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X(1), X(3)

excenters

midpoints of ABC

Ix-anticevian points, see Table 23

points at infinity of the Thomson cubic

Q025 is the locus of point P such that the anticevian and circumcevian triangles of P are orthologic.

Q025 is a bicircular septic having three real asymptotes parallel to those of the Thomson cubic. The seven points A, B, C, I, Ia, Ib, Ic are all double points. The tangents at A, B, C are the bisectors and those at the in/excenters are parallel to the asymptotes of the corresponding Feuerbach-Boutin hyperbola (i.e. the isogonal transform of the line through O and the relative in/excenter).