text: # If O is the circumcentre of Triangle ABC and OD prependicular to BC. Prove that Angle BOD = Angle A
  
  O is the circumcentre of ∆ABC and OD⊥BC.
  
  ∴ O is the point of intersection of perpendicular bisectors of the sides of ∆ABC.
  
  ⇒  D is the mid point of BC.
  
  ⇒ BD = DC
  
  In ∆OBD and ∆OCD,
  
  OB = OC  (Radius of the circle)
  
  OD = OD  (Common)
  
  BD = DC  (Proved)
  
  ∴ ∆OBD ≅ ∆OCD (SSS Congruence criterion)
  
  ⇒∠BOD = ∠COD  (CPCT)
  
  We know that, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  
  ∴ ∠BOC = 2 ∠BAC
  
  ⇒ 2∠BOD = 2 ∠A        [ Using (1) ]
  
  ⇒ ∠BOD = ∠A
  
  • 68
  
  plz provide a figure for it
  
  • 5
  
  I too don't hav any figure. You just have to proove it by making your own figure.
  
  • -3
  
  look angle BOD = 1/2 OF angle BOC  (as OD IS THE PERPENDICULAR to BC )...(1)
  
  angle A = 1/2 OF Angle BOC (angle subtended at the centre by the chord is double than the angle subtended by it at any other point on the remaining part of the circle)  ..........(2)
  
  from equation 1 and 2 it is clear that angle BOD = angle A.
  
  HOPE IT HELPS YOU
  
  good luck.......
  
  • 7
  What are you looking for?
explanation: The document contains a detailed geometric proof that Angle BOD is equal to Angle A, given that O is the circumcentre of Triangle ABC and OD is perpendicular to BC. The proof is followed by a discussion and a request for a figure. The document includes both a question and an answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # If O is the circumcentre of Triangle ABC and OD prependicular to BC. Prove that Angle BOD = Angle A
  
  O is the circumcentre of ∆ABC and OD⊥BC.
  
  ∴ O is the point of intersection of perpendicular bisectors of the sides of ∆ABC.
  
  ⇒  D is the mid point of BC.
  
  ⇒ BD = DC
  
  In ∆OBD and ∆OCD,
  
  OB = OC  (Radius of the circle)
  
  OD = OD  (Common)
  
  BD = DC  (Proved)
  
  ∴ ∆OBD ≅ ∆OCD (SSS Congruence criterion)
  
  ⇒∠BOD = ∠COD  (CPCT)
  
  We know that, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  
  ∴ ∠BOC = 2 ∠BAC
  
  ⇒ 2∠BOD = 2 ∠A        [ Using (1) ]
  
  ⇒ ∠BOD = ∠A
  
  • 68
  
  plz provide a figure for it
  
  • 5
  
  I too don't hav any figure. You just have to proove it by making your own figure.
  
  • -3
  
  look angle BOD = 1/2 OF angle BOC  (as OD IS THE PERPENDICULAR to BC )...(1)
  
  angle A = 1/2 OF Angle BOC (angle subtended at the centre by the chord is double than the angle subtended by it at any other point on the remaining part of the circle)  ..........(2)
  
  from equation 1 and 2 it is clear that angle BOD = angle A.
  
  HOPE IT HELPS YOU
  
  good luck.......
  
  • 7
  What are you looking for?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a detailed geometric proof that Angle BOD is equal to Angle A, given that O is the circumcentre of Triangle ABC and OD is perpendicular to BC. The proof is followed by a discussion and a request for a figure. The document includes both a question and an answer.
  
  Label: question-and-answer