Problem. Hyperbolic geometry. Call two hyperbolic lines asymptotically parallel if they have no intersection points in D but share a common ideal point. Call two hyperbolic lines hyperparallel if they have no intersection points in D and have no common ideal points. (a) Prove that if L and M are hyperparallel hyperbolic lines, then there is a unique hyperbolic line perpendicular to both L and M. (b) Prove that if L and M are asymptotically parallel hyperbolic lines, then there is no hyperbolic line N perpendicular to both L and M. [Hint: suppose such a line N exists. Apply a transformation in '/{ to simplify the picture, and find a contradiction.]