A Pentagon, Hexagon And A Decagon Walk Into A Bar

Geometry Level 3

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 \(1\) and the area of the triangle formed by the three polygons can be written as \(\frac{\sqrt{a}-b}{c}\), where \(a\), \(b\) and \(c\) are coprime integers, what is \(a+b+c\)?

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