Question 58
Let $ABC$ be a non-isosceles triangle in $A$. Let $M$ be the midpoint of the segment $[BC]$, $H$ the orthocenter of the triangle $ABC$, $O_{1}$ the midpoint of the segment $[AH]$ and $O_{2}$ The center of the circle circumscribed to triangle $CBH$. Show that the quadrilateral $O_{1}AMO_{2}$ is a parallelogram. 