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X(5), X(8), X(20), X(3091) cusps of the Steiner deltoid of ABC vertices of the cevian triangle of X(69) infinite points of the cubic pK(X6, X1656) vertices of the 2nd Conway triangle, see ETC X(9776) |
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The cubics passing through the cusps of the Steiner deltoid of ABC, the vertices of the cevian triangle of X(69), the centers X(5), X(20) form a pencil which contains one circum-cubic namely the Steiner-McCay cubic K071. Each cubic of the pencil meets the Euler line at a third point X and then also contains the infinite points of the isogonal pK with pivot the reflection of X about X(5). When X = X(3091), the cubic is K649 and the pK is pK(X6, X1656). The cubic and the pK meet at six other finite points which lie on a same rectangular hyperbola and all these hyperbolas belong to a same pencil. |
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