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 Asymptotegeometrycircumcircleangle bisectorperpendicular bisectorgeometry proposed