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K1132a : X(4), X(13), X(16), X(61), X(511), X(622), X(1338), X(5613), X(11600), X(32618), X(32619) K1132b : X(4), X(14), X(15), X(62), X(511), X(621), X(1337), X(5617), X(11601), X(32618), X(32619) |
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Geometric properties : |
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K1132a and K1132b are two focal cubics with respective singular foci X(13) and X(14). They are two members of the pencil described at K1131 and each one is the antigonal image of the other. It follows that, if M is a point on one cubic, the antipode N of M on the rectangular circum-hyperbola passing through M is a point on the other cubic. The midpoint of MN lies on the nine points circle. The isogonal transforms of K1132a and K1132b are also two focal cubics, namely K1133a and K1133b with respective singular foci X(6104) and X(6105). |