Question 41
Given a cyclic hexagon $ABCDEF$, let $BD$ and $CF$ meet at $G$, $AC$ and $BE$ meet at $H$, $AD$ and $CE$ meet at $I$. Suppose that $BD$ is perpendicular to $CF$ and $AI = CI$. Show that $CH = AH + DE$ if and only if $GH \cdot BD = BC \cdot DE$.