# 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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