Carnot's theorem (conics)

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

6 points on the sides of triangle and their common conic section

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

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  • 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, ISBN 9783662530344, pp. 40, 168–173 (German)
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