Carnot's theorem (inradius, circumradius)
id:
carnot-s-theorem-inradius-circumradius-241-8512678
title:
Carnot's theorem (inradius, circumradius)
text:
In Euclidean geometry, Carnot's theorem states that the sum of the signed distances from the circumcenter D to the sides of an arbitrary triangle ABC is where r is the inradius and R is the circumradius of the triangle. Here the sign of the distances is taken to be negative if and only if the open line segment DX (X = F, G, H) lies completely outside the triangle. In the diagram, DF is negative and both DG and DH are positive. The theorem is named after Lazare Carnot (1753–1823). It is used in a
brand slug:
wiki
category slug:
encyclopedia
description:
Gives the sum of the distances from the circumcenter to the sides of an arbitrary triangle
original url:
https://en.wikipedia.org/wiki/Carnot%27s_theorem_(inradius,_circumradius)
date created:
date modified:
2023-03-14T22:10:47Z
main entity:
{"identifier":"Q1141747","url":"https://www.wikidata.org/entity/Q1141747"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/7/79/Carnot_theorem2.svg","width":475,"height":433}
fields total:
13
integrity:
15