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## Putnam A6 2005

Let $n$ be given, $n \geq 4$, and suppose that $P_1,P_2, \dots,P_n$ are $n$ randomly, independently and uniformly, chosen points on a circle. Consider the convex $n$-gon whose vertices are $P_i$.

• What is the probability that at least one of the vertex angles of this polygon is acute ?
Source: Putnam 2005

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