BALKAN-SL 2014 G6

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 $\angle ADE$ .