At least one vertex of a tetrahedron projects to the interior of the opposite triangle

Question

How i can give a fast proof of the following fact: Given four points on $\mathbb{R}^3$ not contained in a plane we can choose one such that its projection to the plane passing through the others is in the triangle generated by the three others points.

Thanks in advance.

Answer 1

Suppose the four points are the vertices of a square?