LHIRT's POD #2

The problem derives itself from an old puzzle book that solves this problem in a very clever way. I am looking for the real solution, which isn't more difficult than the original method to solve it.

Take a pair of concentric circles, that share a center O. Take a point on the inner circle, and extend its tangent to its intersection with the outer circle at points P and Q. Given only the length of this chord PQ of the outer circle, calculate the area between the two concentric circles.

I will give both solutions in the morning, but I am looking for the one that does not assume that a formula exists in the first place.