Question 66
Let $ABCD$ be a convex quadrilateral such that the line $BD$ bisects the angle $ABC$. Suppose that the circumcircle of triangle $ABC$ intersects the sides $AD$ and $CD$ in the points $P$ and $Q$, respectively. The line through $D$ and parallel to $AC$ intersects the lines $BC$ and $BA$ at the points $R$ and $S$, respectively. Prove that the points $P$, $Q$, $R$ and $S$ lie on a common circle.