First Brocard Cevian Triangle

Author

Eric W. Weisstein
February 11, 2005

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{3,5}}];
Show[Graphics[{
t,
{Red,Cartesian[CevianTriangle[BrocardPoint[1]][t]]},
{Blue,Cartesian[#[t]]&/@Cevians[BrocardPoint[1]]},
PointLabels[Join[
Transpose[{VertexPoints[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{VertexPoints[Cartesian[CevianTriangle[BrocardPoint[1]][t]]],{"A'","B'","C'"}}],
{
{BrocardPoint[1][t],"Ω",Blue}
}
],LabelOffset->.03]
}],AspectRatio->Automatic,PlotRange->All]

Area

FullSimplify[Area[CevianTriangle[BrocardPoint[1]]],TriangleQ[]]//TraditionalForm

Side Lengths

Refine[Factor//@FullSimplify[Refine[ToSidelengths[SideLengths[CevianTriangle[BrocardPoint[1]]]],TriangleQ[]],TriangleQ[]],TriangleQ[]]//TraditionalForm

Derivation

CevianTriangle[BrocardPoint[1]]