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See the general equation in Table 32

K421 = Cev(Ω), where Ω is the Brocard angle

see also Cev(–Ω) = K322

X(2), X(6), X(83), X(384), X(458), X(1031), X(3114), X(3329), X(3407)

X(2275)*, X(2276)*

K421 and K322 are the Kiepert Cevian Mates of the Brocard (fourth) cubic K020. See explanations in Table 32.

K421 is a pK with pole X(3407), the isogonal conjugate of X(3094), and isopivot X(83) hence it is tangent at A, B, C to the cevians of X(83).

Its pivot is X(14617), the intersection of the lines X(6)X(3114) and X(2)X(3407).