Incenter-Excenter Circle

Author

Eric W. Weisstein
October 19, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Incenter-ExcenterCircle.nb.

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

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

Equation

Circles

Figure

?Circumcircle

Excenters[t]

t=Triangle[{{0.,0.},{1.,0.},{.2,.7}}];
c=Circumcircle[Coordinates/@Append[Rest[VertexPoints[t]],Incenter[t]]];
Show[Graphics[{
{Purple,Incircle[t]},
Circumcircle[t],
{
Blue,
c,
Line[Coordinates/@{VertexPoints[t][[1]],Excenters[t][[1]]}]
},
{Red,Excircles[t]},
{PointSize[.02],Point[c[[1]]],
Incenter[t],Excenters[t][[1]]},
{Thickness[.01],t}
},
AspectRatio->Automatic]
]