Third Lemoine Circle

Author

Eric W. Weisstein
December 24, 2004

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{3/10,5/10}}]//N[#,10]&;
Show[Graphics[
{
t,
{
Blue,
LemoineTriangle[t],
Cartesian/@Through[Cevians[X[598]][t]]
},
{Red,ThirdLemoineCircle[t]},
{Green,LemoineTriangle[t]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[LemoineTriangle[t]],{"(Subscript[X, A])","(Subscript[X, B])","(Subscript[X, C])"}}],
{
{X[598][t],"(Subscript[X, 598])",Blue}
}
],LabelOffset->.04,PointSize[.025]]
}
],AspectRatio->Automatic,PlotRange->{{-.1,1.1},{-.1,.6}}]

Center

Center[ThirdLemoineCircle][[1]]//TraditionalForm

IncidentCenters[KimberlingCenters,Center[ThirdLemoineCircle]]//Timing

Circle Function

CircleFunction[ThirdLemoineCircle]//TraditionalForm

IncidentCenters[KimberlingCenters,CyclicTrilinears[CircleFunction[ThirdLemoineCircle]]]//Timing

Radius

CircleRadius[ThirdLemoineCircle]//TraditionalForm

Incident Centers

IncidentCenters[KimberlingCenters,ThirdLemoineCircle]//Timing

CenterName[X[115]]