Triple Tangent Circles

Geometry Level 3

Three circles, each with a radius of \(10\), are mutually tangent to each other. The area enclosed by the three circles can be written as \(a\sqrt{b} - c\pi\), where \(a\), \(b\) and \(c\) are positive integers, and \(b\) is not divisible by a square of a prime. What is the value of \(a + b + c\)?

Details and assumptions

The enclosed area does not include the area within the circles.

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