IGO 2019 I4

Let $ABCD$ be a parallelogram and let $K$ be a point on line $AD$ such that $BK=AB$ . Suppose that $P$ is an arbitrary point on $AB$ , and the perpendicular bisector of $PC$ intersects the circumcircle of triangle $APD$ at points $X$ , $Y$ . Prove that the circumcircle of triangle $ABK$ passes through the orthocenter of triangle $AXY$ .

Proposed by Iman Maghsoudi