Brocard circle
[Image:Brocard Circle.svg|250px|right]
In geometry, the Brocard circle is a circle derived from a given triangle. It passes through the circumcenter and symmedian point of the triangle, and is centered at the midpoint of the line segment joining them.
Equation
In terms of the side lengths,, and of the given triangle, and the areal coordinates for points inside the triangle, the Brocard circle consists of the points satisfying the equationRelated points
The two Brocard points lie on this circle, as do the vertices of the Brocard triangle.These five points, together with the other two points on the circle, justify the name "seven-point circle".
The Brocard circle is concentric with the first Lemoine circle.