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X(3), X(15329)

infinite points of K024

vertices of the circumtangential triangle

The line L passing through P on the circumcircle (O) and its isogonal conjugate P* is the axis of a parabola inscribed in ABC. When P traverses (O), L envelopes the anticomplement of the Steiner deltoid.

K723 is the locus of the pole of L in (O).

K723 is an acnodal equilateral trefoil with an isolated singularity at O. It has three real inflexional asymptotes homothetic to the sidelines of the circumtangential triangle under the homothety with center O, ratio 2/3.

It is tritangent to (O) at the vertices T1, T2, T3 of the circumtangential triangle. It follows that K723 and K024 meet at six finite points lying on a conic (C) passing through T1, T2, T3 and also X(110), X(1624).