Isogonal Conjugate of Line Through the Circumcenter
- Steve Phelps
Take any line through the circumcenter, intersecting the circumcircle in antipodal points D and D'. The locus of the isogonal conjugates of this line is a rectangular hyperbola through the vertices and orthocenter. The asymptotes are the Simson lines of the two antipodal points. Please download this sketch to see the construction.