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Regular tetrahedron inscribed in another.

Source: ILL 1979-36

June 2, 2011
geometry3D geometrytetrahedrongeometry unsolved

Problem Statement

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}.
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