MathNet 2007-part-03 — 185 problems (EN–VI) Question 61

Let the incircle of $ABCD$ be tangent to sides $AB$, $BC$, $CD$, and $AD$ at points $P$, $Q$, $R$, and $S$, respectively. Show that $ABCD$ is cyclic if and only if $PR \perp QS$.