In ` A B C ,A D` is the median through `A` and `E` is the mid-point of `A D` . `B E` produced meets `A C` in `F` (Figure). Prove that `A F=1/3A Cdot`

Explanation

To prove that \( AF = \frac{1}{3} AC \) in triangle \( ABC \) with median \( AD \) and midpoint \( E \) of \( AD \), we can follow these steps:

### Step 1: Understand the Given Information
We have triangle \( ABC \) with \( AD \) as the median. This means that \( D \) is the midpoint of side \( BC \). Also, \( E \) is the midpoint of \( AD \).

**Hint:** Recall that a median divides the opposite side into two equal segments.

### Step 2: Draw a Line Parallel to \( BF \)
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