Assume we got a big circle with radius $R$. Another circle with radius $r$ is uniformly distributed inside the big ones. Now I want to calculate the probability that a randomly distributed chord of the big circle intersects the small circle.
I have an idea: Assigned $D$ as the distance between the center of the small circle to the chord and $D$ is also followed an uniform distribution of $(0,2R)$. However I am not sure about it.
Everyone please gives me some ideas about this problem. Thank you very much!
Edit : Sorry for the inconvenience. The small circle need to be inside the larger one. And for the chord, it was created by selecting two point randomly on the perimeter of the big circle.