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X(2), X(63), X(394), X(493), X(494), X(3083), X(3084), X(5408), X(5409), X(6503), X(6504), X(6505), X(6513), X(8222), X(8223) isotomic conjugates of X(1585), X(1586), now X(11090) and X(11091) in ETC (2016-12-02) midpoints of ABC with tangents passing through X(6503) vertices of the anticevian triangle of X(63) foci of the inconic with center X(3757) |
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K857 is the isogonal transform of K678, the isotomic transform of pK(X2052, X2052) see CL007, the complement of pK(X2, X6515). K857 is also : • the barycentric quotient of K006 by X(4). Recall that the barycentric product of K006 by X(4) is K678. K857 is therefore anharmonically equivalent to the Orthocubic K006. • the transform of the Orthocubic K006 under the mapping f described in the page K856 which is an analogous cubic. • the transform of the Thomson cubic K002 under the symbolic substitution SS{a –> cosA}. See ETC, X(6503) and below. K857 and K678 generate a pencil which contains nK0(X6, X512) and pK(X6, X3757). It follows that all these cubics pass through the foci of the inconic with center X(3757). |