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The Circumcircle, Brocard Circle, Lemoine Line, and Isodynamic Points belong to a Coaxal System orthogonal to the Apollonius Circles, called the Schoute coaxal system. In general, there are 12 points whose Pedal Triangles with regard to a given Triangle have a given form. They lie six by six on two Circles of the Schoute coaxal system.
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 297-299, 1929.