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 solve the problem, we need to prove that \( AF = \frac{1}{3} AC \) in triangle \( ABC \) with median \( AD \) and \( E \) as the midpoint of \( AD \).

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Triangle \( ABC \) with median \( AD \).
- \( E \) is the midpoint of \( AD \).
- Line \( BE \) produced meets \( AC \) at point \( F \).
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