Brocard Line

Author

Eric W. Weisstein
February 17, 2003

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

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

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

Initialization

<<PlaneGeometry`;

Diagram

t=Triangle[{{0.,0.},{2.,0.},{1.1,1.2}}];
cev1=Cevians[t,BrocardPoint[1][t]];
cev2=Cevians[t,BrocardPoint[2][t]];

Show[Graphics[{
t,
{
Red,
cev1
},
{
Blue,
cev2
},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"(Subscript[A, 1])","(Subscript[A, 2])","(Subscript[A, 3])"}}],
Append[#,Red]&/@Transpose[{EndPoint/@cev1,{"(Subscript[W, 1])","(Subscript[W, 2])","(Subscript[W, 3])"}}],
Append[#,Blue]&/@Transpose[{EndPoint/@cev2,{"W(Subscript[', 1])","W(Subscript[', 2])","W(Subscript[', 3])"}}],
Transpose[{BrocardPoint[#][t]&/@{1,2},{"Ω","Ω'"},{Red,Blue}}]
],
{PointSize[.025],LabelOffset->{-.02,-.05}1.5}
]
}],AspectRatio->Automatic,PlotRange->All]