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# Brocard Line

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) (2) (3)

Distances involving the point satisfy

 (4)

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).

## See also

Brocard Axis, Brocard Circle, Brocard Diameter, Brocard Points, Brocard Triangles, Isogonal Conjugate, Symmedian Point, Triangle Median

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## References

Emmerich, A. Die Brocardschen Gebilde und ihre Beziehungen zu den verwandten merkwürdigen Punkten und Kreisen des Dreiecks. Berlin: Reimer, 1891.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 263-286, 1929.

Brocard Line

## Cite this as:

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