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K914

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X(4), X(6), X(23), X(671), X(3534), X(7712), X(11645), X(14388), X(14458), X(14479)

F1 = reflection of O in the singular focus F = X(11636)

Ua*, Ub*, Uc* mentioned in the Neuberg cubic page. See also table 16 and table 18.

K330 and its isogonal transform K914 are two circular circum-cubics sharing the same singular focus F = X(11636).

They generate a pencil of cubics having the same property. This contains the decomposed cubic into the line at infinity and the circumcircle (O), also pK(X6, X11645).

K914 meets

• the Euler line at X(4), X(23), X(3534),

• (O) at A, B, C, the circular points at infinity, F' = X(14388) = X(11645)*,

• the circle C(O, 2R) at Ua*, Ub*, Uc*, F1, the circular points at infinity,

• the Kiepert hyperbola at A, B, C, X(4), X(671), X(14458).

• the Neuberg cubic K001 at A, B, C, X(4), Ua*, Ub*, Uc*, the circular points at infinity,

• K330 at A, B, C, X(11645), F' = X(14388) and the circular points at infinity each counted twice.