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X(1), X(3), X(186), X(1147), X(2574), X(2575) excenters circular points at infinity J1, J2 Q1, Q2, Q3 : vertices of the CircumNormal triangle, see Table 25 isogonal conjugates of the Ixanticevian points, see Table 23 other points below 

The isogonal transform of the circular quintic Q159 is Q160. Q160 is a circular circumquartic with two imaginary asymptotes passing through X(186) and two real asymptotes parallel to those of the Jerabek hyperbola. These meet at X on the lines {X5, X578}, {X30, X110}, {X49, X140}, {X155, X1192}, {X156, X550}, etc, SEARCH = 2.54688454278036. Q160 is a member of the pencil of circular circumquartics generated by the two following decomposed curves :
The circle (CA) passing through A, X(3), X(186) is tangent at A to Q160. It meets the Abisectors of ABC at A1, A2 on Q160. The points B1, B2 and C1, C2 are defined similarly. Q160 meets the Jerabek hyperbola at A, B, C, O, X(2574), X(2575) and two other points on the line{578, 1199, 1204, etc}. *** Q160 and the Euler pencil, see Table 27 Every cubic (K) of the Euler pencil is a pK(X6, P) with P on the Euler line. It meets Q160 at 8 fixed points namely A, B, C, X(1), X(3) and the excenters. Hence, it must have 4 other common points with Q160. The following table gives a few remarkable examples. 


