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X(187), X(538), X(671), X(729)

foci of the inscribed Steiner ellipse, see also Table 48.

Brocard points

K248 is an isogonal circular focal nK with root X(512), singular focus X(729).

It is the locus of foci of inscribed conics centered on the line X(2)X(39) or equivalently tangent to the trilinear polar of X(512). Hence, the cubic contains the foci F1, F2 of the inscribed Steiner ellipse (S) and the Brocard points, foci of the Brocard ellipse (B). The trilinear polar of X(512) is obviously tangent to these two ellipses at X(1084) and the point a^2(b^2 - c^2)^2 : : (not in ETC) respectively.