<s>[INST] This is the algorithm for which the functions are given below:

"1. Given a circle of radius r centered at the origin with 2D coordinates (x,y).
2. An object is to move along the circumference of this circle from initial coordinates (x0, y0) to final coordinates (xf, yf).
3. To reach destination, the object must follow these constraints:
- The object must only move along the circumference of the circle.
- The object must not move away from the point which is at angle theta along the circle from point (x0, y0).
- The object moves only in a counterclockwise direction.
- The angle theta can vary (decrease or increase) up to a certain range between the minimum and maximum angle (theta_min, theta_max).
4. A safe distance D is defined as the distance between two objects. 
5. When the object reaches destination, it must not have exceeded the maximum allowed safe distance D from point (x0, y0)."

To satisfy the constraint of not exceeding maximum allowed safe distance, I have to limit angle theta. The problem is how to limit it?[/INST]