ['70\u00b0', '90\u00b0', '110\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10708.jpg"
-  },
-  {
-    "id": 11014,
-    "problem_id": 10709,
-    "problem": "<image>As shown in the diagram, line a is perpendicular to line c, and line b is perpendicular to line c. If \u22201=70\u00b0, then \u22202=(). A, B, C, D choices are ['70\u00b0', '90\u00b0', '110\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10709.jpg"
-  },
-  {
-    "id": 11015,
-    "problem_id": 10710,
-    "problem": "<image>As shown in the figure, \u25b3ABC is inscribed in \u2299O, AD is the diameter of \u2299O, and \u2220ABC=35\u00b0. What is the degree measure of \u2220CAD? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10710.jpg"
-  },
-  {
-    "id": 11016,
-    "problem_id": 10711,
-    "problem": "<image>As shown in the figure, \u25b3ABC is inscribed in \u2299O, AD is the diameter of \u2299O, and \u2220ABC=35\u00b0. What is the degree measure of \u2220CAD? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10711.jpg"
-  },
-  {
-    "id": 11017,
-    "problem_id": 10712,
-    "problem": "<image>As shown in the figure, line AB is parallel to line CD, and \u22201 = 50\u00b0, \u22202 = 110\u00b0. What is the size of \u2220E?. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10712.jpg"
-  },
-  {
-    "id": 11018,
-    "problem_id": 10713,
-    "problem": "<image>As shown in the figure, line AB is parallel to line CD, and \u22201 = 50\u00b0, \u22202 = 110\u00b0. What is the size of \u2220E?. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10713.jpg"
-  },
-  {
-    "id": 11019,
-    "problem_id": 10714,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O and CD is a chord of circle O. If \u2220BAC is 23\u00b0, what is the size of \u2220ADC? (). A, B, C, D choices are ['23\u00b0', '57\u00b0', '67\u00b0', '77\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10714.jpg"
-  },
-  {
-    "id": 11020,
-    "problem_id": 10715,
-    "problem": "<image>As shown in the figure, it is known that point E is on the edge BC of the diamond ABCD, and \u2220DAE=\u2220B=80\u00b0. What is the degree measure of angle CDE? (). A, B, C, D choices are ['20\u00b0', '25\u00b0', '30\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10715.jpg"
-  },
-  {
-    "id": 11021,
-    "problem_id": 10716,
-    "problem": "<image>As shown in the figure, a math interest group deforms a square wire frame ABCD with a side length of 6 into a sector DAB with A as the center and AB as the radius (ignoring the thickness of the wire). The area of the sector DAB is () .. A, B, C, D choices are ['12', '14', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10716.jpg"
-  },
-  {
-    "id": 11022,
-    "problem_id": 10717,
-    "problem": "<image>As shown in the figure, a math interest group deforms a square wire frame ABCD with a side length of 6 into a sector DAB with A as the center and AB as the radius (ignoring the thickness of the wire). The area of the sector DAB is () .. A, B, C, D choices are ['12', '14', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10717.jpg"
-  },
-  {
-    "id": 11023,
-    "problem_id": 10718,
-    "problem": "<image>As shown in the figure, a math interest group deforms a square wire frame ABCD with a side length of 6 into a sector DAB with A as the center and AB as the radius (ignoring the thickness of the wire). The area of the sector DAB is () .. A, B, C, D choices are ['12', '14', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10718.jpg"
-  },
-  {
-    "id": 11024,
-    "problem_id": 10719,
-    "problem": "<image>As shown in the figure, a math interest group deforms a square wire frame ABCD with a side length of 6 into a sector DAB with A as the center and AB as the radius (ignoring the thickness of the wire). The area of the sector DAB is () .. A, B, C, D choices are ['12', '14', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10719.jpg"
-  },
-  {
-    "id": 11025,
-    "problem_id": 10720,
-    "problem": "<image>As shown in the figure, a math interest group deforms a square wire frame ABCD with a side length of 6 into a sector DAB with A as the center and AB as the radius (ignoring the thickness of the wire). The area of the sector DAB is () .. A, B, C, D choices are ['12', '14', '16', '36'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10720.jpg"
-  },
-  {
-    "id": 11027,
-    "problem_id": 10721,
-    "problem": "<image>As shown in the figure, AB and CD are both diameters of circle O. If \u2220AOC is 50\u00b0, what is the degree measure of \u2220C? (). A, B, C, D choices are ['20\u00b0', '25\u00b0', '30\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10721.jpg"
-  },
-  {
-    "id": 11028,
-    "problem_id": 10722,
-    "problem": "<image>In the diagram, line a is parallel to line b, and \u22201 = 120\u00b0. What is the degree measure of \u22202? (). A, B, C, D choices are ['120\u00b0', '50\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10722.jpg"
-  },
-  {
-    "id": 11031,
-    "problem_id": 10723,
-    "problem": "<image>As shown in the diagram, point O is on the line AB, and OC is perpendicular to OD. If \u2220COA = 35\u00b0, then the size of \u2220DOB is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10723.jpg"
-  },
-  {
-    "id": 11032,
-    "problem_id": 10724,
-    "problem": "<image>As shown in the diagram, point O is on the line AB, and OC is perpendicular to OD. If \u2220COA = 35\u00b0, then the size of \u2220DOB is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10724.jpg"
-  },
-  {
-    "id": 11033,
-    "problem_id": 10725,
-    "problem": "<image>As shown in the diagram, point O is on the line AB, and OC is perpendicular to OD. If \u2220COA = 35\u00b0, then the size of \u2220DOB is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10725.jpg"
-  },
-  {
-    "id": 11034,
-    "problem_id": 10726,
-    "problem": "<image>As shown in the diagram, point O is on the line AB, and OC is perpendicular to OD. If \u2220COA = 35\u00b0, then the size of \u2220DOB is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10726.jpg"
-  },
-  {
-    "id": 11035,
-    "problem_id": 10727,
-    "problem": "<image>As shown in the diagram, point O is on the line AB, and OC is perpendicular to OD. If \u2220COA = 35\u00b0, then the size of \u2220DOB is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10727.jpg"
-  },
-  {
-    "id": 11036,
-    "problem_id": 10728,
-    "problem": "<image>As shown in the diagram, point O is on the line AB, and OC is perpendicular to OD. If \u2220COA = 35\u00b0, then the size of \u2220DOB is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10728.jpg"
-  },
-  {
-    "id": 11037,
-    "problem_id": 10729,
-    "problem": "<image>As shown in the figure, if chord AC is parallel to OB and \u2220B is 25\u00b0, then \u2220O is ().. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10729.jpg"
-  },
-  {
-    "id": 11038,
-    "problem_id": 10730,
-    "problem": "<image>As shown in the figure, if chord AC is parallel to OB and \u2220B is 25\u00b0, then \u2220O is ().. A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10730.jpg"
-  },
-  {
-    "id": 11039,
-    "problem_id": 10731,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u22201=\u22202, \u2220A=60\u00b0, then \u2220ADC=(). A, B, C, D choices are ['65\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10731.jpg"
-  },
-  {
-    "id": 11040,
-    "problem_id": 10732,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u22201=\u22202, \u2220A=60\u00b0, then \u2220ADC=(). A, B, C, D choices are ['65\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10732.jpg"
-  },
-  {
-    "id": 11041,
-    "problem_id": 10733,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u22201=\u22202, \u2220A=60\u00b0, then \u2220ADC=(). A, B, C, D choices are ['65\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10733.jpg"
-  },
-  {
-    "id": 11042,
-    "problem_id": 10734,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u22201=\u22202, \u2220A=60\u00b0, then \u2220ADC=(). A, B, C, D choices are ['65\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10734.jpg"
-  },
-  {
-    "id": 11043,
-    "problem_id": 10735,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u22201=\u22202, \u2220A=60\u00b0, then \u2220ADC=(). A, B, C, D choices are ['65\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10735.jpg"
-  },
-  {
-    "id": 11044,
-    "problem_id": 10736,
-    "problem": "<image>In the quadrilateral ABCD shown in the figure, \u22201=\u22202, \u2220A=60\u00b0, then \u2220ADC=(). A, B, C, D choices are ['65\u00b0', '60\u00b0', '110\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10736.jpg"
-  },
-  {
-    "id": 11045,
-    "problem_id": 10737,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, AD=CD, \u22202=40\u00b0, then what is the degree of \u22201? (). A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10737.jpg"
-  },
-  {
-    "id": 11046,
-    "problem_id": 10738,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, AD=CD, \u22202=40\u00b0, then what is the degree of \u22201? (). A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10738.jpg"
-  },
-  {
-    "id": 11047,
-    "problem_id": 10739,
-    "problem": "<image>As shown in the diagram, AB\u2225CD, AD=CD, \u22202=40\u00b0, then what is the degree of \u22201? (). A, B, C, D choices are ['80\u00b0', '75\u00b0', '70\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10739.jpg"
-  },
-  {
-    "id": 11048,
-    "problem_id": 10740,
-    "problem": "<image>As shown in the figure, it is known that AB is parallel to CD, and the line MN intersects AB and CD at points M and N respectively. NG bisects \u2220MND. If \u22201 = 70\u00b0, what is the degree measurement of \u22202?. A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10740.jpg"
-  },
-  {
-    "id": 11049,
-    "problem_id": 10741,
-    "problem": "<image>As shown in the figure, it is known that AB is parallel to CD, and the line MN intersects AB and CD at points M and N respectively. NG bisects \u2220MND. If \u22201 = 70\u00b0, what is the degree measurement of \u22202?. A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10741.jpg"
-  },
-  {
-    "id": 11050,
-    "problem_id": 10742,
-    "problem": "<image>As shown in the figure, it is known that AB is parallel to CD, and the line MN intersects AB and CD at points M and N respectively. NG bisects \u2220MND. If \u22201 = 70\u00b0, what is the degree measurement of \u22202?. A, B, C, D choices are ['10\u00b0', '15\u00b0', '20\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10742.jpg"
-  },
-  {
-    "id": 11051,
-    "problem_id": 10743,
-    "problem": "<image>In triangle ABC as shown, where \u2220ABC=45\u00b0 and AC=8cm, F is the intersection point of altitudes AD and BE. What is the length of BF? (). A, B, C, D choices are ['4cm', '6cm', '8cm', '9cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10743.jpg"
-  },
-  {
-    "id": 11052,
-    "problem_id": 10744,
-    "problem": "<image>In triangle ABC as shown, where \u2220ABC=45\u00b0 and AC=8cm, F is the intersection point of altitudes AD and BE. What is the length of BF? (). A, B, C, D choices are ['4cm', '6cm', '8cm', '9cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10744.jpg"
-  },
-  {
-    "id": 11053,
-    "problem_id": 10745,
-    "problem": "<image>As shown in the picture, Xiaoming used a bamboo pole with a length of 3.2 meters as a measuring tool to measure the height of the school flagpole. He moved the bamboo pole so that the shadows of the bamboo pole and the top of the flagpole fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8 meters, and the distance between the bamboo pole and the flagpole is 22 meters. What is the height of the flagpole? (). A, B, C, D choices are ['12m', '9.6m', '8m', '6.6m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10745.jpg"
-  },
-  {
-    "id": 11054,
-    "problem_id": 10746,
-    "problem": "<image>As shown in the picture, Xiaoming used a bamboo pole with a length of 3.2 meters as a measuring tool to measure the height of the school flagpole. He moved the bamboo pole so that the shadows of the bamboo pole and the top of the flagpole fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8 meters, and the distance between the bamboo pole and the flagpole is 22 meters. What is the height of the flagpole? (). A, B, C, D choices are ['12m', '9.6m', '8m', '6.6m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10746.jpg"
-  },
-  {
-    "id": 11055,
-    "problem_id": 10747,
-    "problem": "<image>As shown in the picture, Xiaoming used a bamboo pole with a length of 3.2 meters as a measuring tool to measure the height of the school flagpole. He moved the bamboo pole so that the shadows of the bamboo pole and the top of the flagpole fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8 meters, and the distance between the bamboo pole and the flagpole is 22 meters. What is the height of the flagpole? (). A, B, C, D choices are ['12m', '9.6m', '8m', '6.6m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10747.jpg"
-  },
-  {
-    "id": 11056,
-    "problem_id": 10748,
-    "problem": "<image>As shown in the picture, Xiaoming used a bamboo pole with a length of 3.2 meters as a measuring tool to measure the height of the school flagpole. He moved the bamboo pole so that the shadows of the bamboo pole and the top of the flagpole fell exactly on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8 meters, and the distance between the bamboo pole and the flagpole is 22 meters. What is the height of the flagpole? (). A, B, C, D choices are ['12m', '9.6m', '8m', '6.6m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10748.jpg"
-  },
-  {
-    "id": 11057,
-    "problem_id": 10749,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]\n\n**Additional Insight:**\n\nIt's important to note that in problems involving parallel lines and transversals, identifying the relationships between angles (such as corresponding angles, alternate interior angles, and same-side interior angles) is crucial. In this case, recognizing that \u2220BAC and \u2220ACD are alternate interior angles due to AB \u2225 CD and AC being the transversal, and then recognizing that \u2220ACD and \u2220CDF are corresponding angles due to AC \u2225 DF and CD being the transversal, allows us to establish that \u2220CDF = \u2220BAC = 120\u00b0. This method ensures a systematic approach to solving such geometric problems.</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10749.jpg"
-  },
-  {
-    "id": 11058,
-    "problem_id": 10750,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10750.jpg"
-  },
-  {
-    "id": 11059,
-    "problem_id": 10751,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10751.jpg"
-  },
-  {
-    "id": 11060,
-    "problem_id": 10752,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10752.jpg"
-  },
-  {
-    "id": 11061,
-    "problem_id": 10753,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10753.jpg"
-  },
-  {
-    "id": 11062,
-    "problem_id": 10754,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10754.jpg"
-  },
-  {
-    "id": 11063,
-    "problem_id": 10755,
-    "problem": "<image>Given the diagram, AB\u2225CD\u2225EF and AC\u2225DF. If \u2220BAC=120\u00b0, then \u2220CDF=(). A, B, C, D choices are ['120\u00b0', '150\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10755.jpg"
-  },
-  {
-    "id": 11064,
-    "problem_id": 10756,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle D. If \u2220ABC is 70\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['35\u00b0', '130\u00b0', '125\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10756.jpg"
-  },
-  {
-    "id": 11065,
-    "problem_id": 10757,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle D. If \u2220ABC is 70\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['35\u00b0', '130\u00b0', '125\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10757.jpg"
-  },
-  {
-    "id": 11066,
-    "problem_id": 10758,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle D. If \u2220ABC is 70\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['35\u00b0', '130\u00b0', '125\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10758.jpg"
-  },
-  {
-    "id": 11067,
-    "problem_id": 10759,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle D. If \u2220ABC is 70\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['35\u00b0', '130\u00b0', '125\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10759.jpg"
-  },
-  {
-    "id": 11068,
-    "problem_id": 10760,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle D. If \u2220ABC is 70\u00b0, then what is the degree measure of \u2220ADC? (). A, B, C, D choices are ['35\u00b0', '130\u00b0', '125\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10760.jpg"
-  },
-  {
-    "id": 11069,
-    "problem_id": 10761,
-    "problem": "<image>As shown in the diagram, in triangle ABC, the trisectors of angles ABC and ACB intersect at points E and D. If angle BFC is 132\u00b0 and angle BGC is 118\u00b0, what is the degree measure of angle A? (). A, B, C, D choices are ['65\u00b0', '66\u00b0', '70\u00b0', '78\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10761.jpg"
-  },
-  {
-    "id": 11070,
-    "problem_id": 10762,
-    "problem": "<image>As shown in the diagram, in triangle ABC, the trisectors of angles ABC and ACB intersect at points E and D. If angle BFC is 132\u00b0 and angle BGC is 118\u00b0, what is the degree measure of angle A? (). A, B, C, D choices are ['65\u00b0', '66\u00b0', '70\u00b0', '78\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10762.jpg"
-  },
-  {
-    "id": 11071,
-    "problem_id": 10763,
-    "problem": "<image>As shown in the diagram, in triangle ABC, the trisectors of angles ABC and ACB intersect at points E and D. If angle BFC is 132\u00b0 and angle BGC is 118\u00b0, what is the degree measure of angle A? (). A, B, C, D choices are ['65\u00b0', '66\u00b0', '70\u00b0', '78\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10763.jpg"
-  },
-  {
-    "id": 11072,
-    "problem_id": 10764,
-    "problem": "<image>In triangle ABC shown in the figure, where angle B is 44\u00b0 and angle C is 54\u00b0, AD bisects angle BAC and intersects BC at D. DE is parallel to AB and intersects AC at E. What is the measure of angle ADE?. A, B, C, D choices are ['36\u00b0', '41\u00b0', '40\u00b0', '49\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10764.jpg"
-  },
-  {
-    "id": 11073,
-    "problem_id": 10765,
-    "problem": "<image>In triangle ABC shown in the figure, where angle B is 44\u00b0 and angle C is 54\u00b0, AD bisects angle BAC and intersects BC at D. DE is parallel to AB and intersects AC at E. What is the measure of angle ADE?. A, B, C, D choices are ['36\u00b0', '41\u00b0', '40\u00b0', '49\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10765.jpg"
-  },
-  {
-    "id": 11074,
-    "problem_id": 10766,
-    "problem": "<image>As shown in the figure, line AB intersects with CD at point O. If \u2220COB=140\u00b0, then what are the degree measures of \u22201 and \u22202? (). A, B, C, D choices are ['140\u00b0,40\u00b0', '40\u00b0,150\u00b0', '40\u00b0,140\u00b0', '150\u00b0,40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10766.jpg"
-  },
-  {
-    "id": 11075,
-    "problem_id": 10767,
-    "problem": "<image>As shown in the figure, line AB intersects with CD at point O. If \u2220COB=140\u00b0, then what are the degree measures of \u22201 and \u22202? (). A, B, C, D choices are ['140\u00b0,40\u00b0', '40\u00b0,150\u00b0', '40\u00b0,140\u00b0', '150\u00b0,40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10767.jpg"
-  },
-  {
-    "id": 11076,
-    "problem_id": 10768,
-    "problem": "<image>As shown in the figure, line AB intersects with CD at point O. If \u2220COB=140\u00b0, then what are the degree measures of \u22201 and \u22202? (). A, B, C, D choices are ['140\u00b0,40\u00b0', '40\u00b0,150\u00b0', '40\u00b0,140\u00b0', '150\u00b0,40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10768.jpg"
-  },
-  {
-    "id": 11077,
-    "problem_id": 10769,
-    "problem": "<image>As shown in the figure, line AB intersects with CD at point O. If \u2220COB=140\u00b0, then what are the degree measures of \u22201 and \u22202? (). A, B, C, D choices are ['140\u00b0,40\u00b0', '40\u00b0,150\u00b0', '40\u00b0,140\u00b0', '150\u00b0,40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10769.jpg"
-  },
-  {
-    "id": 11078,
-    "problem_id": 10770,
-    "problem": "<image>As shown in the figure, line AB intersects with CD at point O. If \u2220COB=140\u00b0, then what are the degree measures of \u22201 and \u22202? (). A, B, C, D choices are ['140\u00b0,40\u00b0', '40\u00b0,150\u00b0', '40\u00b0,140\u00b0', '150\u00b0,40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10770.jpg"
-  },
-  {
-    "id": 11079,
-    "problem_id": 10771,
-    "problem": "<image>In triangle ABC, as shown in the figure, \u2220ACB=90\u00b0. The line DF passing through point C is parallel to the bisector AE of \u2220BAC. If \u2220B=50\u00b0, then the value of \u2220BCF is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10771.jpg"
-  },
-  {
-    "id": 11080,
-    "problem_id": 10772,
-    "problem": "<image>In triangle ABC, as shown in the figure, \u2220ACB=90\u00b0. The line DF passing through point C is parallel to the bisector AE of \u2220BAC. If \u2220B=50\u00b0, then the value of \u2220BCF is (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '70\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10772.jpg"
