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X(3), X(4), X(6), X(32), X(1995), X(3425), X(8743) isogonal conjugates of X(1689), X(1690) on the Kiepert hyperbola (K) G1, G2, G3 : vertices of the Grebe triangle imaginary foci of MacBeath inconic |
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K835 is the isogonal transform of K527, two spKs cubics as in CL055. These cubics generate a pencil, invariant under isogonal conjugation, which contains the two isogonal cubics K005, K164 and two other pKs namely pK(X571, X4) and pK(X2165, X847) passing through {X3, X4, X24, X155, X1147, X2904} and {X3, X4, X68, X254, X847} respectively. K835 and the Grebe cubic K102 meet at six points A, B, C, G1, G2, G3 on the circumcircle and three other points X6, P1, P2. These two latter points are isogonal conjugates on the line X6, X5 although not necessarily real. See also Table 57. |