MathNet 2004 — Part 02 Question 7

In triangle $A B C$, $A D$ ($D \in B C$) is a median, $E$ is a point on $A C$, and $F$ is the intersection of $B E$ with $A D$.
Prove: If $\frac{B F}{F E}=\frac{B C}{A B}+1$, then $B E$ is an angle bisector.