RO-TST 2012 Problem 11

Let $\gamma$ be a circle and $l$ a line in its plane. Let $K$ be a point on $l$ , located outside of $\gamma$ . Let $KA$ and $KB$ be the tangents from $K$ to $\gamma$ , where $A$ and $B$ are distinct points on $\gamma$ . Let $P$ and $Q$ be two points on $\gamma$ . Lines $PA$ and $PB$ intersect line $l$ in two points $R$ and respectively $S$ . Lines $QR$ and $QS$ intersect the second time circle $\gamma$ in points $C$ and $D$ . Prove that the tangents from $C$ and $D$ to $\gamma$ are concurrent on line $l$ .