Question 61
Let $ABC$ be an acute-angled triangle with altitude $AK$. Let $H$ be its orthocentre and $O$ be its circumcentre. Suppose $KOH$ is an acute-angled triangle and $P$ its circumcentre. Let $Q$ be the reflection of $P$ in the line $HO$. Show that $Q$ lies on the line joining the mid-points of $AB$ and $AC$.