IMO Shortlist 1972 problem 2
Dodao/la:
arhiva2. travnja 2012. We are given
![3n](/media/m/7/8/c/78cd35d74888c04183ced68aa3701e51.png)
points
![A_1,A_2, \ldots , A_{3n}](/media/m/8/4/4/844677b2c0b4b23ae1cca30ab87a138a.png)
in the plane, no three of them collinear. Prove that one can construct
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
disjoint triangles with vertices at the points
%V0
We are given $3n$ points $A_1,A_2, \ldots , A_{3n}$ in the plane, no three of them collinear. Prove that one can construct $n$ disjoint triangles with vertices at the points $A_i.$
Izvor: Međunarodna matematička olimpijada, shortlist 1972