Ceva Conjugate

Author

Eric W. Weisstein
November 15, 2004

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{.4,.7}}];
p=Incenter[t];
q=Circumcenter[t];
pt=CevianTriangle[t,p];
qt=AnticevianTriangle[t,q];
x=Perspector[pt,qt];
Show[Graphics[{
t,
{Red,pt},
{Blue,qt},
{Purple,Line[{Coordinates[x],#}]&/@Vertices[qt]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[pt],{"(Subscript[P, A])","(Subscript[P, B])","(Subscript[P, C])"}}],
Append[#,Blue]&/@Transpose[{VertexPoints[qt],{"(Subscript[Q, A])","(Subscript[Q, B])","(Subscript[Q, C])"}}],
{
{p,"P",Red},
{q,"Q",Blue},
{x,"X",Purple}
}
],LabelOffset->.06]
}],AspectRatio->Automatic,PlotRange->All]