Question 67
Given an acute triangle $ABC$. Let $(\omega, I)$ be the inscribed circle of $ABC$, $(\Omega, O)$ be the circumscribed circle of $ABC$ and $A_0$ be the midpoint of $AH$ altitude. $\omega$ touches $BC$ at point $D$. $A_0D \cap \omega = P$ and the perpendicular from $I$ to $A_0D$ intersects $BC$ at the point $M$. $MR$ and $MS$ lines touch $\Omega$ at $R$ and $S$ respectively. Prove that the points $R$, $P$, $D$ and $S$ are concyclic.