IMO 1968 SL 20

Origin: CZS

Problem

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 $120^\circ$.