ÖMO 2000 Problem 2

A trapezoid $ABCD$ with $AB \parallel CD$ is inscribed in a circle $k$ . Points $P$ and $Q$ are chose on the arc $ADCB$ in the order $A-P -Q-B$ . Lines $CP$ and $AQ$ meet at $X$ , and lines $BP$ and $DQ$ meet at $Y$ . Show that points $P,Q,X, Y$ lie on a circle.