IMO Shortlist 1968 problem 20


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April 2, 2012
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Given 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^\circ, prove that these points can be denoted by A_1,A_2, \ldots,A_n in such a way that for each i, j, k, 1 \leq i < j < k \leq n, angle A_iA_jA_k is greater than or equal to 120^\circ .
Source: Međunarodna matematička olimpijada, shortlist 1968