IGO 2017 A3

Let $O$ be the circumcenter of triangle $ABC$ . Line $CO$ intersects the altitude from $A$ at point $K$ . Let $P,M$ be the midpoints of $AK$ , $AC$ respectively. If $PO$ intersects $BC$ at $Y$ , and the circumcircle of triangle $BCM$ meets $AB$ at $X$ , prove that $BXOY$ is cyclic.

Proposed by Ali Daeinabi - Hamid Pardazi