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K1254

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X(80), X(104), X(119), X(153), X(2950), X(6326), X(11570), X(12665), X(46435)

X(46435) = isogonal conjugate of X(2077) = reflection of X(2950) in X(119)

X153* = barycentric quotient X(8609) รท X(153), the isopivot

cevians of X(153)

other points below

Geometric properties :

K1254 is a central cubic with center X(119). Its three real asymptotes are the cevian lines of X(119) with respect to the medial triangle A'B'C'. They are parallel to the cevian lines of X(104) in ABC.

The reflections of A, B, C in X(119) are the isoconjugates of the points at infinity.

***

Since X(119) lies on the nine points circle, the isogonal transform of K1254 is an axial cubic (blue curve). Its axis of symmetry is the line {3,513} and its perpendicular at X(6) is the real inflexional asymptote. The other two asymptotes are real when ABC is obtusangle. They concur at F = X(3)X(513) /\ X(25)X(517) obviously on the axis of symmetry.