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K875

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X(2), X(4), X(13), X(14), X(542)

two imaginary points S1, S2 on the Kiepert hyperbola, the orthocentroidal circle, the line X(115)X(125)

Q = X(4)X(542) /\ X(115)X(125), SEARCH = 0.959105222135810

See Table 59 for other similar cubics and a generalization.

K875 is the locus of contacts of the tangents drawn through X(4) to the circles passing through the Fermat points X(13), X(14).

The singular focus is X(4) and the real asymptote is the parallel at X(2) to the Fermat axis.

The polar conic (C) of X(4) is the circle passing through X4, X13, X14, X2132, X2394.