IMO 1984 LL BUL10

Origin: BUL

Problem

Assume that the bisecting plane of the dihedral angle at edge AB of the tetrahedron ABCD meets the edge CD at point E. Denote by S1, S2, S3, respectively the areas of the triangles ABC, ABE, and ABD. Prove that no tetrahedron exists for which S1, S2, S3 (in this order) form an arithmetic or geometric progression.