I have a simpler solution to the above explanation your solution rocks but we wont have that much time in the GMAT exam to solve this question anyways

here it goes....

64(3)^1/2 - 32pie is the area of the shaded region hence the area of triangle will be equal to 64(3)^1/2 and area of three corresponding circle is 32pie

i will take the area of triangle you can take the area of circles segments

Therefore, 64(3)^1/2 = area of Equilateral Triangle = ((3)^1/2)/4 * Side^2

Hence (side)^2 = 64*4 = 2^8 ==> Side = 2^4 =16

Remember this is the side of the Triangle

Side of Triangle = 2(Radius of the Circle)

therefore radius of circle = 8

Answer B

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