X(2), X(6), X(17), X(18), X(61), X(62)
imaginary foci of the Lemoine ellipse
K249 is an isogonal focal nK passing through the Napoleon points X(17), X(18). Its root is R = X(14610), the intersection of the lines X110-X930, X351-X523, etc.
The singular focus F is X(14658), on the circumcircle.
It is a member of the class CL061.
K249 is the locus of foci of inscribed conics with center on the line passing through the midpoints X(597), X(8259), X(8260) of GK, X(17)X(61), X(18)X(62) respectively, or equivalently tangent to the trilinear polar of R.