The best algorithm to generate a point in a circle is to generate a point in a square with the same width as the circle diameter and then rerun the algorithm until this random point is inside the circle. This algorithm might need to run a couple of times before finding a suitable point but will be faster than a more algorithmic solutions.

Pseudo code:

- Randomize a point in the square
- If this point is outside the circle then jump to 1
- Done