Show that there are countably many circles with three rational points.
My interpretation of this question is to prove that there are infinitely countable circles that contain at least three rational points (points x/y where x,y are integers). So far I think one must show that the set of rationals Q has a bijection with the naturals, then a rational point ( QxQ) has a bijection with the naturals, and finally that three rational points (QxQ)^3 has a bijection with the naturals. The bijections will prove that such sets are countable. Note that points cannot be collinear.