# 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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