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stereometric inequality

Source: Tuymaada 2013, Day 2, Problem 7 Seniors

July 26, 2013
inequalitiesgeometry3D geometrytetrahedronsphereAMCUSA(J)MO

Problem Statement

Points A1A_1, A2A_2, A3A_3, A4A_4 are the vertices of a regular tetrahedron of edge length 11. The points B1B_1 and B2B_2 lie inside the figure bounded by the plane A1A2A3A_1A_2A_3 and the spheres of radius 11 and centres A1A_1, A2A_2, A3A_3. Prove that B1B2<max⁡{B1A1,B1A2,B1A3,B1A4}B_1B_2 < \max\{B_1A_1, B_1A_2, B_1A_3, B_1A_4\}.
A. Kupavsky
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