OME 2022 Problem 3

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