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Brocard

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.