OIM 2008 Problem 2

Given a triangle $ABC$ , let $r$ be the external bisector of $\angle ABC$ . $P$ and $Q$ are the feet of the perpendiculars from $A$ and $C$ to $r$ . If $CP \cap BA = M$ and $AQ \cap BC=N$ , show that $MN$ , $r$ and $AC$ concur.