RU-SPB 2021 Problem 106

A line $\ell$ passes through vertex $C$ of the rhombus $ABCD$ and meets the extensions of $AB, AD$ at points $X,Y$ . Lines $DX, BY$ meet $(AXY)$ for the second time at $P,Q$ . Prove that the circumcircle of $\triangle PCQ$ is tangent to $\ell$ A. Kuznetsov