The first is the most straightforward. We know the distance between a point xy and 10 is determined by the Euclidean norm ie. Given a unit circle how may one measure the distance between the point 10 and a point on the circle subtended by the angle th call this point x y.
Given two points x 1 y 1 and x 2 y 2 recall that their horizontal distance from one another is D x x 2 x 1 and their vertical distance from one another is D y y 2 y 1.
OC 2 OA 2 - AC 2. A line through three-dimensional space between points of interest on a spherical Earth is the chord of the great circle between the points. To find the distance between their boundaries we subtract the radius of each circle from the distance between their centers. The central angle between the two points can be determined from the chord length.