A challenging geometric problem

Geometry Level 5

Two concentric circles have a center $$O$$ have radii 2016 and 2017 respectively. $$ABC$$ is an equilateral triangle inscribed inside the smaller circle. Let $$P$$ be a point on the circumference of the larger circle. Given that a triangle with side lengths $$PA,PB$$ and $$PC$$ has an area of $$\dfrac{a\sqrt b}c$$, where $$a,b$$ and $$c$$ are positive integers with $$a,c$$ coprime and $$b$$ square-free. Find $$a+b+c$$.

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