Let $PQRS$ be a cyclic quadrilateral with $\angle PSR = 90^o$, and let $H,K$ be the projections of $Q$ on the lines $PR$ and $PS$, respectively. Prove that the line $HK$ passes through the midpoint of the segment $SQ$.
Problem
Source: 2000 Estonia National Olympiad Final Round grade 11 p2
Tags: bisects segment, cyclic quadrilateral, right triangle