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X(1), X(104), X(517), X(1339), X(5088), X(41391), X(45766), X(46357), X(46358), X(52478), X(52479), X(52480), X(52481), X(52482), X(61427), X(61428), X(61429), X(61430), X(61431), X(68239), X(68240), X(68242), X(68243), X(68244), X(68245), X(68246), X(68247), X(68248), X(68249), X(68250), X(68251), X(68252)

Geometric properties :

K1397 = cK(#X1, X905) = nK(X6, X905, X1) is an isogonal strophoid. See CL003.

It is the locus of foci of inconics centered on the line (L) through the incenter X(1) and the circumcenter X(3).

It is also the pedal curve with respecto to X(1) of the parabola (P) with focus X(1768), directrix (L), which is the pivotal conic of the cubic. (P) is actually the Kiepert parabola of the excentral triangle.

Its real point at infinity is X(517) and the isogonal conjugate of X(517) is the singular focus F = X(104).

The nodal tangents at X(1) are parallel to the asymptotes of the rectangular circum-hyperbola with center X(124), perspector X(6589), passing through X(4), X(58), X(102), X(573), X(959), X(994), etc.

K1397 is also spK(X517, X1) in CL055. K1397 is the excentral version of K591.