Brocard circle
Encyclopedia
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the Brocard circle (or seven-point circle) for a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
is a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
having a diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of the line segment
Line segment
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment...
between the circumcenter and symmedian
Symmedian
Symmedians are three particular geometrical lines associated with every triangle. They are constructed by taking a median of the triangle , and reflecting the line over the corresponding angle bisector...
. It contains the Brocard points. The Brocard circle is named for Henri Brocard
Henri Brocard
Pierre René Jean Baptiste Henri Brocard was a French meteorologist and mathematician, in particular a geometer...
.