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K811

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X(3), X(4), X(30), X(74), X(187), X(5609), X(6328)

X3-OAP points, see Table 53

K811 is a circular cubic with singular focus X(1151), the midpoint of X(3), X(110).

It contains the four X3-OAP points described in Table 53. See also K006, K026, K405, K762, K810, all passing through X(3), X(4), the X3-OAP points and Table 54, column P = S.

The isogonal transform of K811 is K854 hence passing through the isogonal conjugates of the X3-OAP points.

These two cubics belong to the pencil generated by the Neuberg cubic K001 and the union of the Euler line and the circumcircle, also containing the focal cubic K187. See Table 54, line Q = X30 in the table.