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X(5), X(20), X(30), X(1553) cusps of the Steiner deltoid of ABC vertices of the cevian triangle of X(69) infinite points of the Neuberg cubic |
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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(30), the cubic is K648 and the pK is the Neuberg cubic hence K648 is a circular cubic with singular focus X(14677). 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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