Question 41
Let the bisectors of the angles $\angle CAD$ and $\angle ADB$ intersect the circumcircle of a cyclic quadrilateral $ABCD$ at $P$ and $Q$. The lines $AP$ and $DQ$ intersect at $R$, and the lines $CQ$ and $BP$ intersect at $S$. Prove that the lines $PQ$ and $RS$ are perpendicular.