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X(3), X(20), X(30), X(616), X(617), X(3648), X(6224) points Ua, Ub, Uc mentioned in the Neuberg cubic page. See also table 16 and table 18. vertices of the antimedial triangle anticomplements of the points on K060 |
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K753 is the anticomplement of K060 hence it is a circular cubic with focus F = X(14683), the anticomplement of X(3448) and the reflection of X(4) in X(399). The polar conic of F is the circle passing through X(99), X(477) with center S on the line X(20)-X(512). K753 and K001 meet the line at infinity at the same points hence they must have six other finite common points which are X(3), X(616), X(617) and the three (blue) points Ua, Ub, Uc. These finite points lie on a same (green) rectangular hyperbola homothetic to the Kiepert hyperbola. |