The chord did it

Geometry Level 3

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 \(BC\).

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