ÖMO 2003 Problem 6

Let $ABC$ be an acute-angled triangle. The circle $k$ with diameter $AB$ intersects $AC$ and $BC$ again at $P$ and $Q$ , respectively. The tangents to $k$ at $A$ and $Q$ meet at $R$ , and the tangents at $B$ and $P$ meet at $S$ . Show that $C$ lies on the line $RS$ .