$\mathrm{O}(0,0)$ and $\mathrm{A}(1,0)$ are centres of two unit circles $\mathrm{C}_1$ and $\mathrm{C}_2$ respectively. $\mathrm{C}_3$ is also a unit circle having its centre above $\mathrm{X}$-axis and passing through $\mathrm{O}$ and $\mathrm{A}$. The equation of the common tangent to $\mathrm{C}_1$ and $\mathrm{C}_3$ which does not intersect the circle $\mathrm{C}_2$ is

• Correct answer
  A

  $\sqrt{3} x-y+2=0$
• B

  $x+\sqrt{3} y+2=0$
• C

  $\sqrt{3} x-y-2=0$
• D

  $x+\sqrt{3} y-2=0$

Hence, the correct answer is option: 'A'.