SHARYGIN 2019 Problem 20

Let $O$ be the circumcenter of triangle ABC, $H$ be its orthocenter, and $M$ be the midpoint of $AB$ . The line $MH$ meets the line passing through $O$ and parallel to $AB$ at point $K$ lying on the circumcircle of $ABC$ . Let $P$ be the projection of $K$ onto $AC$ . Prove that $PH \parallel BC$ .