Question 90
Let $ABC$ be an equilateral triangle, and $P$ a point on the circumcircle of the triangle $ABC$ and distinct from $A$, $B$ and $C$. If the lines through $P$ and parallel to $BC$, $CA$, $AB$ intersect the lines $CA$, $AB$, $BC$ at $M$, $N$ and $Q$ respectively, prove that $M$, $N$ and $Q$ are collinear.