The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line belongs to the plane determined by the three points in which the remaining three (concurrent) edges of the tetrahedron are met by the internal bisecting planes of the respectively opposite dihedral angle.
Cesàro's Theorem
Explore with Wolfram|Alpha
References
Altshiller-Court, N. "Cesàro's Theorem." §237 in Modern Pure Solid Geometry. New York: Chelsea, p. 71, 1979.Le Grand; Ferriot; Lambert; Vecten; Labrousse; Rochat; Penjon; Gobert; Beaucourt, C.; Français, J. F.; etc. "Questions résolues. Démonstrations des deux théorèmes de géométrie énoncés à la page 196 de ce volume." Ann. de Math. 3, 317-323, 1812-1813.Referenced on Wolfram|Alpha
Cesàro's TheoremCite this as:
Weisstein, Eric W. "Cesàro's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CesarosTheorem.html