Carnot's theorem (perpendiculars)

For other uses, see Carnot's theorem (disambiguation).
Carnot's theorem: if three perpendiculars on triangle sides intersect in a common point F, then
blue area = red area

Carnot's theorem (named after Lazare Carnot) describes a necessary and sufficient condition for three lines that are perpendicular to the (extended) sides of a triangle having a common point of intersection. The theorem can also be thought of as a generalization of the Pythagorean theorem.