Isogonal Mittenpunkt

Author

Eric W. Weisstein
February 1, 2003

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

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

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

Initialization

<<PlaneGeometry`;

Graphic

{
CollinearQ[{Circumcenter,Incenter,IsogonalMittenpunkt}],
CollinearQ[{Centroid,GergonnePoint,Mittenpunkt,IsogonalMittenpunkt}]
}

t=Triangle[{{0,0},{1,0},{.3,.5}}];
Show[Graphics[{
t,
{Red,
LongestLine[Coordinates/@Through[{Centroid,GergonnePoint,Mittenpunkt,IsogonalMittenpunkt}[t]]]
},
{Blue,
LongestLine[Coordinates/@Through[{Circumcenter,Incenter,IsogonalMittenpunkt}[t]]]
},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
Append[#,Red]&/@{
{Centroid[t],"G"},
{GergonnePoint[t],"Ge"},
{Mittenpunkt[t],"M"}
},
Append[#,Blue]&/@{
{Circumcenter[t],"O"},
{Incenter[t],"I"}
},
{{IsogonalMittenpunkt[t],"M'",Purple}}
],{PointSize[.025],LabelOffset->-.03{1.2,1.2}}]
}]]