Question 51
Consider the excircles of a triangle $ABC$ tangent to the sides $AB$ and $AC$. Denote by $M$, $N$ and $P$ the tangent points of the first circle to the side $AB$ and the extensions of the sides $BC$ and $CA$ and by $S$, $Q$ and $R$ the tangent points of the second circle to the side $AC$ and the extensions of the sides $AB$ and $BC$. Let $X$ be the intersection point of the lines $MN$ and $RS$ and $Y$ be the intersection point of the lines $PN$ and $RQ$. Prove that the points $X$, $A$ and $Y$ are colinear.