Brocard circle
In geometry, the Brocard circle (or seven-point circle) for a triangle is a circle defined 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 segment is a diameter).
The two Brocard points lie on this circle, as do the vertices of the Brocard triangle.[1] It is concentric with the first Lemoine circle.[2]
If the triangle is equilateral, the circumcenter and symmedian coincide and therefore the Brocard circle reduces to a single point.[3]
The Brocard circle is named for Henri Brocard,[4] who presented a paper on it to the French Association for the Advancement of Science in Algiers in 1881.[5]
References
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External links
See also
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