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Four points in space and segments to form a triangle

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October 31, 2010
geometry unsolvedgeometry

Problem Statement

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