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X(1), X(3), X(4), X(8), X(355), X(5903), X(10570), X(13746), X(22836), X(59282), X(59283), X(59284), X(59285), X(59286)

imaginary foci of the MacBeath inconic

infinite points of the internal bisectors

points of pK(X6,X355) on (O)

Geometric properties :

K1345 is a MacBeath cubic as in Table 80. It is the isogonal transform of K1340.

A spK(P, X5) meets the line at infinity on the cevian lines of a certain point Z if and only if Z is a point on K003,

For example, with Z = X(4), these cevian lines are the altitudes of ABC and the cubic of Table 80 is K846 = spK(X20, X5).

With Z = X(3), the cubic of Table 80 is the isogonal transform K1346 of K1344 = spK(X5889, X5).

With Z = X(1), these cevian lines are the internal bisectors of ABC and the cubic is K1345 = spK(X1, X5).