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K451

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X(13), X(14), X(690), X(9180)

P, P' : see below

K451 is an axial orthopivotal cubic with orthopivot P, the intersection of the parallel at X(99) and the perpendicular at G to the Fermat line. SEARCH = 5.16053527203514. P is now X(11006) in ETC (2016-11-23).

The real asymptote contains the centers of the Jerabek and Kiepert hyperbolas. Its perpendicular at X(1649) is the axis of symmetry of the cubic.

K451 is a circular cubic with singular focus F = X(1649) obviously on the axis of symmetry. X(1649) is the tripolar centroid of X(524).

The reflection P' of X(99) in X(1649) lies on the cubic. It is the reflection of P about the axis of the cubic. P' = X(9180) in ETC.

See also K450, K293a and K293b, three other axial orthopivotal cubics.