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2018 MMATHS Tiebreaker p3 - center of circle in interior of cyclic n-gon

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October 8, 2023
combinatoricsgeometrycombinatorial geometryMMATHS

Problem Statement

Suppose nn points are uniformly chosen at random on the circumference of the unit circle and that they are then connected with line segments to form an nn-gon. What is the probability that the origin is contained in the interior of this nn-gon? Give your answer in terms of nn, and consider only n≥3n \ge 3.
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