SAT Math IX

Geometry Level 2

In the figure above, $$ACDF$$ is a rectangle and the circle with center $$O$$ has a radius of $$r$$. $$\overline { AC }$$ is tangent to the circle at point $$B$$, $$\overline { DF }$$ is tangent to the circle at point $$E$$, and $$\angle COE$$ measures $$120°$$. If $$\overline { CF }$$ (not shown) passes through $$O$$, then what is the length of $$\overline { CF }$$ in terms of $$r$$?

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