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X(2), X(13), X(14), X(616), X(617), X(3413), X(3414)

Ga, Gb, Gc vertices of the antimedial triangle

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

Q051 is a circular quartic with singular focus G which passes through the points Ua, Ub, Uc.

It has two real asymptotes parallel to those of the Kiepert hyperbola intersecting at X = (b^2-c^2)^2+8(2a^2SA-b^2c^2) : : , a point on the line GX(99).

G is a flex on the curve and the tangent at G contains X(187). It meets the quartic again at E(371) on the line X(30)-X(76).

The tangents at Ga, Gb, Gc, X(616), X(617) pass through G. More generally, the locus of P in the plane whose polar line (with respect to the quartic) pass through G is a central focal cubic, the anticomplement of K065.