Lines with a given orthopole P

1) Let X, Y, Z be the points with Simson line through P (construction 39).
2) The lines XY, YZ, ZX have P as orthopole.
When there is only a point with Simson line through P (X in the figure on the right):
1') Let Q be the isogonal of the infinite point of the orthogonal to HP, H being the orthocenter.
2') The parallel from Q to the Simson line of X cuts HP at R.
3) The perpendicular bisector between Q and R has P as orthopole.