MathDB

10

Part of 1984 IMO Longlists

Problems(1)

Areas forming arithmetic or geometric progression

Source:

10/12/2010
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.
geometry3D geometrytetrahedronratiovectorinequalitiesgeometry unsolved