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K605
equK605

X(1), X(2), X(19), X(75), X(279), X(304), X(346), X(2184)

vertices of the antimedial triangle

vertices of the cevian triangle of X(304)

The radical triangle is the triangle TaTbTc formed by the radical axes of the circumcircle and the three excircles.

It is perspective to ABC at X(19) and to the cevian triangle of any point P that lies on the Ayme-Moses cubic K605 (Hyacinthos #19710).

K605 is the isotomic pivotal cubic with pivot X(304), the isotomic conjugate of the Clawson point X(19).

The locus of the perspectors is another pivotal cubic with pole X(10) x X(612), pivot the intersection P of the lines X(1)X(2) and X(19)X(346), passing through X(10), X(19), X(612), X(3610).

K605a