Let $ABC$ be a triangle, and $M$, $N$, and $P$ be the midpoints of $AB$, $BC$, and $CA$ respectively, such that $MBNP$ is a parallelogram. Let $R$ and $S$ be the points in which the line $MN$ intersects the circumcircle of $ABC$. Prove that $AC$ is tangent to the circumcircle of triangle $RPS$.