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X(6)

other points described below

K375 is the only equilateral pK of the class CL043 of pivotal cubics with pivot P and isopivot K.

It is obtained when P is the isotomic conjugate of the intersection of the lines X(3)X(523) and X(315)X(524), now X(18880) in ETC.

It meets the circumcircle at A, B, C and three other points Q1, Q2, Q3 such that the tangents at these points are concurrent at X. Furthermore, these tangents make 60° angles with one another.

The tangents at A, B, C are the symmedians.