seven-point circle

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle Δ A B C as its diameter (known as the Brocard diameter). This circle also passes through the first and second Brocard points Ω and Ω', respectively. It also passes through Kimberling centers X_i for i = 3, 6, 1083, and 1316.

Brocard angle | Brocard diameter | Brocard line | Brocard points | Brocard triangles | cosine circle