Brocard triangle

{{Short description|Triangle constructed from another triangle}}

Image:Brocard triangle.svgs.]]

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 by forming the Brocard triangle of the Brocard triangle and continuing this pattern.{{citation

| last = Gentry | first = F. C.

| journal = National Mathematics Magazine

| jstor = 3028804

| mr = 0006038

| pages = 127–140

| title = Analytic geometry of the triangle

| volume = 16

| year = 1941| issue = 3

| doi = 10.2307/3028804

}}. The Brocard triangle is inscribed in the Brocard circle.{{mathworld|urlname=FirstBrocardTriangle|title=First Brocard Triangle}} It is named for Henri Brocard.[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Brocard.html Brocard biography]