Question 100
Let $A$, $B$, and $C$ be points on line $l$ such that $B$ is between points $A$ and $C$. Points $D$ and $E$ lie on the same side of line $l$ such that $AD = BD$, $BC = EC$, and triangles $\triangle ADB$ and $\triangle ECB$ are similar. The lines $AE$ and $CD$ intersect at point $F$. Prove that the line $CD$ is the angle bisector of $\angle BFE$. (Khulan Tumenbayar)