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X(2), X(4), X(6), X(28), X(284), X(580), X(943), X(1172), X(1175), X(2982), X(40395), X(40570), X(40571), X(40572), X(40573), X(40574), X(40575)

Ω = X(40570), on circum-hyperbola (H) through G, K

P = X(40395) = cevapoint(X6, X28), on Kiepert hyperbola

P1 = X(40571) = {2,6} /\ {943,1175}

Geometric properties :

K1174 is the locus of M whose anticevian triangle is perspective to the circumcevian triangle of X(28). As such, K1174 is a member of CL043.

The locus of the perspector is a pK with same pole, a circumcevian cubic of CL072 passing through X(1), X(21), X(28), X(943), X(1612), X(2218) and the vertices of the circumcevian triangle of X(28).

K1174 is the isogonal transform of K1419 = pK(X18591, X2).

K1174 meets (O) again at Q1, Q2, Q3 (not always all real) on (K) = pK(X6, P1) hence P1 is the othocenter of Q1Q2Q3. Note that (H) and (K) meet at A, B, C, G, K and the isogonal conjugate of P1. The tangents at Q1, Q2, Q3 to K1174 concur but not on the curve.