OIM 2014 Problem 5

Let $ABC$ be an acute triangle and $H$ its orthocenter. Let $D$ be the intersection of the altitude from $A$ to $BC$ . Let $M$ and $N$ be the midpoints of $BH$ and $CH$ , respectively. Let the lines $DM$ and $DN$ intersect $AB$ and $AC$ at points $X$ and $Y$ respectively. If $P$ is the intersection of $XY$ with $BH$ and $Q$ the intersection of $XY$ with $CH$ , show that $H, P, D, Q$ lie on a circumference.