Triangles with given circumcircle c and with a given point N in c as ninecenter

1) Let O be the center of c, and draw the circle d with center d and going through the midpoint of ON.
2) Let D be a point in the arc of d inside c.
3) The perpendicular from D to OD cuts c in B, C.
4) Let X be the antipodal of D in d.
5) Let A be a point such that ODXA is a paralellogram; then ABC is the requested triangle.