MathDB
tetrahedron and its area surfaces

Source: 30-th Vietnamese Mathematical Olympiad 1992

February 17, 2007
geometry3D geometrytetrahedrongeometry unsolved

Problem Statement

Let ABCDABCD be a tetrahedron satisfying i)ACD^+BCD^=1800\widehat{ACD}+\widehat{BCD}=180^{0}, and ii)BAC^+CAD^+DAB^=ABC^+CBD^+DBA^=1800\widehat{BAC}+\widehat{CAD}+\widehat{DAB}=\widehat{ABC}+\widehat{CBD}+\widehat{DBA}=180^{0}. Find value of [ABC]+[BCD]+[CDA]+[DAB][ABC]+[BCD]+[CDA]+[DAB] if we know AC+CB=kAC+CB=k and ACB^=α\widehat{ACB}=\alpha.
Back to ProblemsView on AoPS