A Brocard line is a line from any of the vertices of a triangle to the first or second Brocard point. Let the angle at a vertex also be denoted , and denote the intersections of and with as and . Then the angles involving these points are
(1)
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(2)
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(3)
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Distances involving the point satisfy
(4)
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where is the Brocard angle (Johnson 1929, pp. 267-268).
If is the triangle centroid and is the symmedian point of a triangle , then the lines , , and meet at a point . Similarly, , , and meet at a point which is the isogonal conjugate point of (Johnson 1929, pp. 268-269).