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单词 Carnot theorem
释义

Carnot theorem

中文百科

卡诺定理 Carnot's theorem

(重定向自Carnot theorem)
Teorema de Carnot en el caso agudo.
Teorema de Carnot en el caso obtuso.

设ABC为三角形,O为其外心。则O到ABC各边的距离之和为

OOA + OOB + OOC = R + r

其中r为内切圆半径,R为外置圆半径。这个定理叫做卡诺定理,以拉扎尔·卡诺为名。

英语百科

Carnot's theorem 卡诺定理

(重定向自Carnot theorem)
Teorema de Carnot en el caso agudo.
Teorema de Carnot en el caso obtuso.

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.

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更新时间:2025/6/21 3:30:53