A couple of days ago i read somewhere about the following problem, but can not find it again.
Uniformly at random, $n$ points are generated independently within the unit circle. Then, the task is to find the uniquely defined smallest circle containing all $n$ points. The question was about the probability that the so generated circle is completely contained within the unit circle. The somewhat counter intuitive answer was, by guessing it, $1-\frac{n-1}{2n-1}$, namely a probability of $2/3$.
Since finding the smallest circle is already in itself a somewhat cumbersome endeavour, i took on only the case $n=2$.
Here is a simulation result:
Running the simulation longer, it confirms the result mentioned above, for $n=2$.
My question is: Is there any literature on this type of problem? It can't be a novel problem. And I can't find anything as I don't have the right keywords to search with.
EDIT: After typing it showed me the OP here.
