X(3), X(4), X(20)
infinite points of the Orthocubic K006
antipodes of A, B, C on the circumcircle
vertices of the cevian triangle of X(69)
foci of the inconic with center O, perspector X(69)
X4-OAP points, see also Table 53.
See Cubics Related to Coaxial Circles §10.6.
K443 is the isogonal transform of K376.
The Darboux cubic K004 and the decomposed cubic which is the union of the circumcircle and the Euler line generate a pencil of central cubics with center O passing through H, X(20) and the reflections A', B', C' of A, B, C about O.
Each cubic has the same asymptotic directions as one of the isogonal pKs of the Euler pencil.
See also Table 54 where K443 is mentioned in one line and two columns showing that it belongs to three pencils of cubics generated by :
• K004 and the union of the Euler line with the circumcircle, column P = [X20], already mentioned above.
At last, K443 is also a member of the pencil generated by K006 and the union of the Jerabek hyperbola with the line at infinity.