Carnot's Theorem - Maple Help
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Carnot's theorem

Main Concept

Lazare Carnot developed a theorem that illustrates the relationship between the radii of the circumcircle and the incircle of any given triangle ΔABC.


±OE ± OF ± OG = R+r



R is the circumradius

r is the inradius

OE, |OF|, |OG| are the perpendicular distances from the circumcenter O to a side of ΔABC


The sign of the distance is taken to be negative if and only if the corresponding line segment, OE , OF, or OG  lies completely outside ΔABC.

Click or drag on the plot to adjust the points A, B, and C and verify that the identity still holds.








OE = 

OF = 

OG = 

R = 1   

r  = 


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