gaokao 2025 Q7

gaokao · China · national-I_eol 5 marks Circles Circle-Line Intersection and Point Conditions
If the circle $x^2 + (y+2)^2 = r^2$ $(r > 0)$ has exactly 2 points at distance 1 from the line $y = \sqrt{3}x + 2$, then the range of $r$ is
A. $(0,1)$
B. $(1,3)$
C. $(3, +\infty)$
D. $(0, +\infty)$
If the circle $x^2 + (y+2)^2 = r^2$ $(r > 0)$ has exactly 2 points at distance 1 from the line $y = \sqrt{3}x + 2$, then the range of $r$ is\\
A. $(0,1)$\\
B. $(1,3)$\\
C. $(3, +\infty)$\\
D. $(0, +\infty)$