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X(1), X(36), X(80), X(106), X(519), X(1323), X(1785), X(1795), X(4845), X(5127), X(5209), X(5526), X(5620), X(7343), X(34578), X(39162), X(39163), X(39164), X(39165), X(50148), X(61476), X(61477), X(61478), X(61479), X(61480), X(61481), X(61482), X(61483), X(61484), X(67674), X(67686), X(68233), X(68234), X(68235), X(68236), X(68237), X(68238)

X{39162, 39163, 39164, 39165} are the foci of the inscribed Steiner ellipse, see also Table 48.

X = X(61484) is the common tangential of X(519) and the singular focus X(106)

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 §4.3.2. They form the class CL003 of cubics. See also Table 69.

The Gergonne strophoid K086 = nK(X6, X514, X1) is obtained when the root is X(514) the infinite point of the trilinear polar of the Gergonne point. K086 is the locus of foci of inscribed conics centered on the line IG = X(1)X(2).

K086 is spK(X519, P) in CL055 where P is any finite point on the line IG.

See K040, K165 and also Table 46.

The incircle inverse of K086 is the rectangular hyperbola (H) with center Ω = X(18240) passing through X(1), X(7), X(142), X(942), X(946), X(1387), X(3307), X(3308), hence homothetic to the Feuerbach hyperbola.