Question 61
Given is an isosceles triangle $A B C$ with vertex $A$. Let $D$ be the bisector of side $A C$ and let $E$ be the perpendicular projection of point $D$ onto side $B C$. We denote by $F$ the halfway point of the distance $D E$. Prove that the distances $B F$ and $A E$ intersect at right angles exactly when the triangle $A B C$ is equilateral.