MathNet 2015-part-04 — 191 problems (EN–VI) Question 118

Let $ABC$ be an acute triangle such that $AB \neq AC$. Let $M$ be the midpoint of $[BC]$, $H$ be the orthocenter of $ABC$, $O_1$ be the midpoint of $[AH]$ and $O_2$ be the circumcenter of $BCH$. Prove that $O_1AMO_2$ is a parallelogram.

JBMO ShortList 2014