Question 80
On a circle with center $A$ and radius $R$, four distinct points $B,C,G,H$ are chosen in that order so that $G$ lies on the extension of the median of triangle $ABC$ from $B$, and $H$ lies on the extension of the altitude of $ABC$ from $B$. If $X$ is the intersection of the lines $AC$ and $GH$, prove that $AX=2R$.
Supplementary illustration (one configuration):
Supplementary illustration (one configuration):