Brocard circle

In geometry, the Brocard circle (or seven-point circle) for a triangle is a circle defined from a given triangle. It passes through the circumcenter and symmedian of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a diameter).

The two Brocard points lie on this circle, as do the vertices of the Brocard triangle. It is concentric with the first Lemoine circle.

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

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