-  },
-  {
-    "id": 11081,
-    "problem_id": 10773,
-    "problem": "<image>A right-angled triangle board is placed as shown, so that the short leg of the triangle containing a 30\u00b0 angle coincides with one of the legs of the triangle containing a 45\u00b0 angle. What is the degree measure of angle 1? (). A, B, C, D choices are ['75\u00b0', '60\u00b0', '45\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10773.jpg"
-  },
-  {
-    "id": 11082,
-    "problem_id": 10774,
-    "problem": "<image>As shown in the figure, it is known that line a and b are intersected by line c. If a\u2225b, \u22201=110\u00b0, \u22202=40\u00b0, then \u22203=(). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10774.jpg"
-  },
-  {
-    "id": 11083,
-    "problem_id": 10775,
-    "problem": "<image>As shown in the figure, it is a staircase. The height BC is 1.5m, and the hypotenuse AC is 2.5m. If we want to lay carpet on the stairs, at least how much carpet do we need?. A, B, C, D choices are ['2.5m', '3m', '3.5m', '4m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10775.jpg"
-  },
-  {
-    "id": 11084,
-    "problem_id": 10776,
-    "problem": "<image>As shown in the figure, it is a staircase. The height BC is 1.5m, and the hypotenuse AC is 2.5m. If we want to lay carpet on the stairs, at least how much carpet do we need?. A, B, C, D choices are ['2.5m', '3m', '3.5m', '4m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10776.jpg"
-  },
-  {
-    "id": 11085,
-    "problem_id": 10777,
-    "problem": "<image>As shown in the figure, it is a staircase. The height BC is 1.5m, and the hypotenuse AC is 2.5m. If we want to lay carpet on the stairs, at least how much carpet do we need?. A, B, C, D choices are ['2.5m', '3m', '3.5m', '4m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10777.jpg"
-  },
-  {
-    "id": 11086,
-    "problem_id": 10778,
-    "problem": "<image>As shown in the figure, it is a staircase. The height BC is 1.5m, and the hypotenuse AC is 2.5m. If we want to lay carpet on the stairs, at least how much carpet do we need?. A, B, C, D choices are ['2.5m', '3m', '3.5m', '4m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10778.jpg"
-  },
-  {
-    "id": 11087,
-    "problem_id": 10779,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 56\u00b0, \u22202 = 37\u00b0, then the degree of \u22203 is ().. A, B, C, D choices are ['87\u00b0', '97\u00b0', '86\u00b0', '93\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10779.jpg"
-  },
-  {
-    "id": 11090,
-    "problem_id": 10780,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 56\u00b0, \u22202 = 37\u00b0, then the degree of \u22203 is ().. A, B, C, D choices are ['87\u00b0', '97\u00b0', '86\u00b0', '93\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10780.jpg"
-  },
-  {
-    "id": 11091,
-    "problem_id": 10781,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 56\u00b0, \u22202 = 37\u00b0, then the degree of \u22203 is ().. A, B, C, D choices are ['87\u00b0', '97\u00b0', '86\u00b0', '93\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10781.jpg"
-  },
-  {
-    "id": 11092,
-    "problem_id": 10782,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 56\u00b0, \u22202 = 37\u00b0, then the degree of \u22203 is ().. A, B, C, D choices are ['87\u00b0', '97\u00b0', '86\u00b0', '93\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10782.jpg"
-  },
-  {
-    "id": 11093,
-    "problem_id": 10783,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201 = 56\u00b0, \u22202 = 37\u00b0, then the degree of \u22203 is ().. A, B, C, D choices are ['87\u00b0', '97\u00b0', '86\u00b0', '93\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10783.jpg"
-  },
-  {
-    "id": 11094,
-    "problem_id": 10784,
-    "problem": "<image>Given that AE is parallel to BD, \u22201 = 130\u00b0, \u22202 = 30\u00b0, then what is the measure of \u2220C?. A, B, C, D choices are ['30\u00b0', '20\u00b0', '130\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10784.jpg"
-  },
-  {
-    "id": 11095,
-    "problem_id": 10785,
-    "problem": "<image>As shown in the figure, it is known that AD//BC, \u2220B=32\u00b0, DB bisects \u2220ADE, then what is the value of \u2220DEC?. A, B, C, D choices are ['64\u00b0', '66\u00b0', '74\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10785.jpg"
-  },
-  {
-    "id": 11096,
-    "problem_id": 10786,
-    "problem": "<image>As shown in the figure, it is known that AD//BC, \u2220B=32\u00b0, DB bisects \u2220ADE, then what is the value of \u2220DEC?. A, B, C, D choices are ['64\u00b0', '66\u00b0', '74\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10786.jpg"
-  },
-  {
-    "id": 11097,
-    "problem_id": 10787,
-    "problem": "<image>As shown in the figure, AD is the bisector of \u2220EAC, AD\u2225BC, and \u2220B=35\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['55\u00b0', '45\u00b0', '35\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10787.jpg"
-  },
-  {
-    "id": 11098,
-    "problem_id": 10788,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10788.jpg"
-  },
-  {
-    "id": 11099,
-    "problem_id": 10789,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10789.jpg"
-  },
-  {
-    "id": 11100,
-    "problem_id": 10790,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10790.jpg"
-  },
-  {
-    "id": 11101,
-    "problem_id": 10791,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10791.jpg"
-  },
-  {
-    "id": 11102,
-    "problem_id": 10792,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10792.jpg"
-  },
-  {
-    "id": 11103,
-    "problem_id": 10793,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10793.jpg"
-  },
-  {
-    "id": 11104,
-    "problem_id": 10794,
-    "problem": "<image>As shown in the figure, the vertex of a right-angled triangle is placed on one side of a ruler. If \u22202 = 40\u00b0, what is the degree measure of \u22201? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10794.jpg"
-  },
-  {
-    "id": 11106,
-    "problem_id": 10795,
-    "problem": "<image>As shown in the figure, line a is parallel to line b, \u22201=85\u00b0, \u22202=35\u00b0, what is the value of \u22203? (). A, B, C, D choices are ['85\u00b0', '60\u00b0', '50\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10795.jpg"
-  },
-  {
-    "id": 11107,
-    "problem_id": 10796,
-    "problem": "<image>As shown in the figure, BC is perpendicular to AE at point C, CD is parallel to AB, and \u2220B=50\u00b0. Then, what is the measure of \u22201? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10796.jpg"
-  },
-  {
-    "id": 11108,
-    "problem_id": 10797,
-    "problem": "<image>As shown in the figure, BC is perpendicular to AE at point C, CD is parallel to AB, and \u2220B=50\u00b0. Then, what is the measure of \u22201? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10797.jpg"
-  },
-  {
-    "id": 11109,
-    "problem_id": 10798,
-    "problem": "<image>As shown in the figure, BC is perpendicular to AE at point C, CD is parallel to AB, and \u2220B=50\u00b0. Then, what is the measure of \u22201? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10798.jpg"
-  },
-  {
-    "id": 11110,
-    "problem_id": 10799,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10799.jpg"
-  },
-  {
-    "id": 11111,
-    "problem_id": 10800,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10800.jpg"
-  },
-  {
-    "id": 11112,
-    "problem_id": 10801,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10801.jpg"
-  },
-  {
-    "id": 11113,
-    "problem_id": 10802,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10802.jpg"
-  },
-  {
-    "id": 11114,
-    "problem_id": 10803,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10803.jpg"
-  },
-  {
-    "id": 11115,
-    "problem_id": 10804,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10804.jpg"
-  },
-  {
-    "id": 11116,
-    "problem_id": 10805,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10805.jpg"
-  },
-  {
-    "id": 11117,
-    "problem_id": 10806,
-    "problem": "<image>Given the diagram, if \u22201=100\u00b0 and \u2220C=70\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '30\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10806.jpg"
-  },
-  {
-    "id": 11118,
-    "problem_id": 10807,
-    "problem": "<image>Given the figure, in circle O, if \u2220ABC = 50\u00b0, then \u2220AOC is equal to (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10807.jpg"
-  },
-  {
-    "id": 11119,
-    "problem_id": 10808,
-    "problem": "<image>Given the figure, in circle O, if \u2220ABC = 50\u00b0, then \u2220AOC is equal to (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10808.jpg"
-  },
-  {
-    "id": 11120,
-    "problem_id": 10809,
-    "problem": "<image>Given the figure, in circle O, if \u2220ABC = 50\u00b0, then \u2220AOC is equal to (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10809.jpg"
-  },
-  {
-    "id": 11121,
-    "problem_id": 10810,
-    "problem": "<image>Given the figure, in circle O, if \u2220ABC = 50\u00b0, then \u2220AOC is equal to (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '90\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10810.jpg"
-  },
-  {
-    "id": 11122,
-    "problem_id": 10811,
-    "problem": "<image>As shown in the figure, two right-angled triangles with angles of 30\u00b0 and 45\u00b0 are combined into the following shape. In the figure, \u2220C=90\u00b0, \u2220B=45\u00b0, \u2220E=30\u00b0. What is the degree of \u2220BFD? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '30\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10811.jpg"
-  },
-  {
-    "id": 11123,
-    "problem_id": 10812,
-    "problem": "<image>As shown in the figure, two right-angled triangles with angles of 30\u00b0 and 45\u00b0 are combined into the following shape. In the figure, \u2220C=90\u00b0, \u2220B=45\u00b0, \u2220E=30\u00b0. What is the degree of \u2220BFD? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '30\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{A}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10812.jpg"
-  },
-  {
-    "id": 11124,
-    "problem_id": 10813,
-    "problem": "<image>As shown in the figure, two right-angled triangles with angles of 30\u00b0 and 45\u00b0 are combined into the following shape. In the figure, \u2220C=90\u00b0, \u2220B=45\u00b0, \u2220E=30\u00b0. What is the degree of \u2220BFD? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '30\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10813.jpg"
-  },
-  {
-    "id": 11125,
-    "problem_id": 10814,
-    "problem": "<image>As shown in the figure, two right-angled triangles with angles of 30\u00b0 and 45\u00b0 are combined into the following shape. In the figure, \u2220C=90\u00b0, \u2220B=45\u00b0, \u2220E=30\u00b0. What is the degree of \u2220BFD? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '30\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10814.jpg"
-  },
-  {
-    "id": 11126,
-    "problem_id": 10815,
-    "problem": "<image>As shown in the figure, two right-angled triangles with angles of 30\u00b0 and 45\u00b0 are combined into the following shape. In the figure, \u2220C=90\u00b0, \u2220B=45\u00b0, \u2220E=30\u00b0. What is the degree of \u2220BFD? (). A, B, C, D choices are ['15\u00b0', '25\u00b0', '30\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10815.jpg"
-  },
-  {
-    "id": 11127,
-    "problem_id": 10816,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, E is a point on AB, ED bisects \u2220BEC and intersects CD at point D, \u2220BEC=100\u00b0. What is the degree measure of \u2220D? (). A, B, C, D choices are ['50\u00b0', '100\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10816.jpg"
-  },
-  {
-    "id": 11128,
-    "problem_id": 10817,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, E is a point on AB, ED bisects \u2220BEC and intersects CD at point D, \u2220BEC=100\u00b0. What is the degree measure of \u2220D? (). A, B, C, D choices are ['50\u00b0', '100\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10817.jpg"
-  },
-  {
-    "id": 11129,
-    "problem_id": 10818,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, E is a point on AB, ED bisects \u2220BEC and intersects CD at point D, \u2220BEC=100\u00b0. What is the degree measure of \u2220D? (). A, B, C, D choices are ['50\u00b0', '100\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10818.jpg"
-  },
-  {
-    "id": 11130,
-    "problem_id": 10819,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, E is a point on AB, ED bisects \u2220BEC and intersects CD at point D, \u2220BEC=100\u00b0. What is the degree measure of \u2220D? (). A, B, C, D choices are ['50\u00b0', '100\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10819.jpg"
-  },
-  {
-    "id": 11131,
-    "problem_id": 10820,
-    "problem": "<image>As shown in the figure, it is known that AB\u2225CD, E is a point on AB, ED bisects \u2220BEC and intersects CD at point D, \u2220BEC=100\u00b0. What is the degree measure of \u2220D? (). A, B, C, D choices are ['50\u00b0', '100\u00b0', '80\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10820.jpg"
-  },
-  {
-    "id": 11132,
-    "problem_id": 10821,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, AD bisects angle BAC, and if angle BAD is 70\u00b0, then what is the degree measure of angle ACD? (). A, B, C, D choices are ['40\u00b0', '35\u00b0', '50\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10821.jpg"
-  },
-  {
-    "id": 11133,
-    "problem_id": 10822,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, AD bisects angle BAC, and if angle BAD is 70\u00b0, then what is the degree measure of angle ACD? (). A, B, C, D choices are ['40\u00b0', '35\u00b0', '50\u00b0', '45\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10822.jpg"
-  },
-  {
-    "id": 11134,
-    "problem_id": 10823,
-    "problem": "<image>As shown in the diagram, points A, B, and C are three points on circle O. If \u2220OBC=50\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10823.jpg"
-  },
-  {
-    "id": 11135,
-    "problem_id": 10824,
-    "problem": "<image>As shown in the diagram, points A, B, and C are three points on circle O. If \u2220OBC=50\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10824.jpg"
-  },
-  {
-    "id": 11136,
-    "problem_id": 10825,
-    "problem": "<image>As shown in the diagram, points A, B, and C are three points on circle O. If \u2220OBC=50\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10825.jpg"
-  },
-  {
-    "id": 11137,
-    "problem_id": 10826,
-    "problem": "<image>As shown in the diagram, points A, B, and C are three points on circle O. If \u2220OBC=50\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10826.jpg"
-  },
-  {
-    "id": 11138,
-    "problem_id": 10827,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10827.jpg"
-  },
-  {
-    "id": 11139,
-    "problem_id": 10828,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10828.jpg"
-  },
-  {
-    "id": 11140,
-    "problem_id": 10829,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10829.jpg"
-  },
-  {
-    "id": 11141,
-    "problem_id": 10830,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10830.jpg"
-  },
-  {
-    "id": 11142,
-    "problem_id": 10831,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10831.jpg"
-  },
-  {
-    "id": 11143,
-    "problem_id": 10832,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10832.jpg"
-  },
-  {
-    "id": 11144,
-    "problem_id": 10833,
-    "problem": "<image>Place a ruler and a triangular board as shown in the figure. If \u22201 = 40\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['125\u00b0', '120\u00b0', '140\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10833.jpg"
-  },
-  {
-    "id": 11145,
-    "problem_id": 10834,
-    "problem": "<image>As shown in the diagram, in triangle ABC, \u2220C=90\u00b0, AC=4cm, AB=7cm, AD bisects \u2220BAC and intersects BC at D, DE \u22a5 AB at E. The length of EB is ().. A, B, C, D choices are ['3\u339d', '4\u339d', '5\u339d', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10834.jpg"
-  },
-  {
-    "id": 11146,
-    "problem_id": 10835,
-    "problem": "<image>As shown in the diagram, in triangle ABC, \u2220C=90\u00b0, AC=4cm, AB=7cm, AD bisects \u2220BAC and intersects BC at D, DE \u22a5 AB at E. The length of EB is ().. A, B, C, D choices are ['3\u339d', '4\u339d', '5\u339d', '\u4e0d\u80fd\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10835.jpg"
-  },
-  {
-    "id": 11147,
-    "problem_id": 10836,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10836.jpg"
-  },
-  {
-    "id": 11148,
-    "problem_id": 10837,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10837.jpg"
-  },
-  {
-    "id": 11149,
-    "problem_id": 10838,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10838.jpg"
-  },
-  {
-    "id": 11150,
-    "problem_id": 10839,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10839.jpg"
-  },
-  {
-    "id": 11151,
-    "problem_id": 10840,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10840.jpg"
-  },
-  {
-    "id": 11152,
-    "problem_id": 10841,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10841.jpg"
-  },
-  {
-    "id": 11153,
-    "problem_id": 10842,
-    "problem": "<image>In the figure, A, C, and B are three points on circle O. If \u2220AOC = 40\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10842.jpg"
-  },
-  {
-    "id": 11154,
-    "problem_id": 10843,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10843.jpg"
-  },
-  {
-    "id": 11155,
-    "problem_id": 10844,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10844.jpg"
-  },
-  {
-    "id": 11156,
-    "problem_id": 10845,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10845.jpg"
-  },
-  {
-    "id": 11157,
-    "problem_id": 10846,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10846.jpg"
-  },
-  {
-    "id": 11158,
-    "problem_id": 10847,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10847.jpg"
-  },
-  {
-    "id": 11159,
-    "problem_id": 10848,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10848.jpg"
-  },
-  {
-    "id": 11160,
-    "problem_id": 10849,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABO = 30\u00b0, what is the measure of \u2220ACB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10849.jpg"
-  },
-  {
-    "id": 11161,
-    "problem_id": 10850,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10850.jpg"
-  },
-  {
-    "id": 11162,
-    "problem_id": 10851,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10851.jpg"
-  },
-  {
-    "id": 11163,
-    "problem_id": 10852,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10852.jpg"
-  },
-  {
-    "id": 11164,
-    "problem_id": 10853,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10853.jpg"
-  },
-  {
-    "id": 11165,
-    "problem_id": 10854,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10854.jpg"
-  },
-  {
-    "id": 11166,
-    "problem_id": 10855,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10855.jpg"
-  },
-  {
-    "id": 11167,
-    "problem_id": 10856,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10856.jpg"
-  },
-  {
-    "id": 11168,
-    "problem_id": 10857,
-    "problem": "<image>Given the figure below, \u25b3OAD\u224c\u25b3OBC, and \u2220O=70\u00b0, \u2220C=25\u00b0, then \u2220OAD=() \n\n(Note: no English parts in the input, so no need to change anything). A, B, C, D choices are ['95\u00b0', '85\u00b0', '75\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10857.jpg"
-  },
-  {
-    "id": 11169,
-    "problem_id": 10858,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10858.jpg"
-  },
-  {
-    "id": 11170,
-    "problem_id": 10859,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10859.jpg"
-  },
-  {
-    "id": 11171,
-    "problem_id": 10860,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10860.jpg"
-  },
-  {
-    "id": 11172,
-    "problem_id": 10861,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10861.jpg"
-  },
-  {
-    "id": 11173,
-    "problem_id": 10862,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10862.jpg"
-  },
-  {
-    "id": 11174,
-    "problem_id": 10863,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10863.jpg"
-  },
-  {
-    "id": 11175,
-    "problem_id": 10864,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC. If \u2220ABC = 40\u00b0, what is the degree measure of \u2220AOC? (). A, B, C, D choices are ['20\u00b0', '40\u00b0', '60\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10864.jpg"
-  },
-  {
-    "id": 11179,
-    "problem_id": 10865,
-    "problem": "<image>In triangle ABC as shown, where angle C is 90 degrees, point D is on side AC, and DE is parallel to AB. If angle ADE is 46 degrees, what is the degree measure of angle B?. A, B, C, D choices are ['34\u00b0', '44\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10865.jpg"
-  },
-  {
-    "id": 11180,
-    "problem_id": 10866,
-    "problem": "<image>In triangle ABC as shown, where angle C is 90 degrees, point D is on side AC, and DE is parallel to AB. If angle ADE is 46 degrees, what is the degree measure of angle B?. A, B, C, D choices are ['34\u00b0', '44\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10866.jpg"
-  },
-  {
-    "id": 11181,
-    "problem_id": 10867,
-    "problem": "<image>In triangle ABC as shown, where angle C is 90 degrees, point D is on side AC, and DE is parallel to AB. If angle ADE is 46 degrees, what is the degree measure of angle B?. A, B, C, D choices are ['34\u00b0', '44\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10867.jpg"
