ELMO SL 2010 G6

Let $ABC$ be a triangle with circumcircle $\Omega$ . $X$ and $Y$ are points on $\Omega$ such that $XY$ meets $AB$ and $AC$ at $D$ and $E$ , respectively. Show that the midpoints of $XY$ , $BE$ , $CD$ , and $DE$ are concyclic.

Carl Lian.