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X(3), X(15), X(16), X(20), X(30), X(368) |
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K894 is a circular cubic passing through the equi-Brocard center X(368). See Table 61 and also K083. K894 is a member of the pencil generated by the Neuberg cubic K001 and the decomposed cubic which is the union of the Brocard axis and the line at infinity counted twice. The focal cubic K463 and the complement K900 of K060 are two other remarkable members. All these cubics are circular and share the same singular focus X(110), the same real asymptote passing through X(30) and X(74), the same orthic line which is the Euler line. They pass through X(3), X(15), X(16) which are their only finite common points. The polar conic of X(30) in K894 is the rectangular hyperbola (H) passing through X(550) whose asymptotes are parallel and perpendicular at X(476) to the Euler line. |