There should be a worked example that deals with something like this in your textbook somewhere...
That said, two ways:
1, Do you know what does "a line does not intersect a circle" means in terms of equations? Hint, it has something to do with roots of a quadratic (what quadratic? Go have a re-read at your textbook).
2, (Probably not the standard way, but faster) If you happen to know the formula for the distance between a point and a line, the maximum our r can take (well, without actually attaining it) is precisely this distance between the origin and the line. Why? Draw a nice picture and see if you notice something.