Question

Two points on the plane \(A\) and \(B\) are given. \(|AB| = 2\). \(C\) is a randomly picked point in the circle of the radius \(R\) with the center in the midpoint of \(AB\). What is the probability that the \(\triangle ABC\) has an obtuse angle?

Answer 1

The angle will be obtuse if the point lies inside the smaller circle. So the ratio of the areas should be the answer. Sounds right?

Answer 2

no wait