30th Junior Turkish Mathematical Olympiad

Let $ABCD$ be a parallelogram. Suppose that a point $P$ is chosen on the arc of the circumcircle of $ABC$ not containing $A$; a point $Q$ is chosen on the extension of the segment $AC$ on the side $C$ such that $\angle PBC=\angle CDQ$. Show that the circumcircle of $APQ$ is tangent to the line $AB$.