On one of the given lines take segment AB and construct its midpoint, M (cf. Problem 8.74). Let A1 and M1 be the intersection points of lines PA and PM with the second of the given lines, Q the intersection point of lines BM1 and MA1. It is easy to verify
that line PQ is parallel to the given lines.
In the case when point P does not lie on line AB, we can make use of the solution of Problem 3.36. If point P lies on line AB, then we can first drop perpendiculars l1 and l2 from some other points...