Question 32
Let $ABC$ be a triangle with $AB \lt AC$, and let $\Gamma$ be its circumcircle. Let $D$, $E$ and $F$ be the points of tangency of the incircle with $BC$, $CA$ and $AB$, respectively. Let $R$ be the point on $EF$ such that $DR$ is an altitude of triangle $DEF$, and let $S$ be the intersection point of the external bisector of the angle $\angle BAC$ with $\Gamma$. Prove that $AR$ and $SD$ meet on $\Gamma$.