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K971

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X(1), X(8), X(85), X(271), X(318), X(6757), X(7057)

vertices of the cevian triangle of X(75)

infinite points of K157 = pK(X9, X1)

Geometric properties :

K971 is a nodal psK+ as in CL067.

The node is X(8) with nodal tangents parallel to the asymptotes of the Feuerbach hyperbola.

The asymptotes are parallel at the midpoint X(3679) of X(2)X(8) to those of K157 = pK(X9, X1). This latter cubic is a pK+ with asymptotes concurring at X(2).

The isotomic transform of K971 is K970, a very similar cubic.

The isogonal transform of K971 is K967. Its X(1)-isoconjugate is K577.

Under the symbolic substitution SS{a -> a^2}, K971 is transformed into K257.