The center lies within ....

Discrete Mathematics Level 5

Pick \(7\) points at random on the circumference of a unit circle. The probability that the center of the circle lies within the (unique) convex polygon defined by these \(7\) random points is \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers.

Find \(a + b\).

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