A challenging geometric problem

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 $a+b+c$ .