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X(74), X(113), X(146), X(265), X(399), X(1986), X(2935) isogonal conjugate of X(2071) reflections A', B', C', E of A, B, C, X(1986) in X(113) 

Let P be a variable point. The perpendiculars dropped from X(110) onto the lines AP, BP, CP meet BC, CA, AB at Pa, Pb, Pc. These three points are collinear if and only if P lies on the rectangular circumhyperbola (H) passing through X(110). They form a triangle perspective to ABC if and only if P lies on the cubic K255. The perspector lies on K256. K255 is a central pK with center X(113), the Jerabek antipode and the center of (H). K255 has three real asymptotes which are the perpendiculars to the cevian lines of X(110) passing through the relative midpoints of ABC. This generalizes for any point Q instead of X(110) on the circumcircle and we always obtain a central cubic with center the midpoint of HQ, a point on the nine point circle. Another description of K255 is the following. The parallel at P to the line AX(74) meets BC at Pa. Define Pb, Pc similarly. ABC and PaPbPc are perspective if and only if P lies on K255. The locus of the perspector is K279. See also Central cubics for a generalization. The isogonal transform of K255 is K528, an axial pK. More generally, the isogonal transform of any central pK with center on the nine points circle is an axial pK. 
