Question 32
Let $ABC$ be an equilateral triangle and $P$ a point on the circumcircle of this triangle, distinct from $A$, $B$ and $C$. The lines through $P$ parallel to $(BC)$, $(CA)$ and $(AB)$ meet the lines $(CA)$, $(AB)$ and $(BC)$ at $M$, $N$ and $Q$ respectively. Show that the points $M$, $N$ and $Q$ are collinear.