geometry - Find point inside circle but outside of n- other circles

There is one green circle and 0 to n red circle(s). I'm trying to find a point inside the green circle, but outside all red circles.

Basically the point have to be in the green area on the given example.

My first attempt was, to loop until I have a point that is inside the green circle and the distance to each red circle is bigger than it's radius.

I think there might be a way better solution without try'n'erroring...

I have the radius und center position of each circle:

Circle | Radius |   X  |   Y
Green  |  12.0  |  9.5 |  6.5
Red C1 |   7.5  |  5.5 | 10.5
Red C2 |   7.5  | 12.0 |  8.5
Red C3 |   7.5  |  5.5 |  5.0