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Here's an attempt. You'll have to imagine a couple of things since I don't have the right equipment on this computer: the parallel lines were "constructed" and the curve shown is a compass mark of length AB with center at A.
Construction Example 1 - Construct the perpendicular bisector of the line connecting the two points on the cressent.
Construction Example 2 - Construct the pendicular to segment OB through O, intersecting arc AB at R. Then bisect angle AOR to locate P on arc AB.
Construction Example 3 - Construct the perpendicular bisector of segment XY, this line will intersect line l in the desired point O.
Construction Example 4 - Construct the perpendicular to segment AB at A, then bisect it. At point B, construct an equilateral triangle having one side on segment AB. Extend the lines to locate point C in triangle ABC.
Still thinking about Construction Example 5