Question 33
Let $AB\Gamma$ be an acute angled triangle with $AB \lt A\Gamma$ and circumcenter $O$. The altitudes $B\Delta$, $\Gamma E$ meet at the point $H$. If $O_1$ is the circumcenter of the triangle $BH\Gamma$, prove that the quadrilateral $AHO_1O$ is a parallelogram.