Set of disjoint circles of radius $1$ on the plane countable?

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Give is a set of disjoint circles of radius $1$ on the plane. Is this set countable ? I don't think so. In my opinion, the set with only one circle with radius 1in the plane is also uncountable, isn't it?

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The hint:

Inside any circle we can take a rational point. It's one to one and ...