Euler Triangle Formula

Author

Eric W. Weisstein
February 15, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/EulerTriangleFormula.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EulerTriangleFormula.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<PlaneGeometry`;

Derivation

Factor[(Distance@@DistanceTrilinears/@{Incenter,Circumcenter})^2]

Factor[FullSimplify[
With[{r=Inradius[{a,b,c}],R=Circumradius[{a,b,c}]},
R(R-2r)
],a>0&&b>0&&c>0
]]