Fletcher Point

Author

Eric W. Weisstein
March 27, 2003

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

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

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

Initialization

<<PlaneGeometry`;
<<KimberlingCenters`;

Figure

t=Triangle[{{0,0},{1,-0.1},{0.4,0.5}}];
n=NobbsPoints[t];
ct=ContactTriangle[t];
Show[Graphics[{
{Blue,
Line/@Map[Coordinates,Transpose[{n,VertexPoints[t]}],{2}],
Line/@Map[Coordinates,Transpose[{n,VertexPoints[ct]}],{2}]
},
{DarkGreen,LongestLine[Coordinates/@n]},
t,
{Purple,
LongestLine[Coordinates/@Flatten[{SoddyCenters[t],Incenter[t],GergonnePoint[t],FletcherPoint[t]}]]
},
{Red,ct},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[ct],{"D","E","F"}}],
Append[#,DarkGreen]&/@Transpose[{NobbsPoints[t],{"D'","E'","F'"}}],
Append[#,Purple]&/@Transpose[{SoddyCenters[t],{"S","S'"}}],
Append[#,Purple]&/@{
{GergonnePoint[t],"Ge"},
{Incenter[t],"I"},
{FletcherPoint[t],"Fl"}
}
],LabelOffset->.07]
}],AspectRatio->Automatic,PlotRange->All
]

Trilinears

Trilinears[FletcherPoint]

BisymmetricQ[FletcherPoint]

IncidentCenters[KimberlingCenters,FletcherPoint]