In geometry

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 triangle of 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 triangle formed by the intersection

Line-line intersection

In Euclidean geometry, the intersection of a line and a line can be the empty set,a point, ora line. Distinguishing these cases, and finding the intersection point have use, for example, in computer graphics, motion planning, and collision detection....

 of line

Line (geometry)

The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...

 from a vertex to its corresponding Brocard point

Brocard point

In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard , a French mathematician.-Definition:...

 and a line from another vertex to its corresponding Brocard point and the other two points constructed using different combinations of vertices and Brocard points. This triangle is also called the first Brocard triangle, as further triangles can be formed be forming the Brocard triangle of the Brocard triangle and continuing this pattern. The Brocard triangle is inscribed in the Brocard circle

Brocard circle

In geometry, the Brocard circle for a triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. The Brocard circle is named for Henri Brocard....

. It is named for Henri Brocard

Henri Brocard

Pierre René Jean Baptiste Henri Brocard was a French meteorologist and mathematician, in particular a geometer...

.