Point P lies within acute angle XOY.
How can we find a point A on OX and a point B on OY such that P is the midpoint of a segment AB drawn between them?
Seeing this puzzle reminded me of a different one: Minimal area
. It has the same setup but a different goal: to minimize the enclosed area. As it turns out in that puzzle the solution involved the line asked for in this puzzle.
A sequel was posted: Constructing Minimal Area
. Of which this puzzle is another version, so its solution will work here as well.