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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.

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