Problem. " Let (' and /) be two non-intersecting clines in CT. Let E be a third cline that is distinct from the first two clines ( E may, of may not, intersect either cline). Prove that there exists a fourth cline F.such that F is perpendicular to each of C. D, and E. " Find the weakest restriction you need to place on E so that the line F above is unique. A. This is a beautiful problem that really shows the effectiveness of the transformational approach to geometry. A key first step is to look at an old homework assignment and figure out how you can use a Mobius transformation to move the clines (' and D) into a very nice arrangement: concentric circles. The problem should be far easier to solve for this particular arrangement, and then you can apply the inverse of your original Mobius transformation to obtain the solution for the original configuration of dines