Brocard triangle

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File:Brocard triangle.svg
The Brocard triangle (in black) of the triangle ABC. B1 and B2 are the two Brocard points.

In geometry, the Brocard triangle of a triangle is a triangle formed by the intersection of lines from a vertex to its corresponding Brocard point 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.[1] The Brocard triangle is inscribed in the Brocard circle.[2] It is named for Henri Brocard.[3]

See also


  1. Gentry, F. C. (1941), "Analytic geometry of the triangle", National Mathematics Magazine, 16: 127–140, JSTOR 3028804, MR 0006038<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
  2. Weisstein, Eric W., "First Brocard Triangle", MathWorld.
  3. Brocard biography