IMO 1978 LL VIE49

Let A, B, C, D be four arbitrary distinct points in space.

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IMO 1978 LL VIE49

Origin: VIE

Problem

Let A, B, C, D be four arbitrary distinct points in space. (a) Prove that using the segments AB + CD, AC + BD and AD + BC it is always possible to construct a triangle T that is nondegenerate and has no obtuse angle. (b) What should these four points satisfy in order for the triangle T to be right-angled?