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X(9), X(57), X(527), X(2291), X(8072), X(8073), X(32622), X(32623)

Foci of the Steiner in-ellipse, see also Table 48.

Foci of the Mandart ellipse (see Generalized Mandart Conics in the Downloads page and also K040)

K352 = nK(X6, X522, X9) is an isogonal focal cubic passing through the foci of the Steiner and Mandart inscribed ellipses, (S) and (M) on the figure.

It is the locus of foci of inscribed conics centered on the line (L) passing through G and X(9). (L) is the axis or orthic line of the cubic.

The singular focus is X(2291) whose polar conic is the circle (C) passing through X(3), X(9), X(57), X(2291), X(14733).

K352 meets the Stevanovic circle (St) at the circular points at infinity, two points X(8072), X(8073) on the line X(4)X(9) and two points X(32622), X(32623) on the line X(1)X(3).

K352 meets the sidelines of ABC at A', B', C' on the trilinear polar of the root X(522). This line is the fourth common tangent to (S) and (M) with contacts X(11) and X(1146) respectively.