Question 60
Let $AB$ be the diameter of the circle $\Gamma$ with centre $O$ and let $C$ and $D$ be points on $\Gamma$, on different sides on $AB$ and such that $AD$ and $CB$ intersect at $R$. The circumscribed circles of the triangles $AOC$ and $BOD$ meet also at $Q$. $CD$ and $AB$ meet at $P$. Show that $Q, P$ and $R$ are collinear.