IMO Shortlist 1968 problem 20
Dodao/la:
arhiva2. travnja 2012. Given
![n \ (n \geq 3)](/media/m/a/1/e/a1e445327e2a4df5c1c29eec7a2248ac.png)
points in space such that every three of them form a triangle with one angle greater than or equal to
![120^\circ](/media/m/f/0/6/f063a54cf240e6d1e674d56b8c9a47a0.png)
, prove that these points can be denoted by
![A_1,A_2, \ldots,A_n](/media/m/5/f/e/5fedc1e779fde3b680e2da3efe47880c.png)
in such a way that for each
![i, j, k, 1 \leq i < j < k \leq n](/media/m/3/a/6/3a6b6d5bb8b34c1d1a88884374bda363.png)
, angle
![A_iA_jA_k](/media/m/d/b/8/db8d58fbeb4d07b68e6d61ddf223cb02.png)
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 $120^\circ .$
Izvor: Međunarodna matematička olimpijada, shortlist 1968