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

Prove it.

(In reply to re: An elegant solution by Brian Smith)

There are probably even more than 3 ways of generating random chords. The most popular have already been mentioned: a random arc length (or central angle) uniformly distributed; a uniformly distributed choice of one point within the circle to serve as a center point of the chord; a line chosen in a uniform distribution of parallel lines intersecting the circle (along a radius or diameter). Another way would be a uniform distribution of angles measured from a point on the circumference. In fact a uniform angular distribution could be made about any point, from the center out to infinity, the latter case being the parallel line case. You could choose random points on two parallel lines on either side of the circle and have them intersect the circle in two resulting points, etc. They would result in different probabilities.

Posted by Charlie on 2003-10-13 15:01:42