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
I will give a Fight till the End
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