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Areas forming arithmetic or geometric progression

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October 12, 2010
geometry3D geometrytetrahedronratiovectorinequalitiesgeometry unsolved

Problem Statement

Assume that the bisecting plane of the dihedral angle at edge ABAB of the tetrahedron ABCDABCD meets the edge CDCD at point EE. Denote by S1,S2,S3S_1, S_2, S_3, respectively the areas of the triangles ABC,ABEABC, ABE, and ABDABD. Prove that no tetrahedron exists for which S1,S2,S3S_1, S_2, S_3 (in this order) form an arithmetic or geometric progression.
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