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<BAC+<CAD+<DAB = <ABC+<CBD+,DBA = 180^o in tetrahedron

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1995 p1

February 20, 2020
anglestetrahedron3D geometrygeometryGeometric Inequalities

Problem Statement

Suppose that tetrahedron ABCDABCD satisfies ∠BAC+∠CAD+∠DAB=∠ABC+∠CBD+∠DBA=180o\angle BAC+\angle CAD+\angle DAB = \angle ABC+\angle CBD+\angle DBA = 180^o. Prove that CD≥ABCD \ge AB.
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