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Carnot's theorem
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Main Concept
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Lazare Carnot developed a theorem that illustrates the relationship between the radii of the circumcircle and the incircle of any given triangle ΔABC.
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where
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 is the circumradius
 is the inradius
 | are the perpendicular distances from the circumcenter  to a side of ΔABC
The sign of the distance is taken to be negative if and only if the corresponding line segment,  ,  , or  lies completely outside ΔABC.
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Click or drag on the plot to adjust the points  ,  , and  and verify that the identity still holds.
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