A geometry problem by A Former Brilliant Member

Geometry Level 3

The figure above consists of four identical big circle of radius 2 feet and one small circle. The area of the shaded part can be expressed as a b π ( c c ) a - b\pi(c - \sqrt c) , where a , b , c a,b,c are all integers.

Find the value of a + b + c a+b+c .


The answer is 26.

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