MathDB

36

Part of 1979 IMO Longlists

Problems(1)

Regular tetrahedron inscribed in another.

Source: ILL 1979-36

6/2/2011
A regular tetrahedron A1B1C1D1A_1B_1C_1D_1 is inscribed in a regular tetrahedron ABCDABCD, where A1A_1 lies in the plane BCDBCD, B1B_1 in the plane ACDACD, etc. Prove that A1B1≥AB3A_1B_1 \ge\frac{ AB}{3}.
geometry3D geometrytetrahedrongeometry unsolved