IMO Shortlist 1968 problem 20


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
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 .
Izvor: Međunarodna matematička olimpijada, shortlist 1968