Question 10
Let $ABC$ be an acute triangle with $AB \lt AC$ and let $H$ and $O$ be its orthocentre and circumcentre, respectively. Let $\Gamma$ be the circle $BOC$. The line $AO$ and the circle of radius $AO$ centred at $A$ cross $\Gamma$ again at $A'$ and $F$, respectively. Prove that $\Gamma$, the circle on diameter $AA'$ and the circle $AFH$ are concurrent.
Romania, Radu-Andrei Lecoiu
Romania, Radu-Andrei Lecoiu