Question 42
Triangle $ABC$ is an acute-angled triangle with orthocenter $H$. Point $P$ is inside triangle $BHC$ such that $3\angle HBC = \angle HPC$ and $3\angle HCB = \angle HPB$. Denote by $X$ and $Y$ the reflections of $P$ with respect to $BH$ and $CH$, respectively. If $S$ is the circumcenter of triangle $AXY$, prove that $\angle CAP = \angle BAS$.