TOPICS

# Brocard Diameter

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) (2) (3)

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) (5)

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

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

## Explore with Wolfram|Alpha

More things to try:

## References

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." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X182.

Brocard Diameter

## Cite this as:

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