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Prove that the angle is not less than 120 degrees

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September 23, 2010
geometry3D geometryanglepermutationpoint setIMO Shortlist

Problem Statement

Given n (n≥3)n \ (n \geq 3) points in space such that every three of them form a triangle with one angle greater than or equal to 120∘120^\circ, prove that these points can be denoted by A1,A2,…,AnA_1,A_2, \ldots,A_n in such a way that for each i,j,k,1≤i<j<k≤ni, j, k, 1 \leq i < j < k \leq n, angle AiAjAkA_iA_jA_k is greater than or equal to 120∘.120^\circ .
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