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

Prove it.

Without loss of generality, choose any point on the circumference of the circle as the starting poinrt for the chord (Q), Draw a chord equal to the length of the radius from this point in each direction - these join the circumference at points P & R. Any chord from Q that joins the circumference on the larger arc PQ of the circle is longer than the radius; any that joins the circumference on the smaller arc PQ is equal to or shorter than the radius. We know that we can draw exactly 6 consecutive arcs equal to the length of the radius around the circumference of the circle; the smaller arc, PQ, comprises 2 of them. Hence the probability of choosing a point on that arc is 1/3. Thw probability of choosing another point on the circumference, giving a chord longer than the radius, is thus 2/3

Posted by DrBob on 2003-10-10 03:31:11