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X(2), X(3), X(3413), X(3414)

centers of the Apollonius circles

X(3413), X(3414) : infinite points of the Kiepert hyperbola

infinite points of the Morley sidelines

imaginary foci of the Brocard ellipse i.e. common points of the Brocard axis and the Kiepert hyperbola

Q065 is the locus of centers of equilateral triangles inscribed in the McCay cubic.

It is a quintic with five real asymptotes : two are parallel to the asymptotes of the Kiepert hyperbola and three are parallel to the Morley sidelines.

Q065 also contains the intersections of the circle OHX(74) and the perpendicular bisector of HX(74).