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K585

See K584

X(1), X(357), X(358), X(3274), X(3275), X(3602) = X(3274)*, X(3603) = X(3275)*

excenters
K585a

K585 is the isogonal pK with pivot the harmonic conjugate P = X(356)' of X(356) wrt X(357) and X(358). P is also the isogonal conjugate of X(3274).

P is now X(3602).

K585 is obtained from the Neuberg cubic K001 when the angles of ABC are trisected. See K584 for further details.

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K585 is the locus of point M whose anticevian triangle is perspective with the Morley triangle. The locus of the perspector is the first Morley cubic K029.

When anticevian triangle is replaced with cevian triangle, we obtain K586.
K585b