Question 17
Let $ABC$ be an acute triangle. Denote its orthocentre by $H$ and let $A'$, $B'$ and $C'$ be the feet of the altitudes from $A$, $B$ and $C$. Let $P$ be the midpoint of $AH$, let $Q$ be the intersection of lines $B'P$ and $AB$ and denote the intersection of segments $A'C'$ and $BB'$ by $R$. Prove that the line $QR$ is perpendicular to the side $BC$.