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X(2), X(3), X(110), X(352), X(511), X(574), X(599), X(7998), X(8724), X(10717), X(10989), X(11178)

X(39162), X(39163), X(39164), X(39165) : foci of the Steiner inellipse

points of pK(X6, X599) on (O)

Geometric properties :

K1295 is a focal cubic, with singular focus X(8724), that passses through the foci of the Steiner inellipse. See Table 48 for other examples.

Locus properties

• locus of M such that X(7998), M, Psi(M) are collinear. Hence, K1295 is a Psi-pivotal cubic, see Table 60.

• locus of foci of conics inscribed in the triangle {X2, X3, X110} having their center on the line {2, 51, 262, etc}. Hence, K1295 is an isogonal nK in this triangle. Note that two isogonal conjugate points share the same tangential which obviously lies on the cubic.

• (more generally), for every P on the cubic, locus of foci of conics inscribed in the triangle {X2, P, Psi(P)} having their center on the line above. Example : {X2, X352, X574}.

• locus of contacts of tangents drawn through X(8724) to the circles passing through G and X(7998).

• locus of M such that the line-angles (MX7998, MX511) and (MX8724, MX2) are equal or supplementary (mod. π). Hence, K1295 is an isoptic cubic.