Geolocations - How to check if 2 circles are overlapping

Question

Let's say we have 2 locations (latitude,longitude) and each location has a radius (it may be different from each other), making a circle. How to check if these 2 circles are overlapping?

Answer 1

Check if the distance between the centers is smaller than the sum of the radii.

Say for circles A and B with radius A_r and B_r respectively, and coordinates (A_x, A_y) and (B_x, B_y) respectively, the distance between the circles is

    D = sqrt( (A_x - B_x)² + (A_y - B_y)² )

They overlap when

    D < A_r + B_r

There's a catch, however: the centers of the circles are placed on a sphere. The shortest distance between them is a straight line, beneath the sphere's surface. The distance between them following the surface will be larger. For instance, the distance between the North and South pole is 2 Earth radii, but the path on the surface will be 2π Earth radii. Also, these circles don't overlap. So, the above equations only hold when the distances are relatively small.