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X(1), X(36), X(80), X(106), X(519), X(1323), X(1785), X(1795) foci of the inscribed Steiner ellipse, see also Table 48. 

All isogonal circular nK with a root on the trilinear polar of the Gergonne point X(7) are strophoids with a node at I. See Special Isocubics ยง4.3.2. They form the class CL003 of cubics. See also Table 69. The Gergonne strophoid K086 is obtained when the root is X(514) the infinite point of the trilinear polar of the Gergonne point : it is the locus of inscribed conics centered on the line IG = X(1)X(2). K086 is spK(X519, P) in CL055 where P is any point on the line IG. 
