The trapezoid is trapped in the circle!

Geometry Level 2

We see circles A and B of radius 1 in the diagram. Find the area of the trapezoid. If this area is expressible in the form \( \dfrac{a \sqrt{b}}{c} \), where \(a, c \) are coprime and \( b \) is square-free, find \( a + b + c \).

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