# Isogonal Conjugate of line through Centroid

- Author:
- Andy Talmadge

- Topic:
- Centroid or Barycenter, Geometry

This sketch shows the isogonal conjugate of line through centroid G is the hyperbola that passes through vertices of triangle.
When line is a median the conjugate is the symmedian. K is the symmedian point.
P is a point on the line and P' its isogonal conjugate. Putting P at a vertex gives you the symmedian.