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a (a^2 - b^2) (a^2 - c^2) x (y^2 - z^2) = 0

X(2), X(662), X(1577), X(2167), X(2580), X(2581), X(2582), X(2583), X(4552), X(4560), X(14213)

vertices of the antimedial triangle

vertices of the cevian triangle of X(662)

Geometric properties :

K1004 is the isogonal transform of K1005.

K316 is the barycentric product X(1) x K1004.