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X(2), X(3), X(187), X(1670), X(1671), X(3413), X(3414)

Ga, Gb, Gc vertices of the antimedial triangle

midpoints of ABC

points Ua, Ub, Uc mentioned in the Neuberg cubic page. See also table 16 and table 18.

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

Q052 is a circular quartic with singular focus X(187) which passes through the points Ua, Ub, Uc.

It has two real asymptotes parallel to those of the Kiepert hyperbola intersecting at X = 5a^2(b^2+c^2)-6b^2c^2-4a^4 : : , a point on the line X(99)-X(187).

It meets the circumcircle at the same points as K169 = pK(X6, X69).