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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