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K854

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X(3), X(4), X(30), X(74), X(671), X(13509), X(14094), X(14366), X(14536)

isogonal conjugates of the X3-OAP points

The isogonal transform K854 of K811 is the only circular circum-cubic passing through the isogonal conjugates of the X3-OAP points of Table 53.

Its singular focus is X(399).

It is the Droz-Farny cubic DF(X3) as in CL039.

K854 and K811 generate a pencil of circular cubics containing the Neuberg cubic K001, the union of the Euler line and the circumcircle, also the focal cubic K187. See Table 54, line Q = X30 in the table.

K854 also belongs to another pencil of cubics passing through the isogonal conjugates of the X3-OAP points. This contains K006, K080, etc. See Table 54, column P = S' in the table. All these cubics are spKs as in CL055.