# Picture this ....

**Calculus**Level 5

Let \(O\) be the center of the smaller circle, and let \(P, Q\) be the endpoints of the chord as described above. The value of \(r\) that maximizes the perimeter of triangle \(OPQ\) can be written as \(\dfrac{a - \sqrt{b}}{c}\), where \(a, b, c\) are positive coprime integers and \(b\) is square-free. Find \(a + b + c\).