Too Ugly?

Geometry

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

3

\pi

2 \sqrt{3}

4

Depends on the length of

AB