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X(1), X(399), X(517), X(3465), X(5526), X(5527), X(6326), X(11697), X(13541), X(13866), X(47623), X(56741), X(64761), X(68402), X(71537), X(71538), X(71539), X(71540), X(71541), X(71542), X(71543), X(71544), X(71545), X(71546)

vertices of the excentral triangle

Geometric properties :

K1448 is the excentral-polar-circle-inverse of the Feuerbach hyperbola.

It is a strophoid with singular focus X(6326) = excentral-polar-circle-inverse of X(80), and node X(1) with nodal tangents parallel to the asymptotes of the Feuerbach hyperbola.

Peter Moses notes that K1448 is K025 of the excentral triangle IaIbIc.

K1448 is the pedal curve with respect to X(1) of the parabola with directrix the line X{1,3} and focus X(5531) which is the excentral-polar-circle-inverse of the Feuerbach point X(11).

A construction of K1448

A variable line (L) passing through the singular focus X(6326) meets the line through X(1), X(3) at M.

The circle (C) with center M, passing through X(1), meets (L) at two points P, Q on K1448.

Let Pa, Pb, Pc and Qa, Qb, Qc be the reflections of P and Q in the internal bisectors of ABC.

These two triangles PaPbPc and QaQbQc are perspective at P', Q' to IaIbIc.

P' and Q' are two other points of K1448 collinear with X(6326).

Obviously, the circle with diameter P'Q' passes through X(1) and its center M' lies on the line through X(1), X(3).