Second Brocard Point

Author

Eric W. Weisstein
February 16, 2003

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

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

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

Initialization

<<PlaneGeometry`;

Distances

(Subscript[A, 1])Ω'

FullSimplify[Distance[Trilinears[BrocardPoint[2]],{1,0,0}],a>0&&b>0&&c>0]

FullSimplify[DistanceTrilinears[Sin[BrocardAngle[{a,b,c}]]b/Sin[A]],a>0&&b>0&&c>0]

(Subscript[A, 2])Ω'/(Subscript[A, 3])Ω'

FullSimplify[((Distance[Trilinears[BrocardPoint[2]],{0,1,0}])/(Distance[Trilinears[BrocardPoint[2]],{0,0,1}])),a>0&&b>0&&c>0]

With[{ω=BrocardAngle[{a,b,c}]},
FullSimplify[TrigExpand[DistanceTrilinears[Sin[#-ω]/Sin[ω]]],a>0&&b>0&&c>0]&/@{A,B,C}
]