Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y) passing through origin and touching the circle C externally, then the radius of T is equal to

Question

$\begin{array}{1 1}(A)\;\large\frac{\sqrt 3}{\sqrt 2}\\(B)\;\large\frac{\sqrt 3}{2}\\(C)\;\large\frac{1}{2}