Carnot's theorem

English

${\begin{aligned}&DG+DH+DF\\={}&|DG|+|DH|+|DF|\\={}&R+r\end{aligned}}$

Proper noun

Carnot's theorem

1. (thermodynamics) A theorem for the maximum efficiency obtainable from a heat engine.

   Synonyms: Carnot's law, Carnot's rule

2. (geometry) A theorem stating that the sum of the signed distances from the circumcenter D to the sides of an arbitrary triangle ABC is DF + DG + DH = R + r, where r is the inradius and R the circumradius of the triangle.
3. A theorem describing a relation between conic sections and triangles.
4. A theorem describing a necessary and sufficient condition for three lines that are perpendicular to the (extended) sides of a triangle having a common point of intersection.