The centre of the circle passing through $(0,0)$ and $(1,0)$ and touching the circle $x^2+y^2=9$ is

• A

  $\left(\frac{1}{2}, \frac{1}{2}\right)$
• Correct answer
  B

  $\left(\frac{1}{2},-\sqrt{2}\right)$
• C

  $\left(\frac{3}{2}, \frac{1}{2}\right)$
• D

  $\left(\frac{1}{2}, \frac{3}{2}\right)$

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