CN-SMO 2005 Problem 2

Circle $C$ (with center $O$ ) does not have common point with line $l$ . Draw $OP$ perpendicular to $l$ , $P \in l$ . Let $Q$ be a point on $l$ ( $Q$ is different from $P$ ), $QA$ and $QB$ are tangent to circle $C$ , and intersect the circle at $A$ and $B$ respectively. $AB$ intersects $OP$ at $K$ . $PM$ , $PN$ are perpendicular to $QB$ , $QA$ , respectively, $M \in QB$ , $N \in QA$ . Prove that segment $KP$ is bisected by line $MN$ .