The First Brocard Point
- Steve Phelps
Construct a circle through vertices A and B, tangent to side BC of the triangle. Symmetrically, construct the other two circles. These three circles intersect at the first Brocard Point of triangle ABC. Cevians through the Brocard point make symmetrically equal angles with the sides of the triangle. The three circles just constructed are also designated as epicycles of triangle ABC. The second Brocard point is constructed in similar fashion, and is the isogonal conjugate of the first Brocard point.