Getting a random point in a circle that has a defined exclusion zone

From what I understand the math would be broken down into the following:

  1. Get the circle intersection points and use that to calculate the allowed angle range between two vectors.

a) Get intersection points:

b) Get the angle between two vectors U and V: Angle between Two Vectors (examples, solutions, videos, worksheets, games, activities)

  1. Get a random angle, draw a vector until it intersects with the outer circle. Calculate the length and subtract it from inner circles radius.