CMO 2011 Problem 2

Let $A B C D$ be a cyclic quadrilateral whose opposite sides are not parallel, $X$ the intersection of $A B$ and $C D$, and $Y$ the intersection of $A D$ and $B C$. Let the angle bisector of $\angle A X D$ intersect $A D, B C$ at $E, F$ respectively and let the angle bisector of $\angle A Y B$ intersect $A B, C D$ at $G, H$ respectively. Prove that $E G F H$ is a parallelogram. fore,