MathDB
prove that 6 planes have a common point, starting with a tetrahedron

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P23

August 2, 2018
geometrytetrahedron3-Dimensional Geometryplanes3D geometry

Problem Statement

A tetrahedron ABCDABCD is given. The incircles of triangles ABC ABC and ABDABD with centers O1,O2O_1, O_2, touch ABAB at points T1,T2T_1, T_2. The plane πAB\pi_{AB} passing through the midpoint of T1T2T_1T_2 is perpendicular to O1O2O_1O_2. The planes πAC,πBC,πAD,πBD,πCD\pi_{AC},\pi_{BC}, \pi_{AD}, \pi_{BD}, \pi_{CD} are defined similarly. Prove that these six planes have a common point.
Back to ProblemsView on AoPS