Nope, I just used intuition, but it could be done with trig and a graph fairly easily. We are searching for the optimal angle a that will yield the shortest distance of line e and arc g. The tough part is the distance of line e. You would have to build an equation to find the distance of line d (trig), then an equation to determine e. Angles c and b = 90 degrees. Arg g can be determined with an equation to calculate angle f.

I haven't done all of this since I believe the best angle would be 90 degrees, but it could be proven.