What is the probability that a randomly drawn chord will be longer than the radius of the circle?

Prove it.

I'll post the program (second method using one fixed point and one random point) as soon as I get it put on this computer. The results were surprising! The average of 4 trials at 10,000 iterations of random chords produced not 66.66% as expected, but...

...75.00125

Which would seem to show that the method used to arrive at 66% (namely the choosing of a second random point on a circle in relation to a fixed point) is faulty somehow (I take it that it's because the point spreads are different from a fixed point). But I'm altogether happy about that! If that is the case, and 75% can be reached by both methods, then this problem isn't a paradox and it does have a real solution regardless of the method taken. I'm pretty sure I was wrong when I wrote my first program and after I find the error, I'll go ahead and post both programs.

Now--I'm only wondering why your program gave you 66%?