Question 32
In triangle $ABC$ with $AB = AC$, $M$ is the midpoint of $BC$, $H$ is the projection of $M$ onto $AB$ and $D$ is arbitrary point on the side $AC$. Let $E$ be the intersection point of the parallel line through $B$ to $HD$ with the parallel line through $C$ to $AB$. Prove that $DM$ is the bisector of $\angle ADE$.
