This actually may work:

1/ We may find the ratio of the area of the double-segment to the yellow area. (That ratio doesn't change with the circle size)

2/ We can use that ratio and calculate the double-segment area.

3/ If CD = 2 then Yellow area = 1.369706513

4/ If CD = 2 then Double-segment area = 0.724688589

PROPORTION:

1.369706513 : 0.724688589 = 1 : x

**x = 0.529083115**

Area of a sector = 1 + x = **1.529083115**

**Area of a circle = 6(1 + x) = 9.17449869**

**AB = 2[sqrt(9.17449869 / pi)] = ***3.417796737*

This is very hard to explain. I don't blame you if you do not understand it...

I checked these numbers, and it works.