Brocard Midpoint

Author

Eric W. Weisstein
December 5, 2004

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

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

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

Figure

t=Triangle[{{0,0},{1,0},{.3,.7}}];
Show[Graphics[{
t,
{Red,
l=Line[Coordinates/@{BrocardPoint[1][t],
BrocardPoint[2][t]}],
EqualSideTicksAboutMidpoint[l,1,.02]
},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
Append[#,Red]&/@{{BrocardPoint[1][t],"Ω"},
{BrocardPoint[2][t],"Ω'"},
{BrocardMidpoint[t],"(Subscript[M, ΩΩ'])"}
}
],
{PointSize[.03],LabelOffset->{.06,-.03}}]
}],AspectRatio->Automatic,PlotRange->All
]
Null

Structures Passing through It

pt=BrocardMidpoint;

Circles

First/@Select[{#,IncidentCenters[{pt},#]}&/@Circles,Last[#]=!={}&]

Circle Centers

First/@Select[{#,IncidentCenters[{pt},CircleCenter[#]]}&/@Circles,Last[#]=!={}&]

Conics

First/@Select[{#,IncidentCenters[{pt},#]}&/@Conics,Last[#]=!={}&]

Cubics

First/@Select[{#,IncidentCenters[{pt},#]}&/@TriangleCubics,Last[#]=!={}&]

Lines

First/@Select[{#,IncidentCenters[{pt},#]}&/@Lines,Last[#]=!={}&]