The midpoint of the first and second Brocard
points 
and 
.
It has equivalent triangle center functions
where 
is the Brocard angle. It is Kimberling
center 
(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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