Can we always draw $n/3$ disjoint triangles from $n$ points in the plane in general position? Suppose we are given $n$ points in the plane, where $n$ is a multiple of $3$ and no three of these points lie on a line. Is it possible to group all of these points into sets of three, so that if we draw the triangles formed by these sets, then no two of the triangles intersect?

Hi guys, I can visualise this question, but I have no idea how to approach it mathematically, any help?

Hint: There are finitely many ways that we can 'triple' up the points to form $n/3$ triangles.
Hint: Consider the configuration which minimizes the total areas of all $n/3$ triangles. Claim: This works.
