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(b^2 + c^2 - 2a^2) x (c^2y^2 - b^2z^2) = 0

X(1), X(2), X(6), X(111), X(524), X(2930), X(5524), X(5525), X(7312), X(7313), X(8591), X(13574)

excenters

Geometric properties :

K1156 is the isogonal circular pK with pivot X(524) and singular focus X(1296).

Locus property

Let P be a point and denote by Oa, Ob, Oc the circumcenters of PBC, PCA, PAB and by Ka, Kb, Kc the symmedian points of PObOc, POcOa, POaOb. These triangles OaObOc and KaKbKc are perspective if and only if P lies on K1156 (Kadir Altintas). Recall that ABC and OaObOc are perspective if and only if P lies on the Neuberg cubic K001 (see locus property 2).