OMM 2015 Problem 1

Let $ABC$ be an acuted-angle triangle and let $H$ be it's orthocenter. Let $PQ$ be a segment through $H$ such that $P$ lies on $AB$ and $Q$ lies on $AC$ and such that $\angle PHB= \angle CHQ$ . Finally, in the circumcircle of $\triangle ABC$ , consider $M$ such that $M$ is the mid point of the arc $BC$ that doesn't contain $A$ . Prove that $MP=MQ$ Proposed by Eduardo Velasco/Marco Figueroa