Cevian Circle

Author

Eric W. Weisstein
January 21, 2005

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

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

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

Figure

tri=Triangle[{{0,0},{1,0},{.2,.7}}];
v=Vertices[tri];
ctr=Point[TrilinearToCartesian[tri,{.2,.3,.5}]];
ct=CevianTriangle[tri,ctr][[1]];
pts={v[[1]],A,v[[2]],B,v[[3]],C};
bluepts={ct[[1]],A',ct[[2]],B',ct[[3]],C'};

Show[Graphics[{
tri,
{
Red,
Cevians[tri,ctr],
PointLabels[tri,{ctr,P},.03,.03]
},
{
Green,
CevianCircle[tri,ctr]
},
{
Blue,
CevianTriangle[tri,ctr],
PointLabels[tri,bluepts,.03,.03]
},
PointLabels[tri,pts,.03,.03]
}],AspectRatio->Automatic,PlotRange->All]