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X(30), X(113), X(2043), X(2044), X(31862), X(31863)

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

Geometric properties :

K800, K1092, K1288, K1289 are members of a same pencil of focal cubics that also contains the decomposed cubic which is the union of the line at infinity and the axes of the Steiner ellipses. All these cubics have their singular focus on the Fermat axis and share the same orthic line, namely the Euler line.

The singular focus of K1288 is X(113) whose polar conic is the circle (C) passing through X(113), X(2043), X(2044).

K1288 is the locus of contacts of tangents drawn through X(113) to the circles passing through X(2043), X(2044).

The polar conic of X(30) is the rectangular hyperbola (H) passing through X(3), X(30), X(523) whose center is the reflection X(25641) of X(113) in the Euler line.

The real asymptote is the line X(30), X(115) and the orthic line is the Euler line.