Question 80
Let $ABC$ be a triangle and let $P$ be a point on $BC$. Points $M$ and $N$ lie on $AB$ and $AC$, respectively, such that $MN$ is not parallel to $BC$ and $AMPN$ is a parallelogram. Line $MN$ meets the circumcircle of $ABC$ at $R$ and $S$. Prove that the circumcircle of triangle $RPS$ is tangent to $BC$.