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

Question

$\begin{array}{1 1}(A)\;\bigg(\frac{1}{2},\frac{1}{2}\bigg) \\(B)\;\bigg(\frac{1}{2},-\sqrt 2\bigg) \\(C)\;\bigg(\frac{3}{2},\frac{1}{2}\bigg) \\(D)\;\bigg(\frac{1}{2},\frac{3}{2}\bigg) \end{array}$