Question 24
Let $\Omega$ be the circumcircle of triangle $ABC$, $O$ its circumcentre and $H$ its orthocentre. Let $S$ be a point on $\Omega$, and let the point $P$ on $BC$ be such that $\angle ASP = 90^\circ$; the line $SH$ meets the circumcircle of $\triangle APS$ at $X \ne S$. Let $OP$ meet $CA$, $AB$ at $Q$, $R$ respectively, and let $QY$, $RZ$ be altitudes of $\triangle AQR$.
Prove that $X$, $Y$, $Z$ are collinear.
Prove that $X$, $Y$, $Z$ are collinear.