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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