# 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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