Question 128
Let $ABC$ be a triangle whose three angles are acute and let $\Gamma$ be its circumcircle. The tangent to $\Gamma$ at $A$ meets $(BC)$ at $P$. Let $M$ be the midpoint of $[AP]$. The line $(BM)$ meets $\Gamma$ again at $R$ and the line $(PR)$ meets $\Gamma$ again at $S$.
Show that $(AP)$ and $(CS)$ are parallel.
Show that $(AP)$ and $(CS)$ are parallel.