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X(2), X(3), X(13), X(14), X(15), X(16), X(30), X(110), X(399)

K883 is a circular cubic invariant under the involution Psi described in the page K018 and in the paper "Orthocorrespondence and Orthopivotal Cubics", §5. See also the analogous focal cubic K508. K883 is a Fermat Psi-cubic as in Table 60 where a generalization is given.

The singular focus is X(9138), the real asymptote is the line passing through X(30), X(110), X(477).

The polar conic (H) of X(30) contains X(395), X(396), X(523), X(549).

The polar conic of X(110) contains X(2), X(15), X(16), X(30) hence the tangents at these points concur at X(110).

K883 is also an isogonal pK with pivot X(30) in the triangle X(2)X(15)X(16) hence it must contain the in/excenters of this latter triangle. These points lie on (H) and on the axes of the Steiner inellipse.

Recall that Psi and isogonal conjugation in X(2)X(15)X(16) coincide on K048. On the other hand, isogonal conjugations in ABC and X(2)X(15)X(16) coincide on K018.

At last, note that K883 and K001 meet at nine identified points namely X(3), X(13), X(14), X(15), X(16), X(30), X(399) and the circular points at infinity.