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X(2), X(3), X(4), X(6), X(51), X(185), X(193), X(511), X(2574), X(2575), X(3167) S1, S2 as in Table 62 P1, P2, P3 described below |
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K907 is JSpK(X51) in Table 62. It is an example of pK with respect to a non proper triangle T, namely the (yellow) triangle with vertices S1, S2, X(511). See the related Q149. It has three real asymptotes, namely the lines X(376)X(511), X(51)X(2574), X(51)X(2575). K907 is invariant under the quadratic involution JS mentioned in Table 62 which may be seen as the isogonal conjugation in T. Its pivot is X(51) and its isopivot is P1 = JS(X51). It must contains P2 = JS(X193) and P3 = JS(X3167). P1 = X(14912) = X(2)X(3167) /\ X(3)X(193) P2 = X(14913) = X(4)X(511) /\ X(6)X(3167) /\ X(51)X(193) P3 = X(14914) = X(4)X(193) /\ X(51)X(3167). K1083 is the image of the cubic K907 under the symbolic substitution SS{a -> √a}. |