Question 36
Let $ABC$ be a triangle inscribed in a circle $K$. The tangent from $A$ to the circle meets the line $BC$ at point $P$. Let $M$ be the midpoint of the line segment $AP$ and let $R$ be the intersection point of the circle $K$ with the line $BM$. The line $PR$ meets again the circle $K$ at the point $S$. Prove that the lines $AP$ and $CS$ are parallel.