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X(3), X(6), X(22), X(25), X(159), X(2353)

E = a^2 / (b^4 + c^4 - a^4) : : = X(32)-isoconjugate of X(22)

F = X(32)-isoconjugate of X(159)

vertices of the tangential triangle

common points of K169 and the circumcircle

K174 is the isogonal transform of K1365 = pK(X2, X315).

K174 is K169 for the tangential triangle. It is the locus of point M such that K, M and the isogonal conjugate of M with respect to the tangential triangle are collinear. Hence, K174 contains the excenters of this triangle, the incenter being O. See K878 for a generalization and other related cubics.

The locus of P whose anticevian triangle is perspective (at Q) to the Ara triangle (see ETC, X5594) is K177. Q lies on K174.