MathDB

20

Part of 1968 IMO Shortlist

Problems(1)

Prove that the angle is not less than 120 degrees

Source:

9/23/2010
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 .
geometry3D geometryanglepermutationpoint setIMO Shortlist