Question 68
Let $ABC$ be an isosceles triangle with $|AB| = |AC|$. The points $D, E$ and $F$ are on the sides $BC, CA$ and $AB$, respectively, such that $\angle FDE = \angle ABC$ and $FE$ is not parallel to $BC$. Prove that $BC$ is tangent to the circumcircle of $\triangle DEF$ if and only if $D$ is the midpoint of $BC$.