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X(1), X(8), X(145), X(188), X(2136), X(3680), X(6553), X(8834)

X(3680) = X(145)* = a (b+c-a) / (b+c-3a) : : , isoconjugate of the pivot = reflection of X(2136) in X(1)

K201 is a central pK with center X(1) incenter, pole X(9) mittenpunkt, pivot X(145) Nagel point of the antimedial triangle.

The tangents at X(1) and X(8) pass through X(9). The asymptotes pass through X(1) and the midpoints of ABC.

The isogonal transform of K201 is pK(X604, X1420) and its isotomic transform is pK(X85, X39126) where X(39126) = (b+c-3a) / [a(b+c-a)] : : , the isotomic conjugate of X(3680).

The symbolic substitution SS{a -> a^2} transforms K201 into K707.

See K830, K831, two other central cubics with center X(1).

All the cubics in {K201, K365, K747, K748, K761, K1077, K1078, K1079, K1082} are anharmonically equivalent.


Locus property

Let PaPbPc be the anticevian triangle of a point P. A', B', C' are the reflections of Pa, Pb, Pc in the incenter X(1). ABC and A'B'C' are perspective if and only if P lies on K1077 (Kadir Altintas). The locus of the perspector is K201.