# 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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