RIOPLATENSE 2016 Problem 3

Let $A B C$ be an acute-angled triangle of circumcenter $O$ and orthocenter $H$ . Let $M$ be the midpoint of $BC, N$ be the symmetric of $H$ with respect to $A, P$ be the midpoint of $NM$ and $X$ be a point on the line A H such that $MX$ is parallel to $CH$ . Prove that $BX$ and $OP$ are perpendicular.