Symmedian

Author

Eric W. Weisstein
December 5, 2005

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

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

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

Graphic

t=Triangle[{{0,0},{1,0},{.35,.5}}];
Show[Graphics[{
t,
{Green,Medians[t]},
{Blue,AngleBisectors[t]},
{Red,Symmedians[t]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Green]&/@Transpose[{VertexPoints[MedialTriangle[t]],{"(Subscript[M, A])","(Subscript[M, B])","(Subscript[M, C])"}}],
Append[#,Red]&/@Transpose[{VertexPoints[SymmedialTriangle[t]],{"(Subscript[K, A])","(Subscript[K, B])","(Subscript[K, C])"}}],
{{SymmedianPoint[t],"K",Red},{Centroid[t],"G",Green},{Incenter[t],"I",Blue}}
],LabelOffset->.035]
}],AspectRatio->Automatic,PlotRange->All]