When r is infinitely close to 2r, the intersection probability should be infinitely close to 1, right?

If yes, then the answer on the second floor is incorrect.

My thoughts

In a circle with the origin as the center and R-r as the radius, any point can be expressed as the distance from the origin and the angle with the X axis. Take any point in R-r, set the distance from the point to the origin as x, and then find the area of the common part of the R-r circle with this point as the center, 2r as the radius. This area is a function of X. In the integration of X, the trajectory of X is a straight line passing through the origin, and the interval is -(R-r) to R-r, and this result is the probability found in the problem.

PS: The angle between any point and the X axis has nothing to do with the result.

I've probably done it, and I find it very troublesome. Maybe I was wrong.

Expert advice! ! ! !