VC Dimension of Origin-Centered Circle

Question

Is the VC dimension of an origin-centered circle 1 or 2?

It seems to me that the VC dimension of an origin centered circle should be 1, because for two points with distances from the origin r1 <= r2, r2 will never be able to be labeled 1 without r1 also being labeled 1, so the r1 = 0, r2 = 1 labeling could never be possible.

However, this and this both say that an origin-centered circle has VC dimension of 2.