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