Brocard circle

It passes through the circumcenter and symmedian point of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a diameter).

, etc), the Brocard circle consists of the points satisfying the equation[1] The two Brocard points lie on this circle, as do the vertices of the Brocard triangle.

[2] These five points, together with the other two points on the circle (the circumcenter and symmedian), justify the name "seven-point circle".

[3] If the triangle is equilateral, the circumcenter and symmedian coincide and therefore the Brocard circle reduces to a single point.

[4] The Brocard circle is named for Henri Brocard,[5] who presented a paper on it to the French Association for the Advancement of Science in Algiers in 1881.