Rollin' Stones

Geometry Level 5

Find the area of the hatched region, if the radii of the two circles in the figure above are 11 and 162+27162+27555\sqrt[5]{162+27\sqrt[5]{162+27\sqrt[5]{\cdots}}}.

If your answer is in the form of abc2bπa\sqrt{b}-\frac{c}{2b}\pi for some positive pairwise coprime integers a,b,ca, b, c. Find a+b+ca+b+c.

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