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∑ a (b + c – a) x (c y^2 – b z^2) = 0 |
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X(7), X(9), X(366) vertices of the cevian triangle of X(9) vertices of the anticevian triangle of X(366) infinite points of pK(X10481, X7) and pK(X1212, X144) |
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Geometric properties : |
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The symbolic substitution SS{a -> √a} transforms the McCay cubic K003 into K977 and K049, K096 into pK(X10481, X7), pK(X1212, X144). These two latter cubics and K977 share the same infinite points. Those of K977 concur at G, the centroid of ABC. A lot of properties of K977 can be obtained from K003 under the same symbolic substitution. For example, K977 passes through Q1, Q2, Q3 obtained from the vertices of the CircumNormal triangle. These points lie on the circum-conic (C) with perspector X(1) and on the rectangular hyperbola (H) with center X(6594), passing through X(9), X(100), X(1001), X(2346), etc. The isogonal, isotomic transforms of K977 are pK(X31, X57), pK(X75, X8) respectively. |