Carnot's Theorem - Maple Help

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 $r$ is the inradius | are the perpendicular distances from the circumcenter $\mathrm{O}$ to a side of ΔABC   The sign of the distance is taken to be negative if and only if the corresponding line segment, , $\mathrm{OF}$, or  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.



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