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K450

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X(13), X(14), X(98), X(542)

P see below

K450 is an axial orthopivotal cubic with orthopivot P, the reflection of the Tarry point X(98) in the perpendicular bisector of the Fermat points X(13) and X(14). SEARCH = -3.14545293138011. P is now X(11005) in ETC (2016-11-23).

This bisector is also the trilinear polar of X(523) and contains the centers of the Jerabek and Kiepert hyperbolas. It is the axis of symmetry of the cubic.

K450 is a circular cubic with singular focus F = X(868) obviously on the axis of symmetry.

The orthic line is the parallel at G to the Fermat line and contains X(98), X(110), etc.

See also K451, K293a and K293b, three other axial orthopivotal cubics.