Question 54
Given an acute triangle $ABC$, let $M$ be the midpoint of $BC$ and $H$ the orthocentre. Let $\Gamma$ be the circle with diameter $HM$, and let $X$, $Y$ be distinct points on $\Gamma$ such that $AX$, $AY$ are tangent to $\Gamma$. Prove that $BXYC$ is cyclic.