Points whose reflections on the altitudes form a triangle perspective with ABC

1) The parallels from A, B, C to the orthic axis o cut the sides at A', B', C'.
2) Let X, Y, Z be the midpoints between A and A', B and B', C and C'.
3) Draw a line r through the orthocenter H.
4) The perpendiculars to r from X, Y, Z cut the sides at X', y', Z'.
5) The lines AX', BY', CZ' intersect at Q.
6) The projection of Q on r is the requested point R.
The figure on the right shows the property.