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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