Home page  Catalogue  Classes  Tables  Glossary  Notations  Links  Bibliography  Thanks  Downloads  Related Curves 

X(2), X(3), X(6), X(67), X(111), X(187), X(468), X(524), X(1560), X(2482), X(6593), X(10354), X(13608) vertices of medial triangle E = X(2482) = (b^2 + c^2  2a^2)^2 : : , complement of X(671), antipode of X(115) on the Steiner inellipse 

K043 is the only circular pK with pivot G = X(2). Its pole is X(187), the Schoute center (inverse of K in the circumcircle). The singular focus is X(14650), the midpoint of X(3)X(111). K043 is :
More generally, given a circumconic (C) with perspector W, the locus of point M such that the trilinear polar and the polar line in (C) of M are parallel is the pK with pole W and pivot G. It is the complement of the isotomic pK with pole W' = anticomplement of W. For example, with W = X(6), (C) is the circumcircle and the cubic is the Thomson cubic, complement of the Lucas cubic. See K007, property 8 and K002, property 12. See also Table 46 and Walsmith triangle at K1091. K043 is the locus of poles of circular pKs whose orthic line passes through X(524). The locus of the pivots is K008. See CL035. See a related pencil in K1156. 
