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This sketch shows the Brocard diameter OK of the Brocard circle. The latter passes through the 1st and 2nd Brocard points, P and Q, respectively. A defining property of the 1st Brocard point is the equality of the three angles, PBC, PCA, PAB, and similarly for the 2nd Brocard point. The special angle is called the Brocard angle of the triangle.

How big can the Brocard angle be?

For more, see GEOMETRY IN ACTION, Chapter 8, Project 4.