Question 109
Let $ABC$ be an acute-angled triangle with $AB \neq AC$, let $M$ be the midpoint of the side $[BC]$, $H$ the orthocentre of the triangle $ABC$, $O_{1}$ the midpoint of $[AH]$, and $O_{2}$ the circumcentre of the triangle $BCH$. Prove that $O_{1}AMO_{2}$ is a parallelogram.