IZhO 2017 Problem 1

Let $ABC$ be a non-isosceles triangle with circumcircle $\omega$ and let $H, M$ be orthocenter and midpoint of $AB$ respectively. Let $P,Q$ be points on the arc $AB$ of $\omega$ not containing $C$ such that $\angle ACP=\angle BCQ < \angle ACQ$ .Let $R,S$ be the foot of altitudes from $H$ to $CQ,CP$ respectively. Prove that thé points $P,Q,R,S$ are concyclic and $M$ is the center of this circle.