The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.
Gergonne's Theorem
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References
Altshiller-Court, N. "Gergonne's Theorem." §235 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
Gergonne's TheoremCite this as:
Weisstein, Eric W. "Gergonne's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GergonnesTheorem.html