Confusing Conics & Circles! Wow!!

Geometry Level 4

Let \(C\) be any circle with centre \[(0,\sqrt{2})\]. At most how many rational points can lie on \(C\).

Details and Assumptions:

  • A rational point is a point both of whose coordinates are rational numbers.
  • This problem is not original.
  • Good Luck 😃😊😁

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