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X(1), X(4), X(265), X(847), X(1113), X(1114) excenters infinite points of K003 Ixanticevian points, see Table 23 other points below 

Denote by M' and M" the isogonal conjugates of M with respect to the anticevian and pedal triangles of M respectively. These three points are collinear if and only if M lies on Q159. The isogonal transform of Q159 is Q160. Q159 is a circular circumquintic with two imaginary asymptotes passing through H and three real asymptotes parallel at X(381) to those of K003. Q159 is a member of the pencil of circular circumquintics generated by the two following decomposed curves : Q159 meets the Euler line at X(4), X(1113), X(1114) and two other points E1, E2 on the circle with center X(3627) – on the Euler line – and radius √5/2 OH. The isogonal conjugates of these points lie on the line {578, 1199, 1204, etc}, obviously on the Jerabek hyperbola and on Q160. The isogonal transform of the tangent at A to the circle (CA) passing through A, X(3), X(186) meets BC at A' on Q159. B' and C' are defined likewise. 
