How to find the length of an arc knowing the coordinates of 2 points on a circle?

Question

Mathematics

In the process of developing a 2d game on unity, I ran into a problem - how to determine the shortest distance from the position of object1 to object2 (each of the positions lies on a circle), given that object1 moves along a circle.

In simple words, the question sounds like this: how to determine the length of the arc between points A and B, knowing the coordinates of these points on the circle and the radius of the circle? For convenience, we can assume that the center of the circle is at the point (0; 0), it does not matter

Answer 1

Angle between points (in radians) multiplied by the radius of the circle.