Question 49
Let $ABC$ be a triangle, $H$ its orthocenter and $M$ the midpoint of the segment $[BC]$. Let $d$ be a straight line passing through the point $M$. It is assumed that $d$ cuts the circle with diameter $[AH]$ in $P$ and $Q$. Show that the orthocenter of the triangle $APQ$ is on the circumscribed circle of the triangle $ABC$. 