Question 72
Let $ABCD$ be a square with circumcircle $\Gamma$. Let $M$ be on minor arc $CD$ of $\Gamma$. Let $BD$ and $AM$ intersect at $P$, $CD$ and $AM$ intersect at $R$, $BM$ and $AC$ intersect at $Q$ and $BM$ and $DC$ intersect at $S$. Show that $PS \perp QR$.