In the circle $G$, the midpoint of the radius $FG$ is $H$ and $AB\perp EF$ at $H$. The semicircle with $AB $ as diameter intersects $EF $ in $I$, line $AI $ intersects circle $G$ in $C$ and line $BI$ intersects the circle $G$ at $D$, then chord $BC$ is drawn.
If the radius of the circle $G$ is $r$, then find length of chord $BC$ in terms of $r$.
