1. The problem statement, all variables and given/known data Given a randomly drawn circle on a sphere, calculate the probability that it will pass within a defined distance of a set point. To make it clear, imagine the example of the the Earth and Mt Everest. What is the probability that a randomly drawn circle will come within, say 3km of Everest? 2. Relevant equations Surface area of sphere: 4*pi*r^2 Circumference of a circle: 2*pi*r 3. The attempt at a solution Let the defined distance (3km in above example) be d. I think that you can approximate the probability for relatively small d (say 1/400th the circumference of a sphere) by calculating the ratio of (the surface area of a strip 2*d units high by the circumference of an averaged sized circle on a sphere) to that of (the entire sphere). I assume that an arbitrarily drawn circle will on average be 1/2 of the great circle circumference of our sphere, or pi*r so the surface area of the strip would be 2*d*pi*r. This would make the probability 2*d*pi*r/4*pi*r^2 or d/2*r for a ballpark figure? It seems very straightforward for a good estimate but I want to bounce it off you all. Thank you for taking a look.