# The First Brocard Point

- Author:
- Steve Phelps

- Topic:
- Geometry

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.