Schoute Center

Author

Eric W. Weisstein
November 16, 2005

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

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

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

Derivation

Symmetrize[ToSidelengths[InversePoint[SymmedianPoint,Circumcircle]]]

Select[KimberlingCenters,StringMatchQ[Name[#],RegularExpression[".*choute.*"]]&]

Trilinears[X[187]]

Figure

t=Triangle[{{0,0},{1,0},{.3,.5}}];
Show[Graphics[{
t,
{Red,Line[Coordinates/@{Circumcenter[t],X[187][t]}]},
{Blue,Circumcircle[t]},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
{
{SymmedianPoint[t],"K",Red},
{X[187][t],"(Subscript[X, 187])",Red},
{Circumcenter[t],"O",Blue}
}
],
{PointSize[.025],LabelOffset->.05}
]
}],AspectRatio->Automatic]