A level Further Maths question help

Hey, got a question for anyone who knows some complex number loci stuff, here’s the question and mark scheme answer:
.the lower bound is okay but finding the maximum value for r I don’t understand how to do.
If anyone wanted to take a look and see if they understand then I would appreciate it

Remember that the line is actually a half-line. The circle can't pass outside the origin of the half-line. If it did, there would only be one intersection. (Also remember that the origin of the half-line isn't part of the half-line).

So the radius can’t pass the half line? I don’t completely understand but if it did then there would be 2 intersections and if it just touched there would be one 1

If you draw a sketch it should be clear that, as the radius increases, there will come a point where the circle touches (2, 0) and one other point on the half-line. Make the radius any bigger and the circle will miss (2, 0), leaving just one intersection with the half-line.