-  },
-  {
-    "id": 11182,
-    "problem_id": 10868,
-    "problem": "<image>In triangle ABC as shown, where angle C is 90 degrees, point D is on side AC, and DE is parallel to AB. If angle ADE is 46 degrees, what is the degree measure of angle B?. A, B, C, D choices are ['34\u00b0', '44\u00b0', '46\u00b0', '54\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10868.jpg"
-  },
-  {
-    "id": 11183,
-    "problem_id": 10869,
-    "problem": "<image>A certain flower and tree farm has an empty land in the shape of an isosceles trapezoid ABCD, with midpoints E, F, G, and H on each side. The diagonal AC measures 10 meters. Now, they want to enclose the area of quadrilateral EFGH with a fence. What is the total length of the fence needed?. A, B, C, D choices are ['40\u7c73', '30\u7c73', '20\u7c73', '10\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10869.jpg"
-  },
-  {
-    "id": 11184,
-    "problem_id": 10870,
-    "problem": "<image>A certain flower and tree farm has an empty land in the shape of an isosceles trapezoid ABCD, with midpoints E, F, G, and H on each side. The diagonal AC measures 10 meters. Now, they want to enclose the area of quadrilateral EFGH with a fence. What is the total length of the fence needed?. A, B, C, D choices are ['40\u7c73', '30\u7c73', '20\u7c73', '10\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10870.jpg"
-  },
-  {
-    "id": 11185,
-    "problem_id": 10871,
-    "problem": "<image>As shown in the figure, if BD = 120m, DC = 60m, and EC = 50m, what is the width AB of the river? (). A, B, C, D choices are ['120m', '100m', '75m', '25m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10871.jpg"
-  },
-  {
-    "id": 11186,
-    "problem_id": 10872,
-    "problem": "<image>As shown in the figure, if BD = 120m, DC = 60m, and EC = 50m, what is the width AB of the river? (). A, B, C, D choices are ['120m', '100m', '75m', '25m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10872.jpg"
-  },
-  {
-    "id": 11187,
-    "problem_id": 10873,
-    "problem": "<image>As shown in the figure, if BD = 120m, DC = 60m, and EC = 50m, what is the width AB of the river? (). A, B, C, D choices are ['120m', '100m', '75m', '25m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10873.jpg"
-  },
-  {
-    "id": 11188,
-    "problem_id": 10874,
-    "problem": "<image>As shown in the figure, if BD = 120m, DC = 60m, and EC = 50m, what is the width AB of the river? (). A, B, C, D choices are ['120m', '100m', '75m', '25m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10874.jpg"
-  },
-  {
-    "id": 11189,
-    "problem_id": 10875,
-    "problem": "<image>As shown in the figure, if BD = 120m, DC = 60m, and EC = 50m, what is the width AB of the river? (). A, B, C, D choices are ['120m', '100m', '75m', '25m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10875.jpg"
-  },
-  {
-    "id": 11190,
-    "problem_id": 10876,
-    "problem": "<image>As shown in the figure, if BD = 120m, DC = 60m, and EC = 50m, what is the width AB of the river? (). A, B, C, D choices are ['120m', '100m', '75m', '25m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10876.jpg"
-  },
-  {
-    "id": 11191,
-    "problem_id": 10877,
-    "problem": "<image>In triangle ABC as shown, angle A is 90 degrees, point D is on side AC, and DE is parallel to BC. If angle 1 is 145 degrees, what is the degree measure of angle B? (). A, B, C, D choices are ['35\u00b0', '25\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10877.jpg"
-  },
-  {
-    "id": 11192,
-    "problem_id": 10878,
-    "problem": "<image>In triangle ABC as shown, angle A is 90 degrees, point D is on side AC, and DE is parallel to BC. If angle 1 is 145 degrees, what is the degree measure of angle B? (). A, B, C, D choices are ['35\u00b0', '25\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10878.jpg"
-  },
-  {
-    "id": 11193,
-    "problem_id": 10879,
-    "problem": "<image>In triangle ABC as shown, angle A is 90 degrees, point D is on side AC, and DE is parallel to BC. If angle 1 is 145 degrees, what is the degree measure of angle B? (). A, B, C, D choices are ['35\u00b0', '25\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10879.jpg"
-  },
-  {
-    "id": 11194,
-    "problem_id": 10880,
-    "problem": "<image>In triangle ABC as shown, angle A is 90 degrees, point D is on side AC, and DE is parallel to BC. If angle 1 is 145 degrees, what is the degree measure of angle B? (). A, B, C, D choices are ['35\u00b0', '25\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10880.jpg"
-  },
-  {
-    "id": 11195,
-    "problem_id": 10881,
-    "problem": "<image>In triangle ABC as shown, angle A is 90 degrees, point D is on side AC, and DE is parallel to BC. If angle 1 is 145 degrees, what is the degree measure of angle B? (). A, B, C, D choices are ['35\u00b0', '25\u00b0', '45\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10881.jpg"
-  },
-  {
-    "id": 11196,
-    "problem_id": 10882,
-    "problem": "<image>As shown in the diagram, AB is parallel to CD and BC is parallel to DE. If \u2220B = 40\u00b0, what is the degree measure of \u2220D? (). A, B, C, D choices are ['40\u00b0', '140\u00b0', '160\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10882.jpg"
-  },
-  {
-    "id": 11198,
-    "problem_id": 10883,
-    "problem": "<image>As shown in the figure, the three vertices of triangle ABC are on lines a and b respectively, and a is parallel to b. If \u22201 = 120\u00b0 and \u22202 = 80\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10883.jpg"
-  },
-  {
-    "id": 11199,
-    "problem_id": 10884,
-    "problem": "<image>As shown in the figure, the three vertices of triangle ABC are on lines a and b respectively, and a is parallel to b. If \u22201 = 120\u00b0 and \u22202 = 80\u00b0, what is the degree measure of \u22203? (). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10884.jpg"
-  },
-  {
-    "id": 11200,
-    "problem_id": 10885,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10885.jpg"
-  },
-  {
-    "id": 11201,
-    "problem_id": 10886,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10886.jpg"
-  },
-  {
-    "id": 11202,
-    "problem_id": 10887,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10887.jpg"
-  },
-  {
-    "id": 11203,
-    "problem_id": 10888,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10888.jpg"
-  },
-  {
-    "id": 11204,
-    "problem_id": 10889,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10889.jpg"
-  },
-  {
-    "id": 11205,
-    "problem_id": 10890,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10890.jpg"
-  },
-  {
-    "id": 11206,
-    "problem_id": 10891,
-    "problem": "<image>During a class activity, Group A and Group B of a school measured some objects on the campus under the sun at the same time. The following is some information they obtained through measurement: Figure 1 shows that Group A measured a bamboo pole standing upright on the ground, with a length of 80cm and a shadow length of 60cm. Figure 2 shows that Group B measured the shadow length of the school flagpole as 900cm. What is the length of the flagpole?. A, B, C, D choices are ['900cm', '1000cm', '1100cm', '1200cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10891.jpg"
-  },
-  {
-    "id": 11207,
-    "problem_id": 10892,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220BCD = 110\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '90\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10892.jpg"
-  },
-  {
-    "id": 11208,
-    "problem_id": 10893,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220BCD = 110\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '90\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10893.jpg"
-  },
-  {
-    "id": 11209,
-    "problem_id": 10894,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220BCD = 110\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '90\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10894.jpg"
-  },
-  {
-    "id": 11210,
-    "problem_id": 10895,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220BCD = 110\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '90\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10895.jpg"
-  },
-  {
-    "id": 11211,
-    "problem_id": 10896,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220BCD = 110\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '90\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10896.jpg"
-  },
-  {
-    "id": 11212,
-    "problem_id": 10897,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If \u2220BCD = 110\u00b0, then what is the degree measure of \u2220BAD? (). A, B, C, D choices are ['140\u00b0', '110\u00b0', '90\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10897.jpg"
-  },
-  {
-    "id": 11213,
-    "problem_id": 10898,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10898.jpg"
-  },
-  {
-    "id": 11214,
-    "problem_id": 10899,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10899.jpg"
-  },
-  {
-    "id": 11215,
-    "problem_id": 10900,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10900.jpg"
-  },
-  {
-    "id": 11216,
-    "problem_id": 10901,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10901.jpg"
-  },
-  {
-    "id": 11217,
-    "problem_id": 10902,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10902.jpg"
-  },
-  {
-    "id": 11218,
-    "problem_id": 10903,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10903.jpg"
-  },
-  {
-    "id": 11219,
-    "problem_id": 10904,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10904.jpg"
-  },
-  {
-    "id": 11220,
-    "problem_id": 10905,
-    "problem": "<image>As shown in the diagram, if the slant height of a cone mold is 10cm and the radius of its base is 5cm, then what is the lateral surface area of this cone mold? (). A, B, C, D choices are ['10\u03c0cm', '50\u03c0cm', '100\u03c0cm', '150\u03c0cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10905.jpg"
-  },
-  {
-    "id": 11221,
-    "problem_id": 10906,
-    "problem": "<image>Given that AB is parallel to CD and \u2220CEF is 110\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10906.jpg"
-  },
-  {
-    "id": 11222,
-    "problem_id": 10907,
-    "problem": "<image>Given that AB is parallel to CD and \u2220CEF is 110\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['90\u00b0', '80\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10907.jpg"
-  },
-  {
-    "id": 11223,
-    "problem_id": 10908,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10908.jpg"
-  },
-  {
-    "id": 11224,
-    "problem_id": 10909,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10909.jpg"
-  },
-  {
-    "id": 11225,
-    "problem_id": 10910,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10910.jpg"
-  },
-  {
-    "id": 11226,
-    "problem_id": 10911,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10911.jpg"
-  },
-  {
-    "id": 11227,
-    "problem_id": 10912,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10912.jpg"
-  },
-  {
-    "id": 11228,
-    "problem_id": 10913,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10913.jpg"
-  },
-  {
-    "id": 11229,
-    "problem_id": 10914,
-    "problem": "<image>As shown in the figure, during a practical activity class, Xiaoming measured the distance between points B and C in a pond. He first selected point A on one side of the pond, and then measured the midpoint of AB and AC, which is point D and E, respectively. DE is 10 meters, so he can calculate the distance between points B and C in the pond, which is ().. A, B, C, D choices are ['5m', '10m', '15m', '20m'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10914.jpg"
-  },
-  {
-    "id": 11230,
-    "problem_id": 10915,
-    "problem": "<image>In triangle ABC as shown, where \u2220A=70\u00b0, point O is the intersection of the perpendicular bisectors of AB and AC. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10915.jpg"
-  },
-  {
-    "id": 11231,
-    "problem_id": 10916,
-    "problem": "<image>In triangle ABC as shown, where \u2220A=70\u00b0, point O is the intersection of the perpendicular bisectors of AB and AC. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10916.jpg"
-  },
-  {
-    "id": 11232,
-    "problem_id": 10917,
-    "problem": "<image>In triangle ABC as shown, where \u2220A=70\u00b0, point O is the intersection of the perpendicular bisectors of AB and AC. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10917.jpg"
-  },
-  {
-    "id": 11233,
-    "problem_id": 10918,
-    "problem": "<image>In triangle ABC as shown, where \u2220A=70\u00b0, point O is the intersection of the perpendicular bisectors of AB and AC. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10918.jpg"
-  },
-  {
-    "id": 11234,
-    "problem_id": 10919,
-    "problem": "<image>In triangle ABC as shown, where \u2220A=70\u00b0, point O is the intersection of the perpendicular bisectors of AB and AC. What is the degree measure of \u2220BCO? (). A, B, C, D choices are ['40\u00b0', '30\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10919.jpg"
-  },
-  {
-    "id": 11235,
-    "problem_id": 10920,
-    "problem": "<image>In parallelogram ABCD shown in the figure, DE is perpendicular to AB at point E, and \u2220EDA=35\u00b0. What is the measure of \u2220C? (). A, B, C, D choices are ['125\u00b0', '105\u00b0', '65\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10920.jpg"
-  },
-  {
-    "id": 11236,
-    "problem_id": 10921,
-    "problem": "<image>As shown in the diagram, the external angle bisectors BD and CD of triangle ABC intersect at point D. If \u2220A=70\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '70\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10921.jpg"
-  },
-  {
-    "id": 11237,
-    "problem_id": 10922,
-    "problem": "<image>As shown in the diagram, the external angle bisectors BD and CD of triangle ABC intersect at point D. If \u2220A=70\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '70\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10922.jpg"
-  },
-  {
-    "id": 11238,
-    "problem_id": 10923,
-    "problem": "<image>As shown in the diagram, the external angle bisectors BD and CD of triangle ABC intersect at point D. If \u2220A=70\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '70\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10923.jpg"
-  },
-  {
-    "id": 11239,
-    "problem_id": 10924,
-    "problem": "<image>As shown in the diagram, the external angle bisectors BD and CD of triangle ABC intersect at point D. If \u2220A=70\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '70\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10924.jpg"
-  },
-  {
-    "id": 11240,
-    "problem_id": 10925,
-    "problem": "<image>As shown in the diagram, the external angle bisectors BD and CD of triangle ABC intersect at point D. If \u2220A=70\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '70\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10925.jpg"
-  },
-  {
-    "id": 11241,
-    "problem_id": 10926,
-    "problem": "<image>As shown in the diagram, the external angle bisectors BD and CD of triangle ABC intersect at point D. If \u2220A=70\u00b0, what is the degree measure of \u2220BDC? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '70\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10926.jpg"
-  },
-  {
-    "id": 11242,
-    "problem_id": 10927,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O. If \u2220AOC = 130\u00b0, then what is the degree of \u2220D? (). A, B, C, D choices are ['20\u00b0', '25\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10927.jpg"
-  },
-  {
-    "id": 11243,
-    "problem_id": 10928,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O. If \u2220AOC = 130\u00b0, then what is the degree of \u2220D? (). A, B, C, D choices are ['20\u00b0', '25\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10928.jpg"
-  },
-  {
-    "id": 11244,
-    "problem_id": 10929,
-    "problem": "<image>In the diamond ABCD shown, where AC=8 and BD=6, what is the area of triangle ABD?. A, B, C, D choices are ['12', '16', '20', '24'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10929.jpg"
-  },
-  {
-    "id": 11245,
-    "problem_id": 10930,
-    "problem": "<image>Given triangle \u25b3ABO \u224c \u25b3DCO as shown in the figure, where \u2220D = 80\u00b0 and \u2220DOC = 70\u00b0, find the measure of \u2220B.. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10930.jpg"
-  },
-  {
-    "id": 11246,
-    "problem_id": 10931,
-    "problem": "<image>Given triangle \u25b3ABO \u224c \u25b3DCO as shown in the figure, where \u2220D = 80\u00b0 and \u2220DOC = 70\u00b0, find the measure of \u2220B.. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10931.jpg"
-  },
-  {
-    "id": 11247,
-    "problem_id": 10932,
-    "problem": "<image>Given triangle \u25b3ABO \u224c \u25b3DCO as shown in the figure, where \u2220D = 80\u00b0 and \u2220DOC = 70\u00b0, find the measure of \u2220B.. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10932.jpg"
-  },
-  {
-    "id": 11248,
-    "problem_id": 10933,
-    "problem": "<image>Given triangle \u25b3ABO \u224c \u25b3DCO as shown in the figure, where \u2220D = 80\u00b0 and \u2220DOC = 70\u00b0, find the measure of \u2220B.. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10933.jpg"
-  },
-  {
-    "id": 11249,
-    "problem_id": 10934,
-    "problem": "<image>Given triangle \u25b3ABO \u224c \u25b3DCO as shown in the figure, where \u2220D = 80\u00b0 and \u2220DOC = 70\u00b0, find the measure of \u2220B.. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10934.jpg"
-  },
-  {
-    "id": 11250,
-    "problem_id": 10935,
-    "problem": "<image>Given triangle \u25b3ABO \u224c \u25b3DCO as shown in the figure, where \u2220D = 80\u00b0 and \u2220DOC = 70\u00b0, find the measure of \u2220B.. A, B, C, D choices are ['35\u00b0', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10935.jpg"
-  },
-  {
-    "id": 11251,
-    "problem_id": 10936,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10936.jpg"
-  },
-  {
-    "id": 11252,
-    "problem_id": 10937,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10937.jpg"
-  },
-  {
-    "id": 11253,
-    "problem_id": 10938,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10938.jpg"
-  },
-  {
-    "id": 11254,
-    "problem_id": 10939,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10939.jpg"
-  },
-  {
-    "id": 11255,
-    "problem_id": 10940,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10940.jpg"
-  },
-  {
-    "id": 11256,
-    "problem_id": 10941,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10941.jpg"
-  },
-  {
-    "id": 11257,
-    "problem_id": 10942,
-    "problem": "<image>Given the diagram, it is known that \u22201+\u22202=180\u00b0, and \u22203=55\u00b0. What is the degree measure of \u22204? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10942.jpg"
-  },
-  {
-    "id": 11258,
-    "problem_id": 10943,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10943.jpg"
-  },
-  {
-    "id": 11259,
-    "problem_id": 10944,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10944.jpg"
-  },
-  {
-    "id": 11260,
-    "problem_id": 10945,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10945.jpg"
-  },
-  {
-    "id": 11261,
-    "problem_id": 10946,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10946.jpg"
-  },
-  {
-    "id": 11262,
-    "problem_id": 10947,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10947.jpg"
-  },
-  {
-    "id": 11263,
-    "problem_id": 10948,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10948.jpg"
-  },
-  {
-    "id": 11264,
-    "problem_id": 10949,
-    "problem": "<image>If a ruler and a triangular board are placed as shown in the figure, and if \u22201 = 60\u00b0, then what is the measure of \u22202? (). A, B, C, D choices are ['150\u00b0', '120\u00b0', '100\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10949.jpg"
-  },
-  {
-    "id": 11265,
-    "problem_id": 10950,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10950.jpg"
-  },
-  {
-    "id": 11266,
-    "problem_id": 10951,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10951.jpg"
-  },
-  {
-    "id": 11267,
-    "problem_id": 10952,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10952.jpg"
-  },
-  {
-    "id": 11268,
-    "problem_id": 10953,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10953.jpg"
-  },
-  {
-    "id": 11269,
-    "problem_id": 10954,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10954.jpg"
-  },
-  {
-    "id": 11270,
-    "problem_id": 10955,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10955.jpg"
-  },
-  {
-    "id": 11271,
-    "problem_id": 10956,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10956.jpg"
-  },
-  {
-    "id": 11272,
-    "problem_id": 10957,
-    "problem": "<image>As shown in the figure, a ladder with a length of 2.5 meters is placed with one end 1.5 meters away from the corner of a wall and the other end leaning against the wall. What is the distance between the top of the ladder and the corner of the wall? (). A, B, C, D choices are ['0.2\u7c73', '0.4\u7c73', '2\u7c73', '4\u7c73'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10957.jpg"
-  },
-  {
-    "id": 11273,
-    "problem_id": 10958,
