IR-TST 2013 Problem 17

In triangle $ABC$ , $AD$ and $AH$ are the angle bisector and the altitude of vertex $A$ , respectively. The perpendicular bisector of $AD$ , intersects the semicircles with diameters $AB$ and $AC$ which are drawn outside triangle $ABC$ in $X$ and $Y$ , respectively. Prove that the quadrilateral $XYDH$ is concyclic.

Proposed by Mahan Malihi