Question 23
Let $ABC$ be a scalene triangle and $r$ the external bisector of angle $ABC$. Let $P$ and $Q$ be the feet of the perpendiculars to the line $r$ through $A$ and $C$, respectively. The lines $CP$ and $AB$ meet at $M$ and the lines $AQ$ and $BC$ meet at $N$. Prove that the lines $AC$, $MN$ and $r$ have a common point.