-    "problem": "<image>Given that line a\u2225b and \u22201 = 110\u00b0, what is the measure of \u22202?. A, B, C, D choices are ['110\u00b0', '90\u00b0', '70\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10958.jpg"
-  },
-  {
-    "id": 11274,
-    "problem_id": 10959,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10959.jpg"
-  },
-  {
-    "id": 11275,
-    "problem_id": 10960,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10960.jpg"
-  },
-  {
-    "id": 11276,
-    "problem_id": 10961,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10961.jpg"
-  },
-  {
-    "id": 11277,
-    "problem_id": 10962,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10962.jpg"
-  },
-  {
-    "id": 11278,
-    "problem_id": 10963,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10963.jpg"
-  },
-  {
-    "id": 11279,
-    "problem_id": 10964,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10964.jpg"
-  },
-  {
-    "id": 11280,
-    "problem_id": 10965,
-    "problem": "<image>In triangle ABC as shown in the figure, points D and E are on sides AB and AC respectively, and DE is parallel to BC. Point F is on the extension of side BC. If \u2220ACF = 140\u00b0 and \u2220ADE = 105\u00b0, what is the measure of \u2220A? (). A, B, C, D choices are ['30\u00b0', '35\u00b0', '50\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10965.jpg"
-  },
-  {
-    "id": 11281,
-    "problem_id": 10966,
-    "problem": "<image>As shown in the figure, if we place the two vertices of a right-angled triangle board with a 45\u00b0 angle on opposite sides of a ruler, and if \u22201=20\u00b0, then \u22202 is equal to (). A, B, C, D choices are ['30\u00b0', '25\u00b0', '20\u00b0', '15\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10966.jpg"
-  },
-  {
-    "id": 11282,
-    "problem_id": 10967,
-    "problem": "<image>Given a cone with a base radius of r=6 and a height of h=8, what is the lateral surface area of the cone?. A, B, C, D choices are ['15\u03c0', '30\u03c0', '45\u03c0', '60\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10967.jpg"
-  },
-  {
-    "id": 11283,
-    "problem_id": 10968,
-    "problem": "<image>Given a cone with a base radius of r=6 and a height of h=8, what is the lateral surface area of the cone?. A, B, C, D choices are ['15\u03c0', '30\u03c0', '45\u03c0', '60\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10968.jpg"
-  },
-  {
-    "id": 11284,
-    "problem_id": 10969,
-    "problem": "<image>Given a cone with a base radius of r=6 and a height of h=8, what is the lateral surface area of the cone?. A, B, C, D choices are ['15\u03c0', '30\u03c0', '45\u03c0', '60\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10969.jpg"
-  },
-  {
-    "id": 11285,
-    "problem_id": 10970,
-    "problem": "<image>Given a cone with a base radius of r=6 and a height of h=8, what is the lateral surface area of the cone?. A, B, C, D choices are ['15\u03c0', '30\u03c0', '45\u03c0', '60\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10970.jpg"
-  },
-  {
-    "id": 11286,
-    "problem_id": 10971,
-    "problem": "<image>Given a cone with a base radius of r=6 and a height of h=8, what is the lateral surface area of the cone?. A, B, C, D choices are ['15\u03c0', '30\u03c0', '45\u03c0', '60\u03c0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10971.jpg"
-  },
-  {
-    "id": 11287,
-    "problem_id": 10972,
-    "problem": "<image>As shown in the diagram, there are three squares A, B, and C on line L. If the areas of squares A and C are 5 and 11 respectively, what is the area of square B?. A, B, C, D choices are ['12', '15', '16', '18'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10972.jpg"
-  },
-  {
-    "id": 11288,
-    "problem_id": 10973,
-    "problem": "<image>As shown in the figure, if the distance from the midpoint M of one side of the rhombus ABCD to the intersection point O of the diagonal is 5cm, then the perimeter of the rhombus ABCD is ().. A, B, C, D choices are ['5cm', '10cm', '20cm', '40cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10973.jpg"
-  },
-  {
-    "id": 11289,
-    "problem_id": 10974,
-    "problem": "<image>As shown in the figure, if the distance from the midpoint M of one side of the rhombus ABCD to the intersection point O of the diagonal is 5cm, then the perimeter of the rhombus ABCD is ().. A, B, C, D choices are ['5cm', '10cm', '20cm', '40cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10974.jpg"
-  },
-  {
-    "id": 11290,
-    "problem_id": 10975,
-    "problem": "<image>As shown in the figure, if the distance from the midpoint M of one side of the rhombus ABCD to the intersection point O of the diagonal is 5cm, then the perimeter of the rhombus ABCD is ().. A, B, C, D choices are ['5cm', '10cm', '20cm', '40cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10975.jpg"
-  },
-  {
-    "id": 11291,
-    "problem_id": 10976,
-    "problem": "<image>As shown in the diagram, if the right angle vertex of the set square is placed on one side of the ruler, \u22201=30\u00b0, \u22202=50\u00b0, then the degree of \u22203 is (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10976.jpg"
-  },
-  {
-    "id": 11292,
-    "problem_id": 10977,
-    "problem": "<image>Given, as shown in the figure, a \u2225 b, \u22201 = 55\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['115\u00b0', '120\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10977.jpg"
-  },
-  {
-    "id": 11293,
-    "problem_id": 10978,
-    "problem": "<image>Given, as shown in the figure, a \u2225 b, \u22201 = 55\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['115\u00b0', '120\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10978.jpg"
-  },
-  {
-    "id": 11294,
-    "problem_id": 10979,
-    "problem": "<image>Given, as shown in the figure, a \u2225 b, \u22201 = 55\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['115\u00b0', '120\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10979.jpg"
-  },
-  {
-    "id": 11296,
-    "problem_id": 10980,
-    "problem": "<image>Given, as shown in the figure, a \u2225 b, \u22201 = 55\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['115\u00b0', '120\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10980.jpg"
-  },
-  {
-    "id": 11297,
-    "problem_id": 10981,
-    "problem": "<image>Given, as shown in the figure, a \u2225 b, \u22201 = 55\u00b0, then the degree of \u22202 is (). A, B, C, D choices are ['115\u00b0', '120\u00b0', '125\u00b0', '135\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10981.jpg"
-  },
-  {
-    "id": 11298,
-    "problem_id": 10982,
-    "problem": "<image>Given the diagram, BE and CF are the altitudes of triangle ABC from sides AC and AB respectively. M is the midpoint of BC, EF = 5, and BC = 8. Find the perimeter of triangle EFM.. A, B, C, D choices are ['21', '18', '15', '13'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\boxed{D}</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10982.jpg"
-  },
-  {
-    "id": 11299,
-    "problem_id": 10983,
-    "problem": "<image>As shown in the diagram, it is a schematic diagram of the famous ancient Chinese \"Zhao Shuangxian diagram\". This diagram is made up of four congruent right triangles. If AE is 10 and BE is 24, then the length of EF is ____.. A, B, C, D choices are ['14', '13', '24', '19.799'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10983.jpg"
-  },
-  {
-    "id": 11300,
-    "problem_id": 10984,
-    "problem": "<image>As shown in the figure, line a \u2225 b, \u22201 = 50\u00b0, \u22202 = 40\u00b0, what is the degree of \u22203? (). A, B, C, D choices are ['40\u00b0', '90\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10984.jpg"
-  },
-  {
-    "id": 11301,
-    "problem_id": 10985,
-    "problem": "<image>As shown in the figure, line a \u2225 b, \u22201 = 50\u00b0, \u22202 = 40\u00b0, what is the degree of \u22203? (). A, B, C, D choices are ['40\u00b0', '90\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10985.jpg"
-  },
-  {
-    "id": 11302,
-    "problem_id": 10986,
-    "problem": "<image>As shown in the figure, line a \u2225 b, \u22201 = 50\u00b0, \u22202 = 40\u00b0, what is the degree of \u22203? (). A, B, C, D choices are ['40\u00b0', '90\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10986.jpg"
-  },
-  {
-    "id": 11303,
-    "problem_id": 10987,
-    "problem": "<image>As shown in the figure, line a \u2225 b, \u22201 = 50\u00b0, \u22202 = 40\u00b0, what is the degree of \u22203? (). A, B, C, D choices are ['40\u00b0', '90\u00b0', '50\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10987.jpg"
-  },
-  {
-    "id": 11304,
-    "problem_id": 10988,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O at points A and B respectively. If \u2220P = 50\u00b0, then what is the value of \u2220C? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10988.jpg"
-  },
-  {
-    "id": 11305,
-    "problem_id": 10989,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O at points A and B respectively. If \u2220P = 50\u00b0, then what is the value of \u2220C? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10989.jpg"
-  },
-  {
-    "id": 11306,
-    "problem_id": 10990,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O at points A and B respectively. If \u2220P = 50\u00b0, then what is the value of \u2220C? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10990.jpg"
-  },
-  {
-    "id": 11307,
-    "problem_id": 10991,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O at points A and B respectively. If \u2220P = 50\u00b0, then what is the value of \u2220C? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10991.jpg"
-  },
-  {
-    "id": 11308,
-    "problem_id": 10992,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O at points A and B respectively. If \u2220P = 50\u00b0, then what is the value of \u2220C? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10992.jpg"
-  },
-  {
-    "id": 11309,
-    "problem_id": 10993,
-    "problem": "<image>As shown in the figure, PA and PB are tangents to circle O at points A and B respectively. If \u2220P = 50\u00b0, then what is the value of \u2220C? (). A, B, C, D choices are ['50\u00b0', '55\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10993.jpg"
-  },
-  {
-    "id": 11310,
-    "problem_id": 10994,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10994.jpg"
-  },
-  {
-    "id": 11311,
-    "problem_id": 10995,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10995.jpg"
-  },
-  {
-    "id": 11312,
-    "problem_id": 10996,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10996.jpg"
-  },
-  {
-    "id": 11313,
-    "problem_id": 10997,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10997.jpg"
-  },
-  {
-    "id": 11314,
-    "problem_id": 10998,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10998.jpg"
-  },
-  {
-    "id": 11315,
-    "problem_id": 10999,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/10999.jpg"
-  },
-  {
-    "id": 11316,
-    "problem_id": 11000,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11000.jpg"
-  },
-  {
-    "id": 11317,
-    "problem_id": 11001,
-    "problem": "<image>As shown in the diagram, it is known that DE is obtained by translating the line segment AB. Also, AB=DC=4cm, EC=3cm. What is the perimeter of triangle DCE?. A, B, C, D choices are ['9cm', '10cm', '11cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11001.jpg"
-  },
-  {
-    "id": 11318,
-    "problem_id": 11002,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11002.jpg"
-  },
-  {
-    "id": 11319,
-    "problem_id": 11003,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11003.jpg"
-  },
-  {
-    "id": 11320,
-    "problem_id": 11004,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11004.jpg"
-  },
-  {
-    "id": 11321,
-    "problem_id": 11005,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11005.jpg"
-  },
-  {
-    "id": 11322,
-    "problem_id": 11006,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11006.jpg"
-  },
-  {
-    "id": 11323,
-    "problem_id": 11007,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11007.jpg"
-  },
-  {
-    "id": 11324,
-    "problem_id": 11008,
-    "problem": "<image>In the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 50\u00b0, what is the degree of \u22204? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '60\u00b0', '124\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11008.jpg"
-  },
-  {
-    "id": 11325,
-    "problem_id": 11009,
-    "problem": "<image>As shown in the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 104\u00b0, what is the degree measurement of \u22204? (). A, B, C, D choices are ['74\u00b0', '76\u00b0', '84\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11009.jpg"
-  },
-  {
-    "id": 11326,
-    "problem_id": 11010,
-    "problem": "<image>As shown in the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 104\u00b0, what is the degree measurement of \u22204? (). A, B, C, D choices are ['74\u00b0', '76\u00b0', '84\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11010.jpg"
-  },
-  {
-    "id": 11327,
-    "problem_id": 11011,
-    "problem": "<image>As shown in the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 104\u00b0, what is the degree measurement of \u22204? (). A, B, C, D choices are ['74\u00b0', '76\u00b0', '84\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11011.jpg"
-  },
-  {
-    "id": 11328,
-    "problem_id": 11012,
-    "problem": "<image>As shown in the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 104\u00b0, what is the degree measurement of \u22204? (). A, B, C, D choices are ['74\u00b0', '76\u00b0', '84\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11012.jpg"
-  },
-  {
-    "id": 11329,
-    "problem_id": 11013,
-    "problem": "<image>As shown in the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 104\u00b0, what is the degree measurement of \u22204? (). A, B, C, D choices are ['74\u00b0', '76\u00b0', '84\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11013.jpg"
-  },
-  {
-    "id": 11330,
-    "problem_id": 11014,
-    "problem": "<image>As shown in the figure, \u22201 + \u22202 = 180\u00b0, \u22203 = 104\u00b0, what is the degree measurement of \u22204? (). A, B, C, D choices are ['74\u00b0', '76\u00b0', '84\u00b0', '86\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11014.jpg"
-  },
-  {
-    "id": 11331,
-    "problem_id": 11015,
-    "problem": "<image>In the quadrilateral ABCD shown below, diagonal AC is perpendicular to diagonal BD, with point O as the foot of the perpendicular. Points E, F, G, and H are the midpoints of sides AB, BC, CD, and AD, respectively. If AC = 10 and BD = 6, what is the area of quadrilateral EFGH?. A, B, C, D choices are ['15', '20', '30', '60'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11015.jpg"
-  },
-  {
-    "id": 11332,
-    "problem_id": 11016,
-    "problem": "<image>In the quadrilateral ABCD shown below, diagonal AC is perpendicular to diagonal BD, with point O as the foot of the perpendicular. Points E, F, G, and H are the midpoints of sides AB, BC, CD, and AD, respectively. If AC = 10 and BD = 6, what is the area of quadrilateral EFGH?. A, B, C, D choices are ['15', '20', '30', '60'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11016.jpg"
-  },
-  {
-    "id": 11333,
-    "problem_id": 11017,
-    "problem": "<image>In the quadrilateral ABCD shown below, diagonal AC is perpendicular to diagonal BD, with point O as the foot of the perpendicular. Points E, F, G, and H are the midpoints of sides AB, BC, CD, and AD, respectively. If AC = 10 and BD = 6, what is the area of quadrilateral EFGH?. A, B, C, D choices are ['15', '20', '30', '60'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11017.jpg"
-  },
-  {
-    "id": 11334,
-    "problem_id": 11018,
-    "problem": "<image>As shown in the figure, OE is the bisector of \u2220AOB. CD is parallel to OB and intersects OA at point C and OE at point D. If \u2220ACD = 50\u00b0, what is the degree measure of \u2220CDO? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11018.jpg"
-  },
-  {
-    "id": 11335,
-    "problem_id": 11019,
-    "problem": "<image>As shown in the figure, OE is the bisector of \u2220AOB. CD is parallel to OB and intersects OA at point C and OE at point D. If \u2220ACD = 50\u00b0, what is the degree measure of \u2220CDO? (). A, B, C, D choices are ['15\u00b0', '20\u00b0', '25\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11019.jpg"
-  },
-  {
-    "id": 11336,
-    "problem_id": 11020,
-    "problem": "<image>In triangle ABC, BF bisects angle ABC and CF bisects angle ACB. If angle BFC is 115 degrees, what is the degree measure of angle A?. A, B, C, D choices are ['50\u00b0', '57.5\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11020.jpg"
-  },
-  {
-    "id": 11337,
-    "problem_id": 11021,
-    "problem": "<image>In triangle ABC, BF bisects angle ABC and CF bisects angle ACB. If angle BFC is 115 degrees, what is the degree measure of angle A?. A, B, C, D choices are ['50\u00b0', '57.5\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11021.jpg"
-  },
-  {
-    "id": 11338,
-    "problem_id": 11022,
-    "problem": "<image>In triangle ABC, BF bisects angle ABC and CF bisects angle ACB. If angle BFC is 115 degrees, what is the degree measure of angle A?. A, B, C, D choices are ['50\u00b0', '57.5\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11022.jpg"
-  },
-  {
-    "id": 11339,
-    "problem_id": 11023,
-    "problem": "<image>In triangle ABC, BF bisects angle ABC and CF bisects angle ACB. If angle BFC is 115 degrees, what is the degree measure of angle A?. A, B, C, D choices are ['50\u00b0', '57.5\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11023.jpg"
-  },
-  {
-    "id": 11340,
-    "problem_id": 11024,
-    "problem": "<image>In triangle ABC, BF bisects angle ABC and CF bisects angle ACB. If angle BFC is 115 degrees, what is the degree measure of angle A?. A, B, C, D choices are ['50\u00b0', '57.5\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11024.jpg"
-  },
-  {
-    "id": 11341,
-    "problem_id": 11025,
-    "problem": "<image>In triangle ABC, BF bisects angle ABC and CF bisects angle ACB. If angle BFC is 115 degrees, what is the degree measure of angle A?. A, B, C, D choices are ['50\u00b0', '57.5\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11025.jpg"
-  },
-  {
-    "id": 11342,
-    "problem_id": 11026,
-    "problem": "<image>Arrange the ruler and the right-angled triangle as shown in the figure. If \u22201=30\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11026.jpg"
-  },
-  {
-    "id": 11343,
-    "problem_id": 11027,
-    "problem": "<image>Arrange the ruler and the right-angled triangle as shown in the figure. If \u22201=30\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]\n</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11027.jpg"
-  },
-  {
-    "id": 11344,
-    "problem_id": 11028,
-    "problem": "<image>Arrange the ruler and the right-angled triangle as shown in the figure. If \u22201=30\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11028.jpg"
-  },
-  {
-    "id": 11345,
-    "problem_id": 11029,
-    "problem": "<image>Arrange the ruler and the right-angled triangle as shown in the figure. If \u22201=30\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11029.jpg"
-  },
-  {
-    "id": 11346,
-    "problem_id": 11030,
-    "problem": "<image>Arrange the ruler and the right-angled triangle as shown in the figure. If \u22201=30\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11030.jpg"
-  },
-  {
-    "id": 11347,
-    "problem_id": 11031,
-    "problem": "<image>Arrange the ruler and the right-angled triangle as shown in the figure. If \u22201=30\u00b0, what is the size of \u22202? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '65\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11031.jpg"
-  },
-  {
-    "id": 11348,
-    "problem_id": 11032,
-    "problem": "<image>In the parallelogram ABCD shown in the figure, CE is perpendicular to AB at point E. If \u2220A = 125\u00b0, then the degree measure of \u2220BCE is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11032.jpg"
-  },
-  {
-    "id": 11349,
-    "problem_id": 11033,
-    "problem": "<image>In the parallelogram ABCD shown in the figure, CE is perpendicular to AB at point E. If \u2220A = 125\u00b0, then the degree measure of \u2220BCE is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11033.jpg"
-  },
-  {
-    "id": 11350,
-    "problem_id": 11034,
-    "problem": "<image>In the parallelogram ABCD shown in the figure, CE is perpendicular to AB at point E. If \u2220A = 125\u00b0, then the degree measure of \u2220BCE is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11034.jpg"
-  },
-  {
-    "id": 11351,
-    "problem_id": 11035,
-    "problem": "<image>In the parallelogram ABCD shown in the figure, CE is perpendicular to AB at point E. If \u2220A = 125\u00b0, then the degree measure of \u2220BCE is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11035.jpg"
-  },
-  {
-    "id": 11352,
-    "problem_id": 11036,
-    "problem": "<image>In the parallelogram ABCD shown in the figure, CE is perpendicular to AB at point E. If \u2220A = 125\u00b0, then the degree measure of \u2220BCE is (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11036.jpg"
-  },
-  {
-    "id": 11353,
-    "problem_id": 11037,
-    "problem": "<image>In the figure, \u25a1ABCD, \u2220C=108\u00b0, BE bisects \u2220ABC, then \u2220AEB is equal to: (). A, B, C, D choices are ['18\u00b0', '36\u00b0', '72\u00b0', '108\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11037.jpg"
-  },
-  {
-    "id": 11354,
-    "problem_id": 11038,
-    "problem": "<image>As shown in the diagram, line AB and line CD intersect at point O. OE is perpendicular to AB at O, and \u2220COE measures 55\u00b0. What is the measure of \u2220BOD? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11038.jpg"
-  },
-  {
-    "id": 11355,
-    "problem_id": 11039,
-    "problem": "<image>As shown in the diagram, line AB and line CD intersect at point O. OE is perpendicular to AB at O, and \u2220COE measures 55\u00b0. What is the measure of \u2220BOD? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11039.jpg"
-  },
-  {
-    "id": 11356,
-    "problem_id": 11040,
-    "problem": "<image>As shown in the diagram, line AB and line CD intersect at point O. OE is perpendicular to AB at O, and \u2220COE measures 55\u00b0. What is the measure of \u2220BOD? (). A, B, C, D choices are ['35\u00b0', '45\u00b0', '30\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11040.jpg"
-  },
-  {
-    "id": 11357,
-    "problem_id": 11041,
-    "problem": "<image>As shown in the figure, b is parallel to c, a is perpendicular to b, and \u22201 = 130\u00b0. What is the measure of \u22202?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11041.jpg"
-  },
-  {
-    "id": 11358,
-    "problem_id": 11042,
-    "problem": "<image>As shown in the figure, b is parallel to c, a is perpendicular to b, and \u22201 = 130\u00b0. What is the measure of \u22202?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11042.jpg"
-  },
-  {
-    "id": 11359,
-    "problem_id": 11043,
-    "problem": "<image>As shown in the figure, b is parallel to c, a is perpendicular to b, and \u22201 = 130\u00b0. What is the measure of \u22202?. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11043.jpg"
-  },
-  {
-    "id": 11360,
-    "problem_id": 11044,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a rhombus, and O is the intersection point of the two diagonals. Three lines passing through point O divide the rhombus into shaded and blank parts. When the lengths of the two diagonals of the rhombus are 6 and 8 respectively, the area of the shaded part is (). A, B, C, D choices are ['24cm', '20cm', '16cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11044.jpg"
-  },
-  {
-    "id": 11361,
-    "problem_id": 11045,
-    "problem": "<image>As shown in the figure, quadrilateral ABCD is a rhombus, and O is the intersection point of the two diagonals. Three lines passing through point O divide the rhombus into shaded and blank parts. When the lengths of the two diagonals of the rhombus are 6 and 8 respectively, the area of the shaded part is (). A, B, C, D choices are ['24cm', '20cm', '16cm', '12cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11045.jpg"
-  },
-  {
-    "id": 11363,
-    "problem_id": 11046,
-    "problem": "<image>Given the diagram, if a//b and \u22201 = 70\u00b0, what is the degree measure of \u22202? (). A, B, C, D choices are ['20\u00b0', '70\u00b0', '110\u00b0', '130\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11046.jpg"
-  },
-  {
-    "id": 11364,
-    "problem_id": 11047,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11047.jpg"
-  },
-  {
-    "id": 11365,
-    "problem_id": 11048,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11048.jpg"
-  },
-  {
-    "id": 11366,
-    "problem_id": 11049,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11049.jpg"
-  },
-  {
-    "id": 11367,
-    "problem_id": 11050,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11050.jpg"
-  },
-  {
-    "id": 11368,
-    "problem_id": 11051,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11051.jpg"
-  },
-  {
-    "id": 11369,
-    "problem_id": 11052,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11052.jpg"
-  },
-  {
-    "id": 11370,
-    "problem_id": 11053,
-    "problem": "<image>As shown in the figure, points A, B, and C are on the circle O, and \u2220ACB = 20\u00b0. What is the degree measure of \u2220AOB? (). A, B, C, D choices are ['10\u00b0', '20\u00b0', '40\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11053.jpg"
-  },
-  {
-    "id": 11371,
-    "problem_id": 11054,
-    "problem": "<image>As shown in the diagram, \u22201=\u22202, AC=AD, \u2220C=\u2220D. If AB=4cm, BC=3cm, and AC=2cm, then what is the length of DE? (). A, B, C, D choices are ['4cm', '3cm', '2cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11054.jpg"
-  },
-  {
-    "id": 11372,
-    "problem_id": 11055,
-    "problem": "<image>As shown in the diagram, \u22201=\u22202, AC=AD, \u2220C=\u2220D. If AB=4cm, BC=3cm, and AC=2cm, then what is the length of DE? (). A, B, C, D choices are ['4cm', '3cm', '2cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11055.jpg"
-  },
-  {
-    "id": 11373,
-    "problem_id": 11056,
-    "problem": "<image>As shown in the diagram, \u22201=\u22202, AC=AD, \u2220C=\u2220D. If AB=4cm, BC=3cm, and AC=2cm, then what is the length of DE? (). A, B, C, D choices are ['4cm', '3cm', '2cm', '\u65e0\u6cd5\u786e\u5b9a'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11056.jpg"
-  },
-  {
-    "id": 11374,
-    "problem_id": 11057,
-    "problem": "<image>As shown in the diagram, a triangle ruler (with the right angle vertex coinciding) is placed on the desktop. If \u2220AOD=150\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11057.jpg"
-  },
-  {
-    "id": 11375,
-    "problem_id": 11058,
-    "problem": "<image>As shown in the diagram, a triangle ruler (with the right angle vertex coinciding) is placed on the desktop. If \u2220AOD=150\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11058.jpg"
-  },
-  {
-    "id": 11376,
-    "problem_id": 11059,
-    "problem": "<image>As shown in the diagram, a triangle ruler (with the right angle vertex coinciding) is placed on the desktop. If \u2220AOD=150\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11059.jpg"
-  },
-  {
-    "id": 11377,
-    "problem_id": 11060,
-    "problem": "<image>As shown in the diagram, a triangle ruler (with the right angle vertex coinciding) is placed on the desktop. If \u2220AOD=150\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11060.jpg"
-  },
-  {
-    "id": 11378,
-    "problem_id": 11061,
-    "problem": "<image>As shown in the diagram, a triangle ruler (with the right angle vertex coinciding) is placed on the desktop. If \u2220AOD=150\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11061.jpg"
-  },
-  {
-    "id": 11379,
-    "problem_id": 11062,
-    "problem": "<image>Given that \u22201 = \u22202 = \u22203 = 62\u00b0 in the diagram, find \u22204.. A, B, C, D choices are ['62\u00b0', '118\u00b0', '128\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11062.jpg"
-  },
-  {
-    "id": 11380,
-    "problem_id": 11063,
-    "problem": "<image>Given that \u22201 = \u22202 = \u22203 = 62\u00b0 in the diagram, find \u22204.. A, B, C, D choices are ['62\u00b0', '118\u00b0', '128\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11063.jpg"
-  },
-  {
-    "id": 11382,
-    "problem_id": 11064,
-    "problem": "<image>Given that \u22201 = \u22202 = \u22203 = 62\u00b0 in the diagram, find \u22204.. A, B, C, D choices are ['62\u00b0', '118\u00b0', '128\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{B}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11064.jpg"
-  },
-  {
-    "id": 11384,
-    "problem_id": 11065,
-    "problem": "<image>Given that \u22201 = \u22202 = \u22203 = 62\u00b0 in the diagram, find \u22204.. A, B, C, D choices are ['62\u00b0', '118\u00b0', '128\u00b0', '38\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11065.jpg"
-  },
-  {
-    "id": 11385,
-    "problem_id": 11066,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11066.jpg"
-  },
-  {
-    "id": 11386,
-    "problem_id": 11067,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11067.jpg"
-  },
-  {
-    "id": 11387,
-    "problem_id": 11068,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11068.jpg"
-  },
-  {
-    "id": 11388,
-    "problem_id": 11069,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11069.jpg"
-  },
-  {
-    "id": 11389,
-    "problem_id": 11070,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11070.jpg"
-  },
-  {
-    "id": 11390,
-    "problem_id": 11071,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11071.jpg"
-  },
-  {
-    "id": 11391,
-    "problem_id": 11072,
-    "problem": "<image>As shown in the figure, \u25b3ADE \u223d \u25b3ABC. If AD = 1 and BD = 2, what is the similarity ratio between \u25b3ADE and \u25b3ABC?. A, B, C, D choices are ['1:2', '1:3', '2:3', '3:2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11072.jpg"
-  },
-  {
-    "id": 11392,
-    "problem_id": 11073,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, BE intersects CD at point F, \u2220B = 45\u00b0, \u2220E = 21\u00b0, then what is the measure of \u2220D? (). A, B, C, D choices are ['21\u00b0', '24\u00b0', '45\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11073.jpg"
-  },
-  {
-    "id": 11393,
-    "problem_id": 11074,
-    "problem": "<image>As shown in the figure, AB is parallel to CD, BE intersects CD at point F, \u2220B = 45\u00b0, \u2220E = 21\u00b0, then what is the measure of \u2220D? (). A, B, C, D choices are ['21\u00b0', '24\u00b0', '45\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11074.jpg"
-  },
-  {
-    "id": 11394,
-    "problem_id": 11075,
-    "problem": "<image>As shown in the diagram, in triangle ABC, D is a point on the extension of BC, and \u2220B=38\u00b0, \u2220A=62\u00b0. Then, \u2220ACD is equal to (). A, B, C, D choices are ['24\u00b0', '38\u00b0', '62\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11075.jpg"
-  },
-  {
-    "id": 11395,
-    "problem_id": 11076,
-    "problem": "<image>As shown in the diagram, in triangle ABC, D is a point on the extension of BC, and \u2220B=38\u00b0, \u2220A=62\u00b0. Then, \u2220ACD is equal to (). A, B, C, D choices are ['24\u00b0', '38\u00b0', '62\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11076.jpg"
-  },
-  {
-    "id": 11396,
-    "problem_id": 11077,
-    "problem": "<image>As shown in the diagram, in triangle ABC, D is a point on the extension of BC, and \u2220B=38\u00b0, \u2220A=62\u00b0. Then, \u2220ACD is equal to (). A, B, C, D choices are ['24\u00b0', '38\u00b0', '62\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11077.jpg"
-  },
-  {
-    "id": 11397,
-    "problem_id": 11078,
-    "problem": "<image>As shown in the diagram, in triangle ABC, D is a point on the extension of BC, and \u2220B=38\u00b0, \u2220A=62\u00b0. Then, \u2220ACD is equal to (). A, B, C, D choices are ['24\u00b0', '38\u00b0', '62\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11078.jpg"
-  },
-  {
-    "id": 11398,
-    "problem_id": 11079,
-    "problem": "<image>As shown in the diagram, in triangle ABC, D is a point on the extension of BC, and \u2220B=38\u00b0, \u2220A=62\u00b0. Then, \u2220ACD is equal to (). A, B, C, D choices are ['24\u00b0', '38\u00b0', '62\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11079.jpg"
-  },
-  {
-    "id": 11399,
-    "problem_id": 11080,
-    "problem": "<image>As shown in the diagram, in triangle ABC, D is a point on the extension of BC, and \u2220B=38\u00b0, \u2220A=62\u00b0. Then, \u2220ACD is equal to (). A, B, C, D choices are ['24\u00b0', '38\u00b0', '62\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11080.jpg"
-  },
-  {
-    "id": 11400,
-    "problem_id": 11081,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11081.jpg"
-  },
-  {
-    "id": 11401,
-    "problem_id": 11082,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11082.jpg"
-  },
-  {
-    "id": 11402,
-    "problem_id": 11083,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11083.jpg"
-  },
-  {
-    "id": 11403,
-    "problem_id": 11084,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11084.jpg"
-  },
-  {
-    "id": 11404,
-    "problem_id": 11085,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11085.jpg"
-  },
-  {
-    "id": 11405,
-    "problem_id": 11086,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11086.jpg"
-  },
-  {
-    "id": 11406,
-    "problem_id": 11087,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11087.jpg"
-  },
-  {
-    "id": 11407,
-    "problem_id": 11088,
-    "problem": "<image>We call the smallest circle that can completely cover a certain plane figure the minimum covering circle of that plane figure. For example, the minimum covering circle of line segment AB is the circle with line segment AB as its diameter, and the minimum covering circle of triangle ABC is its circumcircle. So, what is the radius of the minimum covering circle of a rectangle that is 8cm long and 6cm wide?. A, B, C, D choices are ['10cm', '8cm', '6cm', '5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11088.jpg"
-  },
-  {
-    "id": 11408,
-    "problem_id": 11089,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11089.jpg"
-  },
-  {
-    "id": 11409,
-    "problem_id": 11090,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11090.jpg"
-  },
-  {
-    "id": 11410,
-    "problem_id": 11091,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11091.jpg"
-  },
-  {
-    "id": 11411,
-    "problem_id": 11092,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11092.jpg"
-  },
-  {
-    "id": 11412,
-    "problem_id": 11093,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11093.jpg"
-  },
-  {
-    "id": 11413,
-    "problem_id": 11094,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11094.jpg"
-  },
-  {
-    "id": 11414,
-    "problem_id": 11095,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11095.jpg"
-  },
-  {
-    "id": 11415,
-    "problem_id": 11096,
-    "problem": "<image>As shown in the figure, \u2299O is the circumcircle of \u25b3ABC, \u2220OCB=40\u00b0, then the degree of \u2220A is equal to ().. A, B, C, D choices are ['60\u00b0', '80\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11096.jpg"
-  },
-  {
-    "id": 11416,
-    "problem_id": 11097,
-    "problem": "<image>As shown in the diagram, triangle ABC is inscribed in circle O. AD is the diameter of circle O and \u2220ABC = 30\u00b0. What is the measure of \u2220CAD in degrees? (). A, B, C, D choices are ['45\u00b0', '50\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11097.jpg"
-  },
-  {
-    "id": 11417,
-    "problem_id": 11098,
-    "problem": "<image>As shown in the diagram, triangle ABC is inscribed in circle O. AD is the diameter of circle O and \u2220ABC = 30\u00b0. What is the measure of \u2220CAD in degrees? (). A, B, C, D choices are ['45\u00b0', '50\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11098.jpg"
-  },
-  {
-    "id": 11418,
-    "problem_id": 11099,
-    "problem": "<image>In the figure, in circle O, AB = BC, \u22201 = 45\u00b0, then \u22202 = (). A, B, C, D choices are ['60\u00b0', '30\u00b0', '45\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11099.jpg"
-  },
-  {
-    "id": 11419,
-    "problem_id": 11100,
-    "problem": "<image>In the figure, in circle O, AB = BC, \u22201 = 45\u00b0, then \u22202 = (). A, B, C, D choices are ['60\u00b0', '30\u00b0', '45\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11100.jpg"
-  },
-  {
-    "id": 11420,
-    "problem_id": 11101,
-    "problem": "<image>In the figure, in circle O, AB = BC, \u22201 = 45\u00b0, then \u22202 = (). A, B, C, D choices are ['60\u00b0', '30\u00b0', '45\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11101.jpg"
-  },
-  {
-    "id": 11421,
-    "problem_id": 11102,
-    "problem": "<image>In the figure, in circle O, AB = BC, \u22201 = 45\u00b0, then \u22202 = (). A, B, C, D choices are ['60\u00b0', '30\u00b0', '45\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11102.jpg"
-  },
-  {
-    "id": 11422,
-    "problem_id": 11103,
-    "problem": "<image>As shown in the figure, C and D are two points on the circle O with diameter AB. The arc CB is equal to the arc BD, and angle CAB is 24 degrees. What is the degree measure of angle ABD? (). A, B, C, D choices are ['24\u00b0', '60\u00b0', '66\u00b0', '76\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11103.jpg"
-  },
-  {
-    "id": 11423,
-    "problem_id": 11104,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle o, \u2040{BC}=\u2040{CD}=\u2040{DE}, \u2220COD=35\u00b0, then what is the degree measure of \u2220AOE? (). A, B, C, D choices are ['65\u00b0', '70\u00b0', '75\u00b0', '85\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11104.jpg"
-  },
-  {
-    "id": 11424,
-    "problem_id": 11105,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle o, \u2040{BC}=\u2040{CD}=\u2040{DE}, \u2220COD=35\u00b0, then what is the degree measure of \u2220AOE? (). A, B, C, D choices are ['65\u00b0', '70\u00b0', '75\u00b0', '85\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11105.jpg"
-  },
-  {
-    "id": 11425,
-    "problem_id": 11106,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11106.jpg"
-  },
-  {
-    "id": 11426,
-    "problem_id": 11107,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11107.jpg"
-  },
-  {
-    "id": 11427,
-    "problem_id": 11108,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11108.jpg"
-  },
-  {
-    "id": 11428,
-    "problem_id": 11109,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11109.jpg"
-  },
-  {
-    "id": 11429,
-    "problem_id": 11110,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11110.jpg"
-  },
-  {
-    "id": 11430,
-    "problem_id": 11111,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11111.jpg"
-  },
-  {
-    "id": 11431,
-    "problem_id": 11112,
-    "problem": "<image>As shown in the figure, points A, B, and C lie on the circle O. If \u2220OBC = 40\u00b0, then what is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11112.jpg"
-  },
-  {
-    "id": 11432,
-    "problem_id": 11113,
-    "problem": "<image>As shown in the figure, line l intersects circle O at points A and B, dividing circle O into two segments in the ratio of 3:1. If the radius of circle O is 2cm, what is the area of triangle OAB?. A, B, C, D choices are ['1cm\u00b2', '\u221a{3}cm\u00b2', '2cm\u00b2', '4cm\u00b2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11113.jpg"
-  },
-  {
-    "id": 11433,
-    "problem_id": 11114,
-    "problem": "<image>As shown in the figure, line l intersects circle O at points A and B, dividing circle O into two segments in the ratio of 3:1. If the radius of circle O is 2cm, what is the area of triangle OAB?. A, B, C, D choices are ['1cm\u00b2', '\u221a{3}cm\u00b2', '2cm\u00b2', '4cm\u00b2'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11114.jpg"
-  },
-  {
-    "id": 11434,
-    "problem_id": 11115,
-    "problem": "<image>In the figure, MN is a chord of circle O, \u2220M=50\u00b0, then \u2220MON is equal to ().. A, B, C, D choices are ['50\u00b0', '55\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11115.jpg"
-  },
-  {
-    "id": 11435,
-    "problem_id": 11116,
-    "problem": "<image>In the figure, MN is a chord of circle O, \u2220M=50\u00b0, then \u2220MON is equal to ().. A, B, C, D choices are ['50\u00b0', '55\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11116.jpg"
-  },
-  {
-    "id": 11436,
-    "problem_id": 11117,
-    "problem": "<image>In the figure, MN is a chord of circle O, \u2220M=50\u00b0, then \u2220MON is equal to ().. A, B, C, D choices are ['50\u00b0', '55\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11117.jpg"
-  },
-  {
-    "id": 11437,
-    "problem_id": 11118,
-    "problem": "<image>In the figure, MN is a chord of circle O, \u2220M=50\u00b0, then \u2220MON is equal to ().. A, B, C, D choices are ['50\u00b0', '55\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11118.jpg"
-  },
-  {
-    "id": 11438,
-    "problem_id": 11119,
-    "problem": "<image>In the figure, MN is a chord of circle O, \u2220M=50\u00b0, then \u2220MON is equal to ().. A, B, C, D choices are ['50\u00b0', '55\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11119.jpg"
-  },
-  {
-    "id": 11439,
-    "problem_id": 11120,
-    "problem": "<image>In the figure, MN is a chord of circle O, \u2220M=50\u00b0, then \u2220MON is equal to ().. A, B, C, D choices are ['50\u00b0', '55\u00b0', '65\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11120.jpg"
-  },
-  {
-    "id": 11440,
-    "problem_id": 11121,
-    "problem": "<image>As shown in the figure, it is known that AB is the diameter of circle O, and \u2040{BC}=\u2040{CD}=\u2040{DE}. If \u2220BOC=40\u00b0, then \u2220AOE=(). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11121.jpg"
-  },
-  {
-    "id": 11441,
-    "problem_id": 11122,
-    "problem": "<image>As shown in the figure, it is known that AB is the diameter of circle O, and \u2040{BC}=\u2040{CD}=\u2040{DE}. If \u2220BOC=40\u00b0, then \u2220AOE=(). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11122.jpg"
-  },
-  {
-    "id": 11442,
-    "problem_id": 11123,
-    "problem": "<image>As shown in the figure, it is known that AB is the diameter of circle O, and \u2040{BC}=\u2040{CD}=\u2040{DE}. If \u2220BOC=40\u00b0, then \u2220AOE=(). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11123.jpg"
-  },
-  {
-    "id": 11443,
-    "problem_id": 11124,
-    "problem": "<image>As shown in the figure, it is known that AB is the diameter of circle O, and \u2040{BC}=\u2040{CD}=\u2040{DE}. If \u2220BOC=40\u00b0, then \u2220AOE=(). A, B, C, D choices are ['40\u00b0', '60\u00b0', '80\u00b0', '120\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11124.jpg"
-  },
-  {
-    "id": 11444,
-    "problem_id": 11125,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11125.jpg"
-  },
-  {
-    "id": 11445,
-    "problem_id": 11126,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11126.jpg"
-  },
-  {
-    "id": 11446,
-    "problem_id": 11127,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11127.jpg"
-  },
-  {
-    "id": 11447,
-    "problem_id": 11128,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11128.jpg"
-  },
-  {
-    "id": 11448,
-    "problem_id": 11129,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11129.jpg"
-  },
-  {
-    "id": 11449,
-    "problem_id": 11130,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11130.jpg"
-  },
-  {
-    "id": 11450,
-    "problem_id": 11131,
-    "problem": "<image>In the figure, in circle O, if \u2220B = 37\u00b0, then the degree measure of arc AB is ().. A, B, C, D choices are ['106\u00b0', '126\u00b0', '74\u00b0', '53\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11131.jpg"
-  },
-  {
-    "id": 11451,
-    "problem_id": 11132,
-    "problem": "<image>As shown in the figure, the radius of circle O is 2, point A is a point on circle O, and radius OD is perpendicular to chord BC at point D. If \u2220BAC = 60\u00b0, then what is the length of OD?. A, B, C, D choices are ['2', '\u221a{3}', '1', '\\\\frac{\u221a{3}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11132.jpg"
-  },
-  {
-    "id": 11452,
-    "problem_id": 11133,
-    "problem": "<image>As shown in the figure, the radius of circle O is 2, point A is a point on circle O, and radius OD is perpendicular to chord BC at point D. If \u2220BAC = 60\u00b0, then what is the length of OD?. A, B, C, D choices are ['2', '\u221a{3}', '1', '\\\\frac{\u221a{3}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11133.jpg"
-  },
-  {
-    "id": 11453,
-    "problem_id": 11134,
-    "problem": "<image>As shown in the figure, the radius of circle O is 2, point A is a point on circle O, and radius OD is perpendicular to chord BC at point D. If \u2220BAC = 60\u00b0, then what is the length of OD?. A, B, C, D choices are ['2', '\u221a{3}', '1', '\\\\frac{\u221a{3}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11134.jpg"
-  },
-  {
-    "id": 11454,
-    "problem_id": 11135,
-    "problem": "<image>As shown in the figure, the radius of circle O is 2, point A is a point on circle O, and radius OD is perpendicular to chord BC at point D. If \u2220BAC = 60\u00b0, then what is the length of OD?. A, B, C, D choices are ['2', '\u221a{3}', '1', '\\\\frac{\u221a{3}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11135.jpg"
-  },
-  {
-    "id": 11455,
-    "problem_id": 11136,
-    "problem": "<image>In Figure 1, in circle O, if point C is the midpoint of segment AB and \u2220OAB = 50\u00b0, then the degree measure of \u2220BOC is (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11136.jpg"
-  },
-  {
-    "id": 11456,
-    "problem_id": 11137,
-    "problem": "<image>In Figure 1, in circle O, if point C is the midpoint of segment AB and \u2220OAB = 50\u00b0, then the degree measure of \u2220BOC is (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11137.jpg"
-  },
-  {
-    "id": 11457,
-    "problem_id": 11138,
-    "problem": "<image>In Figure 1, in circle O, if point C is the midpoint of segment AB and \u2220OAB = 50\u00b0, then the degree measure of \u2220BOC is (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11138.jpg"
-  },
-  {
-    "id": 11458,
-    "problem_id": 11139,
-    "problem": "<image>In Figure 1, in circle O, if point C is the midpoint of segment AB and \u2220OAB = 50\u00b0, then the degree measure of \u2220BOC is (). A, B, C, D choices are ['40\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11139.jpg"
-  },
-  {
-    "id": 11459,
-    "problem_id": 11140,
-    "problem": "<image>In the figure, in \u2299O, if \u2220A = 30\u00b0, then \u2220AOB is (). A, B, C, D choices are ['60\u00b0', '90\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11140.jpg"
-  },
-  {
-    "id": 11460,
-    "problem_id": 11141,
-    "problem": "<image>In the figure, in \u2299O, if \u2220A = 30\u00b0, then \u2220AOB is (). A, B, C, D choices are ['60\u00b0', '90\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11141.jpg"
-  },
-  {
-    "id": 11461,
-    "problem_id": 11142,
-    "problem": "<image>In the figure, in \u2299O, if \u2220A = 30\u00b0, then \u2220AOB is (). A, B, C, D choices are ['60\u00b0', '90\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11142.jpg"
-  },
-  {
-    "id": 11462,
-    "problem_id": 11143,
-    "problem": "<image>In the figure, in \u2299O, if \u2220A = 30\u00b0, then \u2220AOB is (). A, B, C, D choices are ['60\u00b0', '90\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11143.jpg"
-  },
-  {
-    "id": 11463,
-    "problem_id": 11144,
-    "problem": "<image>In the figure, in \u2299O, if \u2220A = 30\u00b0, then \u2220AOB is (). A, B, C, D choices are ['60\u00b0', '90\u00b0', '120\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11144.jpg"
-  },
-  {
-    "id": 11464,
-    "problem_id": 11145,
-    "problem": "<image>Given the diagram, AB is the diameter of circle O, BD = CD, and \u2220BOD = 60\u00b0. What is the measure of \u2220AOC?. A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '\u4ee5\u4e0a\u90fd\u4e0d\u6b63\u786e'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11145.jpg"
-  },
-  {
-    "id": 11465,
-    "problem_id": 11146,
-    "problem": "<image>Given the diagram, AB is the diameter of circle O, BD = CD, and \u2220BOD = 60\u00b0. What is the measure of \u2220AOC?. A, B, C, D choices are ['30\u00b0', '45\u00b0', '60\u00b0', '\u4ee5\u4e0a\u90fd\u4e0d\u6b63\u786e'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11146.jpg"
-  },
-  {
-    "id": 11466,
-    "problem_id": 11147,
-    "problem": "<image>As shown in the diagram, chord AE is parallel to diameter CD. Line AO is connected and \u2220AOC = 40\u00b0. Then the degree of the central angle corresponding to \u2040{DE} is (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11147.jpg"
-  },
-  {
-    "id": 11467,
-    "problem_id": 11148,
-    "problem": "<image>As shown in the figure, AB and CD are two diameters of circle O, and \u2220AOC=50\u00b0. AE is drawn parallel to CD passing through A, intersecting circle O at point E. What is the degree measure of \u2220AOE? (). A, B, C, D choices are ['65\u00b0', '70\u00b0', '75\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11148.jpg"
-  },
-  {
-    "id": 11468,
-    "problem_id": 11149,
-    "problem": "<image>If the central angles of the sector shown in the figure are 30\u00b0, 40\u00b0, and 50\u00b0, then the remaining sector is a () of the circle.. A, B, C, D choices are ['\\\\frac{1}{3}', '\\\\frac{2}{3}', '\\\\frac{1}{2}', '\\\\frac{3}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11149.jpg"
-  },
-  {
-    "id": 11469,
-    "problem_id": 11150,
-    "problem": "<image>If the central angles of the sector shown in the figure are 30\u00b0, 40\u00b0, and 50\u00b0, then the remaining sector is a () of the circle.. A, B, C, D choices are ['\\\\frac{1}{3}', '\\\\frac{2}{3}', '\\\\frac{1}{2}', '\\\\frac{3}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11150.jpg"
-  },
-  {
-    "id": 11470,
-    "problem_id": 11151,
-    "problem": "<image>If the central angles of the sector shown in the figure are 30\u00b0, 40\u00b0, and 50\u00b0, then the remaining sector is a () of the circle.. A, B, C, D choices are ['\\\\frac{1}{3}', '\\\\frac{2}{3}', '\\\\frac{1}{2}', '\\\\frac{3}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11151.jpg"
-  },
-  {
-    "id": 11471,
-    "problem_id": 11152,
-    "problem": "<image>If the central angles of the sector shown in the figure are 30\u00b0, 40\u00b0, and 50\u00b0, then the remaining sector is a () of the circle.. A, B, C, D choices are ['\\\\frac{1}{3}', '\\\\frac{2}{3}', '\\\\frac{1}{2}', '\\\\frac{3}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11152.jpg"
-  },
-  {
-    "id": 11472,
-    "problem_id": 11153,
-    "problem": "<image>If the central angles of the sector shown in the figure are 30\u00b0, 40\u00b0, and 50\u00b0, then the remaining sector is a () of the circle.. A, B, C, D choices are ['\\\\frac{1}{3}', '\\\\frac{2}{3}', '\\\\frac{1}{2}', '\\\\frac{3}{4}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11153.jpg"
-  },
-  {
-    "id": 11473,
-    "problem_id": 11154,
-    "problem": "<image>As shown in the diagram, two chords AB and CD intersect at point E, and AB is perpendicular to CD. If \u2220A = 30\u00b0, what is the degree measure of \u2220B? (). A, B, C, D choices are ['30\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11154.jpg"
-  },
-  {
-    "id": 11474,
-    "problem_id": 11155,
-    "problem": "<image>As shown in the figure, it is known that \u2220AOB is the central angle of circle \u2299O, and \u2220AOB=60\u00b0. What is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11155.jpg"
-  },
-  {
-    "id": 11475,
-    "problem_id": 11156,
-    "problem": "<image>As shown in the figure, it is known that \u2220AOB is the central angle of circle \u2299O, and \u2220AOB=60\u00b0. What is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11156.jpg"
-  },
-  {
-    "id": 11476,
-    "problem_id": 11157,
-    "problem": "<image>As shown in the figure, it is known that \u2220AOB is the central angle of circle \u2299O, and \u2220AOB=60\u00b0. What is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11157.jpg"
-  },
-  {
-    "id": 11477,
-    "problem_id": 11158,
-    "problem": "<image>As shown in the figure, it is known that \u2220AOB is the central angle of circle \u2299O, and \u2220AOB=60\u00b0. What is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11158.jpg"
-  },
-  {
-    "id": 11478,
-    "problem_id": 11159,
-    "problem": "<image>As shown in the figure, it is known that \u2220AOB is the central angle of circle \u2299O, and \u2220AOB=60\u00b0. What is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11159.jpg"
-  },
-  {
-    "id": 11479,
-    "problem_id": 11160,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11160.jpg"
-  },
-  {
-    "id": 11480,
-    "problem_id": 11161,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11161.jpg"
-  },
-  {
-    "id": 11481,
-    "problem_id": 11162,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11162.jpg"
-  },
-  {
-    "id": 11482,
-    "problem_id": 11163,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11163.jpg"
-  },
-  {
-    "id": 11483,
-    "problem_id": 11164,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11164.jpg"
-  },
-  {
-    "id": 11484,
-    "problem_id": 11165,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11165.jpg"
-  },
-  {
-    "id": 11485,
-    "problem_id": 11166,
-    "problem": "<image>Given the figure, points A, B, and C are on the circle O. If \u2220AOC = 72\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['28\u00b0', '54\u00b0', '18\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11166.jpg"
-  },
-  {
-    "id": 11486,
-    "problem_id": 11167,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, point C is on circle O, if \u2220OCA=55\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11167.jpg"
-  },
-  {
-    "id": 11487,
-    "problem_id": 11168,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, point C is on circle O, if \u2220OCA=55\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11168.jpg"
-  },
-  {
-    "id": 11488,
-    "problem_id": 11169,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, point C is on circle O, if \u2220OCA=55\u00b0, then \u2220BOC is equal to (). A, B, C, D choices are ['105\u00b0', '110\u00b0', '115\u00b0', '125\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11169.jpg"
-  },
-  {
-    "id": 11489,
-    "problem_id": 11170,
-    "problem": "<image>In circle A with radius 5, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 6 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of the chord BC's distance from the center is ().. A, B, C, D choices are ['4', '3', '\\\\frac{\u221a{34}}{2}', '\\\\frac{\u221a{41}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11170.jpg"
-  },
-  {
-    "id": 11490,
-    "problem_id": 11171,
-    "problem": "<image>In circle A with radius 5, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 6 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of the chord BC's distance from the center is ().. A, B, C, D choices are ['4', '3', '\\\\frac{\u221a{34}}{2}', '\\\\frac{\u221a{41}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11171.jpg"
-  },
-  {
-    "id": 11491,
-    "problem_id": 11172,
-    "problem": "<image>In circle A with radius 5, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 6 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of the chord BC's distance from the center is ().. A, B, C, D choices are ['4', '3', '\\\\frac{\u221a{34}}{2}', '\\\\frac{\u221a{41}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11172.jpg"
-  },
-  {
-    "id": 11492,
-    "problem_id": 11173,
-    "problem": "<image>In circle A with radius 5, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 6 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of the chord BC's distance from the center is ().. A, B, C, D choices are ['4', '3', '\\\\frac{\u221a{34}}{2}', '\\\\frac{\u221a{41}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11173.jpg"
-  },
-  {
-    "id": 11493,
-    "problem_id": 11174,
-    "problem": "<image>In circle A with radius 5, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 6 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of the chord BC's distance from the center is ().. A, B, C, D choices are ['4', '3', '\\\\frac{\u221a{34}}{2}', '\\\\frac{\u221a{41}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11174.jpg"
-  },
-  {
-    "id": 11494,
-    "problem_id": 11175,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, AC and CD are two chords of circle O, CD is perpendicular to AB, and OD is connected. If \u2220CAB = 20\u00b0, then what is the degree of \u2220AOD? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{C}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11175.jpg"
-  },
-  {
-    "id": 11495,
-    "problem_id": 11176,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, AC and CD are two chords of circle O, CD is perpendicular to AB, and OD is connected. If \u2220CAB = 20\u00b0, then what is the degree of \u2220AOD? (). A, B, C, D choices are ['100\u00b0', '120\u00b0', '130\u00b0', '140\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[\\boxed{D}\\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11176.jpg"
-  },
-  {
-    "id": 11496,
-    "problem_id": 11177,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11177.jpg"
-  },
-  {
-    "id": 11497,
-    "problem_id": 11178,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11178.jpg"
-  },
-  {
-    "id": 11498,
-    "problem_id": 11179,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11179.jpg"
-  },
-  {
-    "id": 11499,
-    "problem_id": 11180,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11180.jpg"
-  },
-  {
-    "id": 11500,
-    "problem_id": 11181,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11181.jpg"
-  },
-  {
-    "id": 11501,
-    "problem_id": 11182,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11182.jpg"
-  },
-  {
-    "id": 11502,
-    "problem_id": 11183,
-    "problem": "<image>As shown in the figure, point C is on the circle O. If \u2220ACB = 35\u00b0, then \u2220AOB is equal to (). A, B, C, D choices are ['35\u00b0', '60\u00b0', '70\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11183.jpg"
-  },
-  {
-    "id": 11503,
-    "problem_id": 11184,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11184.jpg"
-  },
-  {
-    "id": 11504,
-    "problem_id": 11185,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11185.jpg"
-  },
-  {
-    "id": 11505,
-    "problem_id": 11186,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11186.jpg"
-  },
-  {
-    "id": 11506,
-    "problem_id": 11187,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11187.jpg"
-  },
-  {
-    "id": 11507,
-    "problem_id": 11188,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11188.jpg"
-  },
-  {
-    "id": 11508,
-    "problem_id": 11189,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11189.jpg"
-  },
-  {
-    "id": 11509,
-    "problem_id": 11190,
-    "problem": "<image>As shown in the figure, in circle O, AB is the diameter of circle O, and C is a point on the circle. If \u2220CAB = 23\u00b0, what is the degree measure of \u2220ABC? (). A, B, C, D choices are ['23\u00b0', '46\u00b0', '57\u00b0', '67\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11190.jpg"
-  },
-  {
-    "id": 11510,
-    "problem_id": 11191,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11191.jpg"
-  },
-  {
-    "id": 11511,
-    "problem_id": 11192,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11192.jpg"
-  },
-  {
-    "id": 11512,
-    "problem_id": 11193,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11193.jpg"
-  },
-  {
-    "id": 11513,
-    "problem_id": 11194,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11194.jpg"
-  },
-  {
-    "id": 11514,
-    "problem_id": 11195,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11195.jpg"
-  },
-  {
-    "id": 11515,
-    "problem_id": 11196,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11196.jpg"
-  },
-  {
-    "id": 11516,
-    "problem_id": 11197,
-    "problem": "<image>As shown in the figure, it is known that \u2220CAB is the circular angle of \u2299O, \u2220CAB=50\u00b0, then the central angle \u2220BOC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11197.jpg"
-  },
-  {
-    "id": 11517,
-    "problem_id": 11198,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, C is a point on circle O (excluding A and B), and \u2220BOD = 44\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['44\u00b0', '22\u00b0', '46\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11198.jpg"
-  },
-  {
-    "id": 11518,
-    "problem_id": 11199,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, C is a point on circle O (excluding A and B), and \u2220BOD = 44\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['44\u00b0', '22\u00b0', '46\u00b0', '36\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11199.jpg"
-  },
-  {
-    "id": 11519,
-    "problem_id": 11200,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11200.jpg"
-  },
-  {
-    "id": 11520,
-    "problem_id": 11201,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11201.jpg"
-  },
-  {
-    "id": 11521,
-    "problem_id": 11202,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11202.jpg"
-  },
-  {
-    "id": 11522,
-    "problem_id": 11203,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11203.jpg"
-  },
-  {
-    "id": 11523,
-    "problem_id": 11204,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11204.jpg"
-  },
-  {
-    "id": 11524,
-    "problem_id": 11205,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11205.jpg"
-  },
-  {
-    "id": 11525,
-    "problem_id": 11206,
-    "problem": "<image>As shown in the figure, the diameter of the circle O is BC=6, A is a point on the circle O, and \u2220C=30\u00b0. The length of AB is (). A, B, C, D choices are ['6', '3', '3\u221a{2}', '3\u221a{3}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11206.jpg"
-  },
-  {
-    "id": 11526,
-    "problem_id": 11207,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ACB=112\u00b0. What is the measure of \u2220\u03b1? (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '134\u00b0', '136\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11207.jpg"
-  },
-  {
-    "id": 11527,
-    "problem_id": 11208,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ACB=112\u00b0. What is the measure of \u2220\u03b1? (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '134\u00b0', '136\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11208.jpg"
-  },
-  {
-    "id": 11528,
-    "problem_id": 11209,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ACB=112\u00b0. What is the measure of \u2220\u03b1? (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '134\u00b0', '136\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11209.jpg"
-  },
-  {
-    "id": 11529,
-    "problem_id": 11210,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ACB=112\u00b0. What is the measure of \u2220\u03b1? (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '134\u00b0', '136\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11210.jpg"
-  },
-  {
-    "id": 11530,
-    "problem_id": 11211,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O, and \u2220ACB=112\u00b0. What is the measure of \u2220\u03b1? (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '134\u00b0', '136\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11211.jpg"
-  },
-  {
-    "id": 11531,
-    "problem_id": 11212,
-    "problem": "<image>As shown in the figure, OA and OB are radii of the circle O, and C is a point on the circle. If angle AOB is 40\u00b0 and angle OCB is 50\u00b0, what is the degree measure of angle OAC? (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11212.jpg"
-  },
-  {
-    "id": 11532,
-    "problem_id": 11213,
-    "problem": "<image>Given quadrilateral ABCD as shown in the figure, where AB\u2225CD, AB=AC=AD=4, BC=2, what is the value of BD?. A, B, C, D choices are ['\u221a{62}', '2\u221a{15}', '2\u221a{10}', '2\u221a{5}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11213.jpg"
-  },
-  {
-    "id": 11533,
-    "problem_id": 11214,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220C=32\u00b0, what is the degree measure of \u2220AOB? (). A, B, C, D choices are ['32\u00b0', '60\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11214.jpg"
-  },
-  {
-    "id": 11534,
-    "problem_id": 11215,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220C=32\u00b0, what is the degree measure of \u2220AOB? (). A, B, C, D choices are ['32\u00b0', '60\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11215.jpg"
-  },
-  {
-    "id": 11535,
-    "problem_id": 11216,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220C=32\u00b0, what is the degree measure of \u2220AOB? (). A, B, C, D choices are ['32\u00b0', '60\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11216.jpg"
-  },
-  {
-    "id": 11536,
-    "problem_id": 11217,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220C=32\u00b0, what is the degree measure of \u2220AOB? (). A, B, C, D choices are ['32\u00b0', '60\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11217.jpg"
-  },
-  {
-    "id": 11537,
-    "problem_id": 11218,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on circle O. If \u2220C=32\u00b0, what is the degree measure of \u2220AOB? (). A, B, C, D choices are ['32\u00b0', '60\u00b0', '64\u00b0', '72\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11218.jpg"
-  },
-  {
-    "id": 11538,
-    "problem_id": 11219,
-    "problem": "<image>As shown in the diagram, points A, B, and C are on the circle O, and \u2220A = 32\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '64\u00b0', '50\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11219.jpg"
-  },
-  {
-    "id": 11539,
-    "problem_id": 11220,
-    "problem": "<image>As shown in the diagram, points A, B, and C are on the circle O, and \u2220A = 32\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '64\u00b0', '50\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11220.jpg"
-  },
-  {
-    "id": 11540,
-    "problem_id": 11221,
-    "problem": "<image>As shown in the diagram, points A, B, and C are on the circle O, and \u2220A = 32\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '64\u00b0', '50\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11221.jpg"
-  },
-  {
-    "id": 11541,
-    "problem_id": 11222,
-    "problem": "<image>As shown in the diagram, points A, B, and C are on the circle O, and \u2220A = 32\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '64\u00b0', '50\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11222.jpg"
-  },
-  {
-    "id": 11542,
-    "problem_id": 11223,
-    "problem": "<image>As shown in the diagram, points A, B, and C are on the circle O, and \u2220A = 32\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '64\u00b0', '50\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11223.jpg"
-  },
-  {
-    "id": 11543,
-    "problem_id": 11224,
-    "problem": "<image>As shown in the diagram, points A, B, and C are on the circle O, and \u2220A = 32\u00b0. What is the degree measure of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '64\u00b0', '50\u00b0', '28\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11224.jpg"
-  },
-  {
-    "id": 11544,
-    "problem_id": 11225,
-    "problem": "<image>In circle O with radius 10 as shown, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 12 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of chord BC is (). A, B, C, D choices are ['18', '16', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11225.jpg"
-  },
-  {
-    "id": 11545,
-    "problem_id": 11226,
-    "problem": "<image>In circle O with radius 10 as shown, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 12 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of chord BC is (). A, B, C, D choices are ['18', '16', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11226.jpg"
-  },
-  {
-    "id": 11546,
-    "problem_id": 11227,
-    "problem": "<image>In circle O with radius 10 as shown, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 12 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of chord BC is (). A, B, C, D choices are ['18', '16', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11227.jpg"
-  },
-  {
-    "id": 11547,
-    "problem_id": 11228,
-    "problem": "<image>In circle O with radius 10 as shown, chord BC and chord ED correspond to central angles \u2220BAC and \u2220EAD, respectively. If DE = 12 and \u2220BAC + \u2220EAD = 180\u00b0, then the length of chord BC is (). A, B, C, D choices are ['18', '16', '10', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11228.jpg"
-  },
-  {
-    "id": 11548,
-    "problem_id": 11229,
-    "problem": "<image>Given the diagram below, A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220OBC? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '100\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11229.jpg"
-  },
-  {
-    "id": 11549,
-    "problem_id": 11230,
-    "problem": "<image>Given the diagram below, A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220OBC? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '100\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11230.jpg"
-  },
-  {
-    "id": 11550,
-    "problem_id": 11231,
-    "problem": "<image>Given the diagram below, A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220OBC? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '100\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11231.jpg"
-  },
-  {
-    "id": 11551,
-    "problem_id": 11232,
-    "problem": "<image>Given the diagram below, A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220OBC? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '100\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11232.jpg"
-  },
-  {
-    "id": 11552,
-    "problem_id": 11233,
-    "problem": "<image>Given the diagram below, A, B, and C are on circle O, and \u2220A = 50\u00b0. What is the degree measure of \u2220OBC? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '100\u00b0', '80\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11233.jpg"
-  },
-  {
-    "id": 11553,
-    "problem_id": 11234,
-    "problem": "<image>As shown in the figure, AC is the diameter of circle O, AB is a chord, and \u2220BOC = 100\u00b0. What is the degree measure of \u2220OAB? (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11234.jpg"
-  },
-  {
-    "id": 11554,
-    "problem_id": 11235,
-    "problem": "<image>As shown in the figure, AC is the diameter of circle O, AB is a chord, and \u2220BOC = 100\u00b0. What is the degree measure of \u2220OAB? (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11235.jpg"
-  },
-  {
-    "id": 11555,
-    "problem_id": 11236,
-    "problem": "<image>As shown in the figure, AC is the diameter of circle O, AB is a chord, and \u2220BOC = 100\u00b0. What is the degree measure of \u2220OAB? (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11236.jpg"
-  },
-  {
-    "id": 11556,
-    "problem_id": 11237,
-    "problem": "<image>As shown in the figure, AC is the diameter of circle O, AB is a chord, and \u2220BOC = 100\u00b0. What is the degree measure of \u2220OAB? (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11237.jpg"
-  },
-  {
-    "id": 11557,
-    "problem_id": 11238,
-    "problem": "<image>As shown in the figure, AC is the diameter of circle O, AB is a chord, and \u2220BOC = 100\u00b0. What is the degree measure of \u2220OAB? (). A, B, C, D choices are ['50\u00b0', '80\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11238.jpg"
-  },
-  {
-    "id": 11558,
-    "problem_id": 11239,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11239.jpg"
-  },
-  {
-    "id": 11559,
-    "problem_id": 11240,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11240.jpg"
-  },
-  {
-    "id": 11560,
-    "problem_id": 11241,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11241.jpg"
-  },
-  {
-    "id": 11561,
-    "problem_id": 11242,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11242.jpg"
-  },
-  {
-    "id": 11562,
-    "problem_id": 11243,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11243.jpg"
-  },
-  {
-    "id": 11563,
-    "problem_id": 11244,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11244.jpg"
-  },
-  {
-    "id": 11564,
-    "problem_id": 11245,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11245.jpg"
-  },
-  {
-    "id": 11565,
-    "problem_id": 11246,
-    "problem": "<image>Given that A, B, and C are three points on circle O, and \u2220BOC = 100\u00b0, what is the degree measure of \u2220BAC? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11246.jpg"
-  },
-  {
-    "id": 11566,
-    "problem_id": 11247,
-    "problem": "<image>As shown in the diagram, A, B, and C are on circle O. The degree of angle ACB is 300\u00b0, and the degree of angle C is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11247.jpg"
-  },
-  {
-    "id": 11567,
-    "problem_id": 11248,
-    "problem": "<image>As shown in the diagram, A, B, and C are on circle O. The degree of angle ACB is 300\u00b0, and the degree of angle C is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11248.jpg"
-  },
-  {
-    "id": 11568,
-    "problem_id": 11249,
-    "problem": "<image>As shown in the diagram, A, B, and C are on circle O. The degree of angle ACB is 300\u00b0, and the degree of angle C is ().. A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11249.jpg"
-  },
-  {
-    "id": 11569,
-    "problem_id": 11250,
-    "problem": "<image>As shown in the figure, AB and BC are two chords of circle O. OA and OB are connected, and \u2220ABC = 130\u00b0. What is the degree measure of \u2220AOC? (). A, B, C, D choices are ['120\u00b0', '100\u00b0', '160\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11250.jpg"
-  },
-  {
-    "id": 11570,
-    "problem_id": 11251,
-    "problem": "<image>As shown in the figure, AB and BC are two chords of circle O. OA and OB are connected, and \u2220ABC = 130\u00b0. What is the degree measure of \u2220AOC? (). A, B, C, D choices are ['120\u00b0', '100\u00b0', '160\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11251.jpg"
-  },
-  {
-    "id": 11571,
-    "problem_id": 11252,
-    "problem": "<image>As shown in the figure, AB and BC are two chords of circle O. OA and OB are connected, and \u2220ABC = 130\u00b0. What is the degree measure of \u2220AOC? (). A, B, C, D choices are ['120\u00b0', '100\u00b0', '160\u00b0', '150\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11252.jpg"
-  },
-  {
-    "id": 11572,
-    "problem_id": 11253,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O. If \u2220ACB = 112\u00b0, then \u2220\u03b1 = (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '136\u00b0', '134\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11253.jpg"
-  },
-  {
-    "id": 11573,
-    "problem_id": 11254,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O. If \u2220ACB = 112\u00b0, then \u2220\u03b1 = (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '136\u00b0', '134\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11254.jpg"
-  },
-  {
-    "id": 11574,
-    "problem_id": 11255,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O. If \u2220ACB = 112\u00b0, then \u2220\u03b1 = (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '136\u00b0', '134\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11255.jpg"
-  },
-  {
-    "id": 11575,
-    "problem_id": 11256,
-    "problem": "<image>As shown in the figure, points A, B, and C are on circle O. If \u2220ACB = 112\u00b0, then \u2220\u03b1 = (). A, B, C, D choices are ['68\u00b0', '112\u00b0', '136\u00b0', '134\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11256.jpg"
-  },
-  {
-    "id": 11576,
-    "problem_id": 11257,
-    "problem": "<image>In the diagram, in circle O, \u2220BAC = 15\u00b0, \u2220ADC = 20\u00b0, then the degree of \u2220ABO is (). A, B, C, D choices are ['70\u00b0', '55\u00b0', '45\u00b0', '35\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11257.jpg"
-  },
-  {
-    "id": 11577,
-    "problem_id": 11258,
-    "problem": "<image>As shown in the diagram, in right triangle ABC, \u2220A=25\u00b0, \u2220ACB=90\u00b0. A circle with center at point C and radius BC intersects AB at point D and intersects AC at point E. What is the degree measure of \u2220DCE? (). A, B, C, D choices are ['30\u00b0', '25\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11258.jpg"
-  },
-  {
-    "id": 11578,
-    "problem_id": 11259,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220C = 35\u00b0. What is the degree measure of \u2220OBA? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11259.jpg"
-  },
-  {
-    "id": 11579,
-    "problem_id": 11260,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220C = 35\u00b0. What is the degree measure of \u2220OBA? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11260.jpg"
-  },
-  {
-    "id": 11580,
-    "problem_id": 11261,
-    "problem": "<image>As shown in the diagram, \u2299O is the circumcircle of \u25b3ABC, and \u2220C = 35\u00b0. What is the degree measure of \u2220OBA? (). A, B, C, D choices are ['50\u00b0', '60\u00b0', '70\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11261.jpg"
-  },
-  {
-    "id": 11581,
-    "problem_id": 11262,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11262.jpg"
-  },
-  {
-    "id": 11582,
-    "problem_id": 11263,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11263.jpg"
-  },
-  {
-    "id": 11583,
-    "problem_id": 11264,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11264.jpg"
-  },
-  {
-    "id": 11584,
-    "problem_id": 11265,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11265.jpg"
-  },
-  {
-    "id": 11585,
-    "problem_id": 11266,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11266.jpg"
-  },
-  {
-    "id": 11586,
-    "problem_id": 11267,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11267.jpg"
-  },
-  {
-    "id": 11587,
-    "problem_id": 11268,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11268.jpg"
-  },
-  {
-    "id": 11588,
-    "problem_id": 11269,
-    "problem": "<image>Given the diagram, A, B, and C are points on circle O. If \u2220AOB = 60\u00b0, what is the degree measure of \u2220ACB? (). A, B, C, D choices are ['60\u00b0', '50\u00b0', '40\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11269.jpg"
-  },
-  {
-    "id": 11589,
-    "problem_id": 11270,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O. Points C and D are on circle O, with \u2220BOC = 110\u00b0. AD is parallel to OC. What is the measure of \u2220ABD? (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11270.jpg"
-  },
-  {
-    "id": 11590,
-    "problem_id": 11271,
-    "problem": "<image>Given that the diameter of circle O is AB = 8cm, point C is on circle O, and \u2220BOC=60\u00b0, what is the length of AC? (). A, B, C, D choices are ['4cm', '4\u221a{3}cm', '5cm', '2.5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11271.jpg"
-  },
-  {
-    "id": 11591,
-    "problem_id": 11272,
-    "problem": "<image>Given that the diameter of circle O is AB = 8cm, point C is on circle O, and \u2220BOC=60\u00b0, what is the length of AC? (). A, B, C, D choices are ['4cm', '4\u221a{3}cm', '5cm', '2.5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11272.jpg"
-  },
-  {
-    "id": 11592,
-    "problem_id": 11273,
-    "problem": "<image>Given that the diameter of circle O is AB = 8cm, point C is on circle O, and \u2220BOC=60\u00b0, what is the length of AC? (). A, B, C, D choices are ['4cm', '4\u221a{3}cm', '5cm', '2.5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11273.jpg"
-  },
-  {
-    "id": 11593,
-    "problem_id": 11274,
-    "problem": "<image>Given that the diameter of circle O is AB = 8cm, point C is on circle O, and \u2220BOC=60\u00b0, what is the length of AC? (). A, B, C, D choices are ['4cm', '4\u221a{3}cm', '5cm', '2.5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11274.jpg"
-  },
-  {
-    "id": 11594,
-    "problem_id": 11275,
-    "problem": "<image>Given that the diameter of circle O is AB = 8cm, point C is on circle O, and \u2220BOC=60\u00b0, what is the length of AC? (). A, B, C, D choices are ['4cm', '4\u221a{3}cm', '5cm', '2.5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11275.jpg"
-  },
-  {
-    "id": 11595,
-    "problem_id": 11276,
-    "problem": "<image>Given that the diameter of circle O is AB = 8cm, point C is on circle O, and \u2220BOC=60\u00b0, what is the length of AC? (). A, B, C, D choices are ['4cm', '4\u221a{3}cm', '5cm', '2.5cm'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11276.jpg"
-  },
-  {
-    "id": 11596,
-    "problem_id": 11277,
-    "problem": "<image>In the diagram, points A, B, and C are on circle O, and \u2220BOC=100\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11277.jpg"
-  },
-  {
-    "id": 11597,
-    "problem_id": 11278,
-    "problem": "<image>In the diagram, points A, B, and C are on circle O, and \u2220BOC=100\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11278.jpg"
-  },
-  {
-    "id": 11598,
-    "problem_id": 11279,
-    "problem": "<image>In the diagram, points A, B, and C are on circle O, and \u2220BOC=100\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11279.jpg"
-  },
-  {
-    "id": 11599,
-    "problem_id": 11280,
-    "problem": "<image>In the diagram, points A, B, and C are on circle O, and \u2220BOC=100\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11280.jpg"
-  },
-  {
-    "id": 11600,
-    "problem_id": 11281,
-    "problem": "<image>In the diagram, points A, B, and C are on circle O, and \u2220BOC=100\u00b0. What is the degree measure of \u2220A? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11281.jpg"
-  },
-  {
-    "id": 11601,
-    "problem_id": 11282,
-    "problem": "<image>As shown in the figure, AB is a chord of circle O, OC is perpendicular to AB and intersects circle O at point C. Point D is a point on circle O, and \u2220ADC=30\u00b0. What is the degree of \u2220BOC? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11282.jpg"
-  },
-  {
-    "id": 11602,
-    "problem_id": 11283,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, and points C, D, and E are all on circle O. If \u2220ACD = 40\u00b0, what is the degree measure of \u2220BED? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11283.jpg"
-  },
-  {
-    "id": 11603,
-    "problem_id": 11284,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, and points C, D, and E are all on circle O. If \u2220ACD = 40\u00b0, what is the degree measure of \u2220BED? (). A, B, C, D choices are ['50\u00b0', '40\u00b0', '30\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11284.jpg"
-  },
-  {
-    "id": 11604,
-    "problem_id": 11285,
-    "problem": "<image>As shown in the figure, in circle O, the central angle \u2220ACB is 50\u00b0. If P is a point above, and \u2220AOP is 55\u00b0, what is the degree measurement of \u2220POB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11285.jpg"
-  },
-  {
-    "id": 11605,
-    "problem_id": 11286,
-    "problem": "<image>As shown in the figure, in circle O, the central angle \u2220ACB is 50\u00b0. If P is a point above, and \u2220AOP is 55\u00b0, what is the degree measurement of \u2220POB? (). A, B, C, D choices are ['30\u00b0', '45\u00b0', '55\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11286.jpg"
-  },
-  {
-    "id": 11606,
-    "problem_id": 11287,
-    "problem": "<image>As shown in the figure, in circle O, the central angles corresponding to chords AB and CD are angles AOB and COD, respectively. If angles AOB and COD are complementary and AB = 2, CD = 4, then the radius of circle O is ().. A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11287.jpg"
-  },
-  {
-    "id": 11607,
-    "problem_id": 11288,
-    "problem": "<image>As shown in the figure, in circle O, the central angles corresponding to chords AB and CD are angles AOB and COD, respectively. If angles AOB and COD are complementary and AB = 2, CD = 4, then the radius of circle O is ().. A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11288.jpg"
-  },
-  {
-    "id": 11608,
-    "problem_id": 11289,
-    "problem": "<image>As shown in the figure, in circle O, the central angles corresponding to chords AB and CD are angles AOB and COD, respectively. If angles AOB and COD are complementary and AB = 2, CD = 4, then the radius of circle O is ().. A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11289.jpg"
-  },
-  {
-    "id": 11609,
-    "problem_id": 11290,
-    "problem": "<image>As shown in the diagram, AD is the diameter of circle O, |AB| = |CD|, and if \u2220AOB = 40\u00b0, then the degree measure of the arc \u2220BPC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11290.jpg"
-  },
-  {
-    "id": 11610,
-    "problem_id": 11291,
-    "problem": "<image>As shown in the diagram, AD is the diameter of circle O, |AB| = |CD|, and if \u2220AOB = 40\u00b0, then the degree measure of the arc \u2220BPC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11291.jpg"
-  },
-  {
-    "id": 11611,
-    "problem_id": 11292,
-    "problem": "<image>As shown in the diagram, AD is the diameter of circle O, |AB| = |CD|, and if \u2220AOB = 40\u00b0, then the degree measure of the arc \u2220BPC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11292.jpg"
-  },
-  {
-    "id": 11612,
-    "problem_id": 11293,
-    "problem": "<image>As shown in the diagram, AD is the diameter of circle O, |AB| = |CD|, and if \u2220AOB = 40\u00b0, then the degree measure of the arc \u2220BPC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11293.jpg"
-  },
-  {
-    "id": 11613,
-    "problem_id": 11294,
-    "problem": "<image>As shown in the diagram, AD is the diameter of circle O, |AB| = |CD|, and if \u2220AOB = 40\u00b0, then the degree measure of the arc \u2220BPC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11294.jpg"
-  },
-  {
-    "id": 11614,
-    "problem_id": 11295,
-    "problem": "<image>As shown in the diagram, AD is the diameter of circle O, |AB| = |CD|, and if \u2220AOB = 40\u00b0, then the degree measure of the arc \u2220BPC is ().. A, B, C, D choices are ['40\u00b0', '50\u00b0', '60\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11295.jpg"
-  },
-  {
-    "id": 11615,
-    "problem_id": 11296,
-    "problem": "<image>In the figure, BC is the diameter of circle O. A and D are two points on circle O. Connect AB, AD, and BD. If \u2220ADB = 70\u00b0, what is the degree measure of \u2220ABC?. A, B, C, D choices are ['20\u00b0', '70\u00b0', '30\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11296.jpg"
-  },
-  {
-    "id": 11616,
-    "problem_id": 11297,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11297.jpg"
-  },
-  {
-    "id": 11617,
-    "problem_id": 11298,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11298.jpg"
-  },
-  {
-    "id": 11618,
-    "problem_id": 11299,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11299.jpg"
-  },
-  {
-    "id": 11619,
-    "problem_id": 11300,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11300.jpg"
-  },
-  {
-    "id": 11620,
-    "problem_id": 11301,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11301.jpg"
-  },
-  {
-    "id": 11621,
-    "problem_id": 11302,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11302.jpg"
-  },
-  {
-    "id": 11622,
-    "problem_id": 11303,
-    "problem": "<image>As shown in the diagram, in circle O, if \u2220O=50\u00b0, then what is the degree of \u2220A? (). A, B, C, D choices are ['50\u00b0', '20\u00b0', '30\u00b0', '25\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11303.jpg"
-  },
-  {
-    "id": 11623,
-    "problem_id": 11304,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11304.jpg"
-  },
-  {
-    "id": 11624,
-    "problem_id": 11305,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11305.jpg"
-  },
-  {
-    "id": 11625,
-    "problem_id": 11306,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11306.jpg"
-  },
-  {
-    "id": 11626,
-    "problem_id": 11307,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11307.jpg"
-  },
-  {
-    "id": 11627,
-    "problem_id": 11308,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11308.jpg"
-  },
-  {
-    "id": 11628,
-    "problem_id": 11309,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11309.jpg"
-  },
-  {
-    "id": 11629,
-    "problem_id": 11310,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11310.jpg"
-  },
-  {
-    "id": 11630,
-    "problem_id": 11311,
-    "problem": "<image>In the figure, points A, B, and C are on circle O, and \u2220OAB = 65\u00b0. What is the degree measure of \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '32.5\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11311.jpg"
-  },
-  {
-    "id": 11631,
-    "problem_id": 11312,
-    "problem": "<image>As shown in the diagram, in circle O, chords AB and CD correspond to central angles \u2220AOB and \u2220COD respectively. If \u2220AOB and \u2220COD are complementary and AB = 2, CD = 4, what is the radius of circle O? (). A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11312.jpg"
-  },
-  {
-    "id": 11632,
-    "problem_id": 11313,
-    "problem": "<image>As shown in the diagram, in circle O, chords AB and CD correspond to central angles \u2220AOB and \u2220COD respectively. If \u2220AOB and \u2220COD are complementary and AB = 2, CD = 4, what is the radius of circle O? (). A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11313.jpg"
-  },
-  {
-    "id": 11633,
-    "problem_id": 11314,
-    "problem": "<image>As shown in the diagram, in circle O, chords AB and CD correspond to central angles \u2220AOB and \u2220COD respectively. If \u2220AOB and \u2220COD are complementary and AB = 2, CD = 4, what is the radius of circle O? (). A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11314.jpg"
-  },
-  {
-    "id": 11634,
-    "problem_id": 11315,
-    "problem": "<image>As shown in the diagram, in circle O, chords AB and CD correspond to central angles \u2220AOB and \u2220COD respectively. If \u2220AOB and \u2220COD are complementary and AB = 2, CD = 4, what is the radius of circle O? (). A, B, C, D choices are ['\u221a{3}', '2', '\u221a{5}', '4'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11315.jpg"
-  },
-  {
-    "id": 11635,
-    "problem_id": 11316,
-    "problem": "<image>In the diagram, in circle O, chord AB and CD are perpendicular and intersect at point P, \u2220A=35\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11316.jpg"
-  },
-  {
-    "id": 11636,
-    "problem_id": 11317,
-    "problem": "<image>In the diagram, in circle O, chord AB and CD are perpendicular and intersect at point P, \u2220A=35\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11317.jpg"
-  },
-  {
-    "id": 11637,
-    "problem_id": 11318,
-    "problem": "<image>In the diagram, in circle O, chord AB and CD are perpendicular and intersect at point P, \u2220A=35\u00b0, what is the measure of \u2220B? (). A, B, C, D choices are ['35\u00b0', '55\u00b0', '65\u00b0', '70\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11318.jpg"
-  },
-  {
-    "id": 11638,
-    "problem_id": 11319,
-    "problem": "<image>As shown in the figure, points B, C, and D are on circle O. If \u2220BCD = 140\u00b0, what is the degree measure of \u2220BOD? (). A, B, C, D choices are ['40\u00b0', '50\u00b0', '80\u00b0', '90\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11319.jpg"
-  },
-  {
-    "id": 11639,
-    "problem_id": 11320,
-    "problem": "<image>In the figure, in circle O, OC is perpendicular to AB, \u2220ADC = 35\u00b0. What is the degree measurement of \u2220OBA? (). A, B, C, D choices are ['35', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11320.jpg"
-  },
-  {
-    "id": 11640,
-    "problem_id": 11321,
-    "problem": "<image>In the figure, in circle O, OC is perpendicular to AB, \u2220ADC = 35\u00b0. What is the degree measurement of \u2220OBA? (). A, B, C, D choices are ['35', '30\u00b0', '25\u00b0', '20\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11321.jpg"
-  },
-  {
-    "id": 11641,
-    "problem_id": 11322,
-    "problem": "<image>As shown in the figure, A and D are two points on the circle O, BC is the diameter. If \u2220D = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '72\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11322.jpg"
-  },
-  {
-    "id": 11642,
-    "problem_id": 11323,
-    "problem": "<image>As shown in the figure, A and D are two points on the circle O, BC is the diameter. If \u2220D = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '72\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11323.jpg"
-  },
-  {
-    "id": 11643,
-    "problem_id": 11324,
-    "problem": "<image>As shown in the figure, A and D are two points on the circle O, BC is the diameter. If \u2220D = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '72\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11324.jpg"
-  },
-  {
-    "id": 11644,
-    "problem_id": 11325,
-    "problem": "<image>As shown in the figure, A and D are two points on the circle O, BC is the diameter. If \u2220D = 32\u00b0, then \u2220AOC = (). A, B, C, D choices are ['64\u00b0', '58\u00b0', '72\u00b0', '55\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11325.jpg"
-  },
-  {
-    "id": 11645,
-    "problem_id": 11326,
-    "problem": "<image>Given the diagram, points B, C, and D are on circle O. If \u2220BCD = 120\u00b0, what is the degree of \u2220BOD? (). A, B, C, D choices are ['60\u00b0', '80\u00b0', '120\u00b0', '240\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11326.jpg"
-  },
-  {
-    "id": 11646,
-    "problem_id": 11327,
-    "problem": "<image>Given the diagram, points B, C, and D are on circle O. If \u2220BCD = 120\u00b0, what is the degree of \u2220BOD? (). A, B, C, D choices are ['60\u00b0', '80\u00b0', '120\u00b0', '240\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11327.jpg"
-  },
-  {
-    "id": 11647,
-    "problem_id": 11328,
-    "problem": "<image>Given the diagram, points B, C, and D are on circle O. If \u2220BCD = 120\u00b0, what is the degree of \u2220BOD? (). A, B, C, D choices are ['60\u00b0', '80\u00b0', '120\u00b0', '240\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11328.jpg"
-  },
-  {
-    "id": 11648,
-    "problem_id": 11329,
-    "problem": "<image>In the diagram, AC is the diameter of circle O, and B and D are points on circle O. If \u2220CAB = 34\u00b0, what is the degree measure of \u2220D? (). A, B, C, D choices are ['44\u00b0', '54\u00b0', '56\u00b0', '66\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11329.jpg"
-  },
-  {
-    "id": 11649,
-    "problem_id": 11330,
-    "problem": "<image>As shown in the diagram, in circle O, OC is perpendicular to AB, \u2220ADC=26\u00b0, what is the degree of \u2220COB? (). A, B, C, D choices are ['52\u00b0', '64\u00b0', '48\u00b0', '42\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11330.jpg"
-  },
-  {
-    "id": 11650,
-    "problem_id": 11331,
-    "problem": "<image>As shown in the figure, the diameter AB of circle O is 10, the chord BC is 6, OD is perpendicular to AC and the foot of the perpendicular is point D. What is the length of OD? (). A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11331.jpg"
-  },
-  {
-    "id": 11651,
-    "problem_id": 11332,
-    "problem": "<image>As shown in the figure, the diameter AB of circle O is 10, the chord BC is 6, OD is perpendicular to AC and the foot of the perpendicular is point D. What is the length of OD? (). A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11332.jpg"
-  },
-  {
-    "id": 11652,
-    "problem_id": 11333,
-    "problem": "<image>As shown in the figure, the diameter AB of circle O is 10, the chord BC is 6, OD is perpendicular to AC and the foot of the perpendicular is point D. What is the length of OD? (). A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11333.jpg"
-  },
-  {
-    "id": 11653,
-    "problem_id": 11334,
-    "problem": "<image>As shown in the figure, the diameter AB of circle O is 10, the chord BC is 6, OD is perpendicular to AC and the foot of the perpendicular is point D. What is the length of OD? (). A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11334.jpg"
-  },
-  {
-    "id": 11654,
-    "problem_id": 11335,
-    "problem": "<image>As shown in the figure, the diameter AB of circle O is 10, the chord BC is 6, OD is perpendicular to AC and the foot of the perpendicular is point D. What is the length of OD? (). A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11335.jpg"
-  },
-  {
-    "id": 11655,
-    "problem_id": 11336,
-    "problem": "<image>As shown in the figure, the diameter AB of circle O is 10, the chord BC is 6, OD is perpendicular to AC and the foot of the perpendicular is point D. What is the length of OD? (). A, B, C, D choices are ['6', '5', '4', '3'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11336.jpg"
-  },
-  {
-    "id": 11656,
-    "problem_id": 11337,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, BC is a chord of circle O, and \u2220AOC = 80\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11337.jpg"
-  },
-  {
-    "id": 11657,
-    "problem_id": 11338,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, BC is a chord of circle O, and \u2220AOC = 80\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11338.jpg"
-  },
-  {
-    "id": 11658,
-    "problem_id": 11339,
-    "problem": "<image>As shown in the diagram, AB is the diameter of circle O, BC is a chord of circle O, and \u2220AOC = 80\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '50\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11339.jpg"
-  },
-  {
-    "id": 11659,
-    "problem_id": 11340,
-    "problem": "<image>As shown in the figure, points A, B, and C are all on the circle O. In quadrilateral ABCO, if \u2220AOC = 140\u00b0, then the degree of \u2220B is ().. A, B, C, D choices are ['110\u00b0', '70\u00b0', '140\u00b0', '100\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11340.jpg"
-  },
-  {
-    "id": 11660,
-    "problem_id": 11341,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and A is the midpoint of arc DC. If \u2220ABD = 15\u00b0, what is the degree measure of \u2220BOC? (). A, B, C, D choices are ['120\u00b0', '150\u00b0', '210\u00b0', '75\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11341.jpg"
-  },
-  {
-    "id": 11661,
-    "problem_id": 11342,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O. OA and OB are connected, and angle ABO is 40\u00b0. What is the degree measure of angle C? (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11342.jpg"
-  },
-  {
-    "id": 11662,
-    "problem_id": 11343,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O. OA and OB are connected, and angle ABO is 40\u00b0. What is the degree measure of angle C? (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11343.jpg"
-  },
-  {
-    "id": 11663,
-    "problem_id": 11344,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O. OA and OB are connected, and angle ABO is 40\u00b0. What is the degree measure of angle C? (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11344.jpg"
-  },
-  {
-    "id": 11664,
-    "problem_id": 11345,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O. OA and OB are connected, and angle ABO is 40\u00b0. What is the degree measure of angle C? (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11345.jpg"
-  },
-  {
-    "id": 11665,
-    "problem_id": 11346,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O. OA and OB are connected, and angle ABO is 40\u00b0. What is the degree measure of angle C? (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11346.jpg"
-  },
-  {
-    "id": 11666,
-    "problem_id": 11347,
-    "problem": "<image>As shown in the figure, triangle ABC is inscribed in circle O. OA and OB are connected, and angle ABO is 40\u00b0. What is the degree measure of angle C? (). A, B, C, D choices are ['100\u00b0', '80\u00b0', '50\u00b0', '40\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11347.jpg"
-  },
-  {
-    "id": 11668,
-    "problem_id": 11348,
-    "problem": "<image>As shown in the figure, AB is the diameter of circle O, point D is a point on circle O, and \u2220ABD=30\u00b0. If BO=4, what is the length of AD? (). A, B, C, D choices are ['3', '4', '4\u221a{3}', '8'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{C} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11348.jpg"
-  },
-  {
-    "id": 11669,
-    "problem_id": 11349,
-    "problem": "<image>In the figure, AB is a chord of circle O with AB = 5. Point C is a moving point on circle O and \u2220ACB = 45\u00b0. Points M and N are the midpoints of AB and AC, respectively. The maximum length of segment MN is () .. A, B, C, D choices are ['5', '\\\\frac{5}{2}', '5\u221a{2}', '\\\\frac{5\u221a{2}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11349.jpg"
-  },
-  {
-    "id": 11670,
-    "problem_id": 11350,
-    "problem": "<image>In the figure, AB is a chord of circle O with AB = 5. Point C is a moving point on circle O and \u2220ACB = 45\u00b0. Points M and N are the midpoints of AB and AC, respectively. The maximum length of segment MN is () .. A, B, C, D choices are ['5', '\\\\frac{5}{2}', '5\u221a{2}', '\\\\frac{5\u221a{2}}{2}'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{D} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11350.jpg"
-  },
-  {
-    "id": 11671,
-    "problem_id": 11351,
-    "problem": "<image>In the circle O as shown, points A, B, and C are on the circle, and \u2220OAB=50\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11351.jpg"
-  },
-  {
-    "id": 11672,
-    "problem_id": 11352,
-    "problem": "<image>In the circle O as shown, points A, B, and C are on the circle, and \u2220OAB=50\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11352.jpg"
-  },
-  {
-    "id": 11673,
-    "problem_id": 11353,
-    "problem": "<image>In the circle O as shown, points A, B, and C are on the circle, and \u2220OAB=50\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11353.jpg"
-  },
-  {
-    "id": 11674,
-    "problem_id": 11354,
-    "problem": "<image>In the circle O as shown, points A, B, and C are on the circle, and \u2220OAB=50\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11354.jpg"
-  },
-  {
-    "id": 11675,
-    "problem_id": 11355,
-    "problem": "<image>In the circle O as shown, points A, B, and C are on the circle, and \u2220OAB=50\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11355.jpg"
-  },
-  {
-    "id": 11676,
-    "problem_id": 11356,
-    "problem": "<image>In the circle O as shown, points A, B, and C are on the circle, and \u2220OAB=50\u00b0. What is the degree measure of \u2220C? (). A, B, C, D choices are ['30\u00b0', '40\u00b0', '50\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11356.jpg"
-  },
-  {
-    "id": 11677,
-    "problem_id": 11357,
-    "problem": "<image>As shown in the figure, a protractor is placed on top of \u2220BAC, and point B is exactly at the 40\u00b0 mark on the protractor. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['40\u00b0', '80\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11357.jpg"
-  },
-  {
-    "id": 11678,
-    "problem_id": 11358,
-    "problem": "<image>As shown in the figure, a protractor is placed on top of \u2220BAC, and point B is exactly at the 40\u00b0 mark on the protractor. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['40\u00b0', '80\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11358.jpg"
-  },
-  {
-    "id": 11679,
-    "problem_id": 11359,
-    "problem": "<image>As shown in the figure, a protractor is placed on top of \u2220BAC, and point B is exactly at the 40\u00b0 mark on the protractor. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['40\u00b0', '80\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11359.jpg"
-  },
-  {
-    "id": 11680,
-    "problem_id": 11360,
-    "problem": "<image>As shown in the figure, a protractor is placed on top of \u2220BAC, and point B is exactly at the 40\u00b0 mark on the protractor. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['40\u00b0', '80\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11360.jpg"
-  },
-  {
-    "id": 11681,
-    "problem_id": 11361,
-    "problem": "<image>As shown in the figure, a protractor is placed on top of \u2220BAC, and point B is exactly at the 40\u00b0 mark on the protractor. What is the degree measure of \u2220BAC? (). A, B, C, D choices are ['40\u00b0', '80\u00b0', '20\u00b0', '10\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11361.jpg"
-  },
-  {
-    "id": 11682,
-    "problem_id": 11362,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11362.jpg"
-  },
-  {
-    "id": 11683,
-    "problem_id": 11363,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11363.jpg"
-  },
-  {
-    "id": 11684,
-    "problem_id": 11364,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11364.jpg"
-  },
-  {
-    "id": 11685,
-    "problem_id": 11365,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11365.jpg"
-  },
-  {
-    "id": 11686,
-    "problem_id": 11366,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{A} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11366.jpg"
-  },
-  {
-    "id": 11687,
-    "problem_id": 11367,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11367.jpg"
-  },
-  {
-    "id": 11688,
-    "problem_id": 11368,
-    "problem": "<image>Given the diagram, if \u2220AOB is the central angle of circle \u2299O and \u2220AOB = 50\u00b0, what is the degree measure of the arc \u2220ACB? (). A, B, C, D choices are ['50\u00b0', '25\u00b0', '100\u00b0', '30\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11368.jpg"
-  },
-  {
-    "id": 11689,
-    "problem_id": 11369,
-    "problem": "<image>As shown in the figure, CD is perpendicular to AB at point E. If \u2220B is 60\u00b0, then \u2220A is equal to (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11369.jpg"
-  },
-  {
-    "id": 11690,
-    "problem_id": 11370,
-    "problem": "<image>As shown in the figure, CD is perpendicular to AB at point E. If \u2220B is 60\u00b0, then \u2220A is equal to (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11370.jpg"
-  },
-  {
-    "id": 11691,
-    "problem_id": 11371,
-    "problem": "<image>As shown in the figure, CD is perpendicular to AB at point E. If \u2220B is 60\u00b0, then \u2220A is equal to (). A, B, C, D choices are ['20\u00b0', '30\u00b0', '40\u00b0', '60\u00b0'] Please give reason process and provide the correct option, such as: answer is A/B/C/D.",
-    "data_type": "image",
-    "problem_type": "free-form",
-    "options": [],
-    "solution": "<answer>\\[ \\boxed{B} \\]</answer>",
-    "data_source": "redstar-geo-r1",
-    "path": "redstar-geo-r1/11371.jpg"
-  }
-]
\ No newline at end of file
+version https://git-lfs.github.com/spec/v1
+oid sha256:09bed19fb7b347c6fccf57836726ec4d976859a5a015ee268abc5270a8bbe1dd
+size 113695968