OMM 2013 Problem 2

Let $ABCD$ be a parallelogram with the angle at $A$ obtuse. Let $P$ be a point on segment $BD$ . The circle with center $P$ passing through $A$ cuts line $AD$ at $A$ and $Y$ and cuts line $AB$ at $A$ and $X$ . Line $AP$ intersects $BC$ at $Q$ and $CD$ at $R$ . Prove $\angle XPY = \angle XQY + \angle XRY$ .