BALTIC-WAY 1995 Problem 18

Let $M$ be the midpoint of the side $A C$ of a triangle $A B C$ and let $H$ be the foot point of the altitude from $B$. Let $P$ and $Q$ be the orthogonal projections of $A$ and $C$ on the bisector of angle $B$. Prove that the four points $M, H, P$ and $Q$ lie on the same circle.