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Find the area of the hatched region, if the radii of the two circles in the figure above are 111 and 162+27162+27⋯555\sqrt[5]{162+27\sqrt[5]{162+27\sqrt[5]{\cdots}}}5162+275162+275⋯.
If your answer is in the form of ab−c2bπa\sqrt{b}-\frac{c}{2b}\piab−2bcπ for some positive pairwise coprime integers a,b,ca, b, ca,b,c. Find a+b+ca+b+ca+b+c.
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