Waste less time on Facebook — follow Brilliant.

Carnot's theorem

In Euclidean geometry, Carnot's theorem, named after Lazare Carnot (1753–1823), is as follows. Let ABC be an arbitrary triangle. Then the sum of the signed distances from the circumcenter D to the sides of triangle ABC is

DF + DG + DH = R + r,\ where r is the inradius and R is the circumradius. Here the sign of the distances is taken negative if and only if the line segment DX (X = F, G, H) lies completely outside the triangle. In the picture DF is negative and both DG and DH are positive.

Note by Deepak Jain
3 years, 6 months ago

No vote yet
1 vote


There are no comments in this discussion.


Problem Loading...

Note Loading...

Set Loading...