# 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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