5

Part of 1958 Polish MO Finals

Problems(1)

plane bisector of any dihedral angle in tetrahedron

Source: Polish MO Finals 1958 p5

Prove the theorem:
In a tetrahedron, the plane bisector of any dihedral angle divides the opposite edge into segments proportional to the areas of the tetrahedron faces that form this dihedral angle.

geometry3D geometrytetrahedron