Given
points in space such that every three of them form a triangle with one angle greater than or equal to
, prove that these points can be denoted by
in such a way that for each
, angle
is greater than or equal to
%V0
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 $120^\circ .$
Školjka