KöMaL 2022 B5260

$G$ and $H$ are points of chord $AB$ of a circle $k$ such that $AG=GH=HB=1$. Let $F$ denote the midpoint of one of the arcs $AB$. The secants $FH$ and $FG$ intersect the circle again at points $C$ and $D$, respectively. Show that $CD=BC^2$.