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X(1), X(7), X(55), X(3160)

isogonal conjugate of X(3160)

A1B1C1 : intouch triangle = cevian triangle of X(7)

A2B2C2 : cevian triangle of X(3160)

Q174 is analogous to Q172, where general properties are given.

Let PaPbPc be the circumcevian triangle of a variable point P. With S = X(55), let X = BC ∩ SPa, Y = CA ∩ SPb, Z = AB ∩ SPc. ABC and XYZ are perspective (at Q) if and only if P lies on the cubic K1253 = pK(X31, X165), a circumcevian cubic of CL072. The locus of the perspector Q is the sextic Q174.

Q174 is an isogonal sextic.

X(1) is a quadruple point on Q174 and A, B, C are double points with tangents passing through X(55) and the isogonal conjugate of X(3160). The tangents at X(55), A1, B1, C1 pass through X(1).

Q104 is another isogonal sextic with a very similar shape.