Algorithm to cover maximal number of points with one circle of given radius

Question

Let\'s imagine we have a plane with some points on it. We also have a circle of given radius.

I need an algorithm that determines such position of the circle that it

Answer 1

If you want something simple, take random position (x,y), calculate number of points inside circle and compare with previous position. Take the maximum. Repeat the operation any times you want.

Why the hell downvote? Ever heard about Monte Carlo methods? Actually for a huge amount of points, deterministic algorithm may not finish in reasonable time.