# Two lines and a point

Two parallel lines, \(m\) and \(n\), and a point \(P\), are given, where \(P\) does not lie between the lines. The distance from \(P\) to \(m\) is double the distance from \(P\) to \(n\). How many uses of a straightedge and compass does it take to draw a line through \(P\) perpendicular to \(m\) and \(n\)?

All terminology in this question is explained in the first note of my straightedge and compass set. More straightedge and compass constructions can be found there.