Carnot's theorem (conics)

Carnot's theorem, named after Lazare Carnot ( , ), describes a relation between conic sections and triangles.

In a triangle with points on the side , on the side and on the side those six points are located on a common conic section if and only if the following equation holds:

.

References Huub P.M. van Kempen: On Some Theorems of Poncelet and Carnot . Forum Geometricorum, Volume 6 (2006), pp. 229–234. Lorenz Halbeisen, Norbert Hungerbühler, Juan Läuchli: Mit harmonischen Verhältnissen zu Kegelschnitten: Perlen der klassischen Geometrie. Springer 2016, , pp. 40, 168–173 (German)

External links Carnot's theorem Carnot's Theorem for Conics at cut-the-knot.org