The Circle passing through the first and second Brocard Points and , the Lemoine
Point , and the Circumcenter of a given Triangle. The Brocard Points and
are symmetrical about the Line
, which is called the Brocard Line.
The Line Segment is called the Brocard Diameter, and it has length

where is the Circumradius and is the Brocard Angle. The distance between either of the Brocard Points and the Lemoine Point is

**References**

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, p. 272, 1929.

© 1996-9

1999-05-26