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X(3), X(6), X(25), X(183), X(11141), X(11142)

barycentric products of pairs {15,18}, {16,17}, {371,486}, {372,485}

Geometric properties :

K1057 is the isogonal transform of K267, also the barycentric products X(6) x K267, X(1) x K457.

It follows that K1057 is the locus of points with barycentrics a^2 tan(A ± t) : : when the real parameter t varies.

K1057 is an acnodal cubic with node X(6) hence it has three real collinear points of inflexion X(25), I1, I2 on a line (L) passing through X(1989), the barycentric product X(13) x X(14). I1, I2 are the X(32)-isoconjugates of J1 = X(11141), J2 = X(11142) hence the barycentric products X(15) x X(18), X(16) x X(17) respectively.

The X(32)-isoconjugate of (L) is the contact conic (C), the circum-conic passing through X(3), X(49), X(1141), X(2965), J1, J2.

The pivotal conic (P) is inscribed in the tangential triangle and passes through X(3), X(759), X(1609) and also J1, J2. It is tangent at X(3) to the Euler line.