Cutting A Hexagon

Geometry Level 3

The figure above shows a regular hexagon inscribed inside a circle with center \(O \) such that \(OA = 1\). Find the area of the shaded region.

If the area can be written as \(\dfrac{a\pi-\sqrt{b}}{c}\), where \(a,b\) and \(c\) are integers with both \(a,b\) primes, submit your answer as \(a+b+c\).

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