Congruent Isoscelzers Point

Author

Eric W. Weisstein
December 20, 2002

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

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

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

Initialization

<<PlaneGeometry`;

Figure

tri=Triangle[{{0,0},{1,0},{.6,.6}}];
v=Vertices[tri];
cip=CongruentIsoscelizersPoint[tri];
pts={v[[1]],"A",v[[2]],"B",v[[3]],"C",cip,"CIP"};

perplines=PerpendicularLine[cip,Line[{#,Coordinates[cip]}]]&/@Vertices[tri];

edgepairs=RotateLeft[Partition[Sides[tri],2,1,1]];

isos=Map[Coordinates,MapThread[Thread[Intersections[#1,#2]]&,{perplines,edgepairs}],{2}];

tris=MapThread[Line/@Partition[Flatten[{{#1},#2},1],2,1,1]&,{v,isos}];

Show[Graphics[{tri,Transpose[{{Red,Green,Blue},tris}],
PointLabels[tri,pts,.02,{.03,.04}]},AspectRatio->Automatic,PlotRange->All]]