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X(1), X(6), X(9), X(55), X(259), X(3158), X(3445) Q1, Q2, Q3 : vertices of the Thomson triangle infinite points of pK(X6, X3873) vertices of the incentral triangle vertices of the anticevian triangle of X(259) |
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K761 is the isogonal transform of K365. K761 meets the line at infinity at the same three points as pK(X6, X3873). These two cubics have six other finite common points which lie on the circum-conic with perspector X(513). K760 and K761 are two members of the pencil of cubics generated by the Thomson cubic K002 and the cubic which is the union of the circumcircle and the line X(1)X(6). They are the only pKs (apart K002) in the pencil. All the cubics in {K201, K365, K747, K748, K761, K1077, K1078, K1079, K1082} are anharmonically equivalent. *** K761 is the locus of the pseudo-poles of central cubics psK with center X(1). The loci of the pseudo-pivots and the pseudo-isopivots are K365 and pK(X220, X1) respectively. See Pseudo-Pivotal Cubics and Poristic Triangles and Central cubics. |