[Greg Woelki]

A Monte Carlo simulation written in python and running on my laptop isn't a great solution if 1 part in a million accuracy is required, but since I had essentially already written the program, I figured that I might as well give it a shot. For the average length of line segments in the interior of an r=1 circle, I got 0.9054124568 after 4e10 trials. I'm not certain whether or not this meets the accuracy requirement. I also made minor modifications so that I could simulate the chord problem, and I got 1.2732310914 after 7e09 trials. This problem requires far fewer trials to get an accurate result and I believe this solution meets the accuracy spec. I can post my code if anyone is interested.