We are given points in the plane, no three of them collinear. Prove that one can construct disjoint triangles with vertices at the points
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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
Školjka 
points 
in the plane, no three of them collinear. Prove that one can construct 
disjoint triangles with vertices at the points 