Strike a chord
Discrete Mathematics
Level
4
Consider concentric circles with respective radii \(\pi\) and \(2\pi\). Choose two points on the larger circle independently and uniformly at random, and then join them to form a chord. If \(P\) is the probability that this chord intersects the smaller circle at at least one point, then find \(\lfloor 1000P \rfloor\).
\(\)
Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.
by
Brian Charlesworth