ILL 1978 Problem 49

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 non-degenerate and has no obtuse angle. $(b)$ What should these four points satisfy in order for the triangle $T$ to be right-angled?