Geometry A 1

Geometry Level 4

Three cirlces, with radii of \(1,1, and 2\) are externally tangent to each other. The minimum possible area of a quadrilateral that contains and is tangent to all three circle can be written as \(a + b\sqrt{c}\) where \(c\) is not divisible by any perfect square larger than 1. Find \(a+b+c\).

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