Carnot's theorem (inradius, circumradius)

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 D F + D G + D H = R + r , {\displaystyle DF+DG+DH=R+r,\ } 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.

Source: Wikipedia — Carnot's theorem (inradius, circumradius) (CC BY-SA 4.0)

Carnot's theorem (inradius, circumradius)

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 D F + D G + D H = R + r , {\displaystyle DF+DG+DH=R+r,\ } 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.

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Source: Wikipedia "Carnot's theorem (inradius, circumradius)" · CC BY-SA 4.0

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