Question 102
In the scalene acute triangle $A B C$, let $D$ be the foot of the angle bisector from $A$ and $E$ the foot of the altitude from $A$. The perpendicular bisector of the segment $A D$ meets the semicircles with diameters $A B$ and $A C$, constructed outside the triangle $A B C$, at $X$ and $Y$, respectively. Prove that the points $X, Y, D$ and $E$ are concyclic.