OME 2012 Problem 6

Let $ABC$ be an acute-angled triangle. Let $\omega$ be the inscribed circle with centre $I$ , $\Omega$ be the circumscribed circle with centre $O$ and $M$ be the midpoint of the altitude $AH$ where $H$ lies on $BC$ . The circle $\omega$ be tangent to the side $BC$ at the point $D$ . The line $MD$ cuts $\omega$ at a second point $P$ and the perpendicular from $I$ to $MD$ cuts $BC$ at $N$ . The lines $NR$ and $NS$ are tangent to the circle $\Omega$ at $R$ and $S$ respectively. Prove that the points $R,P,D$ and $S$ lie on the same circle.