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too complicated to be written here. Click on the link to download a text file. |
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X(2), X(3), X(30), X(110), X(114), X(1511) midpoints of ABC vertices of the Thomson triangle reflections of X(3) in the sidelines of ABC |
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Geometric properties : |
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K1095 is a member of the pencil described in page K913. It is a circular cubic with singular focus X(5609). It has nine identified common points with the Stammler strophoid K038 namely X(3) counted twice, X(30), X(1511), the midpoints of ABC and the circular points at infinity. These two cubics generate a pencil of cubics containing a decomposed cubic which is the union of the line at infinity and the rectangular hyperbola (H) passing through X(3), X(5), X(6), X(113), X(141), X(206), X(942), X(960), X(1147), X(1209), X(1493), X(1511), X(2574), X(2575), X(2883), etc. (H) is the complement of the Jerabek hyperbola, the polar conic of X(3) in K002, the polar conic of X(20) in K003, also the X(2)-Ceva conjugate of the Brocard axis. The pencil above also contains the circum-cubic K446, K900 and the central cubic which is the complement of K530. More generally, the anticomplement of each cubic of this pencil is a circular circum-cubic passing through X(4) counted twice, X(30), X(265). See K025 (nodal), K060 (pK), K427, K449, K530 (focal) and obviously the union of the line at infinity and the Jerabek hyperbola. All have the same orthic line (the Euler line) and a singular focus on the line passing through X(4), X(94), X(143), X(146), X(265), X(568), X(1112), X(1539), X(1986), X(2970), etc. |