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The median AD of the triangle ABC is ...

The median AD of the triangle ABC is bisected at E and BE meets AC at F. Find AF:FC.

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To solve the problem of finding the ratio \( AF:FC \) in triangle \( ABC \) where \( AD \) is the median, \( E \) is the midpoint of \( AD \), and \( BE \) intersects \( AC \) at \( F \), we can follow these steps: ### Step 1: Set up the triangle and assign coordinates Let’s place the triangle \( ABC \) in a coordinate system: - Let point \( A \) be at the origin, \( A(0, 0) \). - Let point \( B \) be at \( B(b_1, b_2) \). - Let point \( C \) be at \( C(c_1, c_2) \). ...
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