ILL 1984 Problem 10

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 $S_1, S_2, S_3$ , respectively the areas of the triangles $ABC, ABE$ , and $ABD$ . Prove that no tetrahedron exists for which $S_1, S_2, S_3$ (in this order) form an arithmetic or geometric progression.