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X(6), X(99), X(187)

points at infinity of ABC sidelines

Given an isoconjugation with pole W(p : q : r), the locus of point P such that the pedal triangles of P and its W-isoconjugate P* are parallelogic is the cubic nK0(W, X6). See CL022. This cubic is a nK+ if and only if W lies on K150.

K150 is a non-pivotal isocubic with pole X(14567) = [ a^4 (b^2 + c^2 - 2a^2) : ... : ... ] = X6 x X187 = X32 x X524 and root G.

It has three real asymptotes parallel to the sidelines of ABC.

Kjp = K024 is the most interesting example with W = X(6). K151 is another example of such nK0+(W, X3) with W = X(99) (Steiner point).