A Pentagon, Hexagon And A Decagon Walk Into A Bar

Geometry Level 2

As shown in the image above, a pentagon, hexagon and decagon are inscribed in three congruent circles, and their endpoints are connected to form a triangle. If the radii of each of the circles is 11 and the area of the triangle formed by the three polygons can be written as abc\frac{\sqrt{a}-b}{c}, where aa, bb and cc are coprime integers, what is a+b+ca+b+c?

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