Taylor Center

Author

Eric W. Weisstein
December 5, 2004

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{.3,.7}}];
Show[Graphics[{
t,
{Blue,h=OrthicTriangle[t],
EqualSideTicksAboutMidpoints[h,.01]
},
{Purple,m=MedialTriangle[h]},
{Red,Incircle[m]},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
Append[#,Blue]&/@Transpose[{Point/@Vertices[h],{"(Subscript[H, A])","(Subscript[H, B])","(Subscript[H, C])"}}],
Append[#,Purple]&/@Transpose[{Point/@Vertices[m],{"(Subscript[M, (Subscript[H, B]) (Subscript[H, C])])","(Subscript[M, (Subscript[H, C]) (Subscript[H, A])])","(Subscript[M, (Subscript[H, A]) (Subscript[H, B])])"}}],
{
{TaylorCenter[t],"Ta = (Subscript[Sp, H])",Red}
}
],
{PointSize[.025],LabelOffset->.04}
]
}],AspectRatio->Automatic,PlotRange->All]

{TaylorCenter[t],SpiekerCenter[h]}

Structures Passing through It

pt=TaylorCenter;

Circles

First/@Select[{#,IncidentCenters[{pt},#]}&/@Circles,Last[#]=!={}&]

Circle Centers

First/@Select[{#,IncidentCenters[{pt},CircleCenter[#]]}&/@Circles,Last[#]=!={}&]

Conics

First/@Select[{#,IncidentCenters[{pt},#]}&/@Conics,Last[#]=!={}&]

Cubics

First/@Select[{#,IncidentCenters[{pt},#]}&/@TriangleCubics,Last[#]=!={}&]

Lines

First/@Select[{#,IncidentCenters[{pt},#]}&/@Lines,Last[#]=!={}&]