IR-MO 2004 Problem 9

Let $ABC$ be a triangle, and $O$ the center of its circumcircle. Let a line through the point $O$ intersect the lines $AB$ and $AC$ at the points $M$ and $N$ , respectively. Denote by $S$ and $R$ the midpoints of the segments $BN$ and $CM$ , respectively. Prove that $\measuredangle ROS=\measuredangle BAC$ .