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Pairwise distance less than radius

Source: LIMIT 2020 Cat 2 Obj P9

May 25, 2020
probabilitylimit

Problem Statement

Three points are chosen randomly and independently on a circle. The probability that all three pairwise distance between the points are less than the radius of the circle is 1K\frac{1}{K}, KNK\in\mathbb{N}. Find KK.