Question 85
Circles $S_1$ and $S_2$ intersect in points $P$ and $Q$ and lay inside an inscribed quadrilateral $ABCD$. $S_1$ touches the sides $AB$, $BC$ and $AD$; $S_2$ touches the sides $CD$, $BC$ and $AD$. The lines $PQ$, $AB$, $CD$ meet in one point. Prove that $BC \parallel AD$.