[

The ratio in which the bisector divides the side

] Similarity

[The ratio of the areas of triangles with a common base or common height] Class In triangle $A B C$, the bisectors $C F$ and $A D$ are drawn. Find the ratio $S_{A F D}: S_{A B C}$, if $A B: A C: B C=21: 28: 20$.

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By the property of the bisector of a triangle $B D: D C=A B: A C=3: 4, A F: F B=A C: C B=7: 5$. Therefore, $S_{A F D}=$ $7 / 12 S_{A B D}={ }^{7} / 12 \cdot 3 / 7 \cdot S_{A B C}=1 / 4 S_{A B C}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_9617f685748a8dfcd82ag-19.jpg?height=254&width=338&top_left_y=2177&top_left_x=860)

## Answer

$1: 4$.