Too Ugly?

Geometry Level 2

In a large circle of diameter 4, we draw two circles that are each internally tangent at \(A\) and \(B.\) We then draw the common interior tangent \(CD.\) If \(AC\) intersects the large circle at \(E\) and \(BD\) intersects the large circle at \(F,\) what is the distance \(EF?\)

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