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K1459

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X(1), X(3), X(517), X(2948), X(5529), X(5672), X(5673), X(6326), X(11752), X(11789), X(63911), X(73207), X(73208), X(73209), X(73210), X(73211)

vertices of the excentral triangle

Geometric properties :

K1460 is a circular cubic with singular focus X(5531), X(3448) of the excentral triangle IaIbIc.

Let P be a point and let Pa, Pb, Pc be its reflections in the sidelines of the excentral triangle = anticevian triangle of the incenter X(1).

PaPbPc and IaIbIc are perspective (at Q) if and only if P lies on K1459 which is the Neuberg cubic of the excentral triangle IaIbIc.

The locus of Q is K1460, the cubic K060 of this triangle.