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X(3), X(5), X(8718), X(33541)

vertices of the CircumNormal triangle

infinite points of pK(X6, X550)

further details below

Geometric properties :

K1328 is the isogonal pK with pivot X(5) with respect to the CircumNormal triangle.

It is a member of the pencil of cubics which contains K003, K725, K1267. This pencil is stable under this isogonal conjugation and K725, K1328 are the only two self-isogonal cubics. K1267 is the transform of K003.

Points on K1328

N1, N2, N3 : vertices of the CircumNormal triangle

Q1, Q2, Q3 : points on (O) and pK(X6, X550), not on K1328

R1, R2, R3 : their antipodes on (O)

S1, S2, S3 : vertices of the cevian triangle of X(5) in the CircumNormal triangle

I1, I2, I3 : excenters of the CircumNormal triangle

F1, F2 : real foci of the inconic of the CircumNormal triangle with center X(5)