Triangle inscribed in the circumcircle and triply perspective and orthologic to ABC

1) Let X', Y', Z' be the three points with Simson line through the third Brocard point J (construction c39).
2) Let X, Y, Z be the antipodals of X', y', Z' in the circumcircle. XYZ is the requested triangle.
The figures show the triple perspective and the triple orthology.