Let $S$ be the set of points on the $X$-axis lying at a distance of $d$ units from $(3, 4)$. Which of the following is true?
- A$S$ is an empty set if $d < 4$
- B$S$ contains infinitely many points if $d < 4$
- C$S$ contains at least two points if $d = 4$
- D$S$ contains exactly three points for any $d > 4$
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