In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the Brocard triangle of a
triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, an ...
is a triangle formed by the
intersection of
lines
Line most often refers to:
* Line (geometry), object with zero thickness and curvature that stretches to infinity
* Telephone line, a single-user circuit on a telephone communication system
Line, lines, The Line, or LINE may also refer to:
Arts ...
from a vertex to its corresponding
Brocard point
In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard (1845–1922), a French mathematician.
Definition
In a triangle ''ABC'' with sides ''a'', ''b'', and ''c'', where the vertices are labeled '' ...
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 by forming the Brocard triangle of the Brocard triangle and continuing this pattern. The Brocard triangle is inscribed in the
Brocard circle
In geometry, the Brocard circle (or seven-point circle) is a circle derived 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 s ...
. It is named for
Henri Brocard
Pierre René Jean Baptiste Henri Brocard (12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, in particular a geometer. His best-known achievement is the invention and discovery of the properties of the Brocard point ...
.
Brocard biography
/ref>
See also
*Henri Brocard
Pierre René Jean Baptiste Henri Brocard (12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, in particular a geometer. His best-known achievement is the invention and discovery of the properties of the Brocard point ...
*Brocard points
In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard (1845–1922), a French mathematician.
Definition
In a triangle ''ABC'' with sides ''a'', ''b'', and ''c'', where the vertices are labeled '' ...
Notes
Triangles
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