Let $ABC$ be an acute scalene triangle. Let $D$ be the foot of the $A$-bisectrix and $E$ be the foot of the $A$-altitude. The perpendicular bisector of the segment $AD$ intersects the semicircles of diameter $AB$ and $AC$ which lie on the outside of triangle $ABC$ at $X$ and $Y$ respectively. Prove that the points $X,Y,D$ and $E$ lie on a circle.