The line segment joining the symmedian point and circumcenter 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
(1)
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(2)
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(3)
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where is the first Brocard point, is the circumradius, and is the Brocard angle. Its midpoint is the center of the Brocard circle, which has equivalent triangle center functions
(4)
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(5)
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where is the Brocard angle, and is Kimberling center (Kimberling 1998, p. 102), which is also the center of the first Lemoine circle.