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Brocard Midpoint

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BrocardMidpoint

The midpoint of the first and second Brocard points Omega and Omega^'. It has equivalent triangle center functions

alpha=a(b^2+c^2)
(1)
alpha=sin(A+omega),
(2)

where omega is the Brocard angle. It is Kimberling center X_(39) (Kimberling 1998, p. 73).

The Brocard midpoint lies on the Brocard axis and is the center of the Gallatly, half-Moses, and Moses circles.

See also

Brocard Points, First Brocard Point, Second Brocard Point

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References

Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(39)=Brocard Midpoint." https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X39.

Referenced on Wolfram|Alpha

Brocard Midpoint

Cite this as:

Weisstein, Eric W. "Brocard Midpoint." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BrocardMidpoint.html

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