Brocard Diameter


The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard axis. The Brocard diameter has length


where Omega is the first Brocard point, R is the circumradius, and omega is the Brocard angle. Its midpoint is the center of the Brocard circle, which has equivalent triangle center functions


where omega is the Brocard angle, and is Kimberling center X_(182) (Kimberling 1998, p. 102), which is also the center of the first Lemoine circle.

See also

Brocard Axis, Brocard Circle, Brocard Line, Brocard Points, Circumcenter, First Brocard Point, Second Brocard Point, Symmedian Point

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Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(182)=Midpoint of Brocard Diameter."

Referenced on Wolfram|Alpha

Brocard Diameter

Cite this as:

Weisstein, Eric W. "Brocard Diameter." From MathWorld--A Wolfram Web Resource.

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