Question 1
$A$, $B$, $C$, $D$ are four "consecutive" points on the circumference of a circle and $P$, $Q$, $R$, $S$ are points on the circumference which are respectively the midpoints of the $\operatorname{arcs}\ AB$, $BC$, $CD$, $DA$. Prove that $PR$ is perpendicular to $QS$.