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X(3), X(4), X(20) P1 = isogonal conjugate of X(382) P2 = its reflection in O infinite points of pK(X6, X382) foci of MacBeath inconic : O, H and two imaginary antipodes of A, B, C on (O) |
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K850 is the isogonal transform of K846 = spK(X20, X5). K850 meets BC at A' on the parallel at X(20) to the line X(382)A, B' and C' likewise. It is a central cubic with center O, a member of the pencil generated by K005 and K187. See Table 54, line Q = X5 in the table. It belongs to the pencil of central cubics generated by K004 and the union of (O) and the Euler line. These cubics are those in the column P = [X20] of Table 54. |