Given a right angle at $O$ (Origin), a point $B$ on one arm, and a point $A$, construct with ruler and compass a circle with center $O$, meeting the arms of the right angle at $C,\, D,$ such that $AD$ is parallel to $BC$. (par 9)
Its not so hard to construct a parallel line passing through $A$ where one side touch's a point on the radius of circle but both is alot harder. we will want the angle to be $45^°$ but I am not sure how to construct it in only nine steps where neither of the parallel lines count as a step.
This is exercie 13.18 in geometry from Hartshorne.