MathDB
inequality with sums of segments in space, starting with a tetrahedron

Source: 2012 Sharygin Geometry Olympiad Final Round 10.6

August 3, 2018
geometry3D geometrytetrahedroninequalities

Problem Statement

Consider a tetrahedron ABCDABCD. A point XX is chosen outside the tetrahedron so that segment XDXD intersects face ABCABC in its interior point. Let A′,B′A' , B' , and C′C' be the projections of DD onto the planes XBC,XCAXBC, XCA, and XABXAB respectively. Prove that A′B′+B′C′+C′A′≤DA+DB+DCA' B' + B' C' + C' A' \le DA + DB + DC.
(V.Yassinsky)
Back to ProblemsView on AoPS