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too complicated to be written here. Click on the link to download a text file. 

X(1), X(3) excenters midpoints of ABC Ixanticevian 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 FeuerbachBoutin hyperbola (i.e. the isogonal transform of the line through O and the relative in/excenter). 
