So, then it is more random. I looked up Jaynes' proposal and it based on the fact that the size of the circle is unknown, here the OP has given us a size. Is throwing straws at a circle a better method than selecting a number at random between 0 and πrI agree with CaptainEd. Jaynes' solution to the Bertrand paradox shows that random radius (method 2) is the only robust theoretical means of choosing random chord.

^{2}, letting that number represent an area and drawing a chord to section off that area?