Dart-Throwing David

Geometry Level 3

David throws a dart that lands at a point \(P\) inside triangle \(ABC\) that has \(BC=5, CA=6,\) and \(AB=7\). If the distance between \(P\) and all of the vertices is greater than 2, than David wins. The probability that David wins can be expressed in the form \(\frac{a-\sqrt{b} \pi}{c}\) in simplest terms. Compute \(a+b+c\).

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