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
where
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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