BALTIC-WAY 2008 Problem 16

Let $A B C D$ be a parallelogram. The circle with diameter $A C$ intersects the line $B D$ at points $P$ and $Q$. The perpendicular to the line $A C$ passing through the point $C$ intersects the lines $A B$ and $A D$ at points $X$ and $Y$, respectively. Prove that the points $P, Q, X$ and $Y$ lie on the same circle.