Far-Out Point

Author

Eric W. Weisstein
December 29, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Far-OutPoint.nb.

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

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

Initialization

<<PlaneGeometry`

Figure

t=Triangle[Reverse/@{{0.,0.},{1.2,.5},{2.,0}}];
v=Vertices[t];
pts={v[[1]],"A",v[[2]],"B",v[[3]],"C"};
redpts={Centroid[t],"G"};
bluepts={FarOutPoint[t],"F"};
greenpts={Circumcenter[t],"O"};
Show[Graphics[{
t,
PointLabels[t,pts,.03,.1],
Circumcircle[t],
{
Green,
PointLabels[t,greenpts,.03,.1],
Line[Coordinates/@{Circumcenter[t],FarOutPoint[t]}]
},
{
Red,
PointLabels[t,redpts,.03,.1]
},
{
Blue,
PointLabels[t,bluepts,.03,.1]
}
},AspectRatio->Automatic,
PlotRange->All
]]

InversePoint[Circumcircle[t],Centroid[t]]==FarOutPoint[t]

Figure of Unknown Origin

tri={{0.,0.},{1.,.8},{2.,-.3}};
act=AnticomplementaryTriangle[tri];
ccact=Circumcircle[Drop[act[[1]],-1]];
Show[
  Graphics[{Triangle[tri],Circumcircle[tri],Medians[tri]}],
  Graphics[{Thickness[.01],act,ccact}],
  AspectRatio->Automatic]