Problem

Source: Greece JBMO TST 2015 p2

Tags: geometry, circumcircle, parallelogram, orthocenter



Let $ABC$ be an acute triangle inscribed in a circle of center $O$. If the altitudes $BD,CE$ intersect at $H$ and the circumcenter of $\triangle BHC$ is $O_1$, prove that $AHO_1O$ is a parallelogram.