X(2), X(99), X(1113), X(1114), X(2418)
traces of the line X(3)X(69) on the sidelines of ABC
Given the isoconjugation with pole W = X(99), the locus of point M such that the trilinear polars of M and its isoconjugate M* are perpendicular is K106. This cubic is a member of the class CL008 of cubics. See also the Simson cubic K010 (perpendicular tripolars isotomic cubic) and K107 (perpendicular tripolars isogonal cubic).
K106 is the nK0 with pole X(99) and root X(4563), the trilinear pole of the line X(3)X(69) and the orthocorrespondent of X(99).
The tangents at A, B, C are independent of W (they join a vertex of ABC to the foot of the orthic axis on the opposite sideline).
K606 is the isotomic transform of K106.