MathDB
Polish 2nd stage 2010, 2nd problem (tetrahedron)

Source:

November 11, 2010
geometry3D geometrytetrahedroncircumcircleincentergeometry proposed

Problem Statement

The orthogonal projections of the vertices A,B,CA, B, C of the tetrahedron ABCDABCD on the opposite faces are denoted by A′,B′,C′A', B', C' respectively. Suppose that point A′A' is the circumcenter of the triangle BCDBCD, point B′B' is the incenter of the triangle ACDACD and C′C' is the centroid of the triangle ABDABD. Prove that tetrahedron ABCDABCD is regular.
Back to ProblemsView on AoPS