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 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.