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X(51), X(511)

inverses in (C) of the points of Q004

(C) is the circle centered at G passing through X(51). (C) is tangent at X(51) to the trilinear polar of X(1989). The inversive image of Q004 in (C) is the circular cubic Q005 (denoted by (k) in Special Isocubics ยง6.7).

The singular focus is G and lies on the real asymptote which is the line GX(51), parallel at G to the Brocard line.

The inverses X(13)', X(14)', X(476)' lie on a parallel to the Euler line. The inverses U', V', W' of U, V, W lie on the circle with diameter GX(51).

Q005 is an isogonal pK with respect to this triangle U'V'W'. Its pivot is X(511), point at infinity of the lines OK and GX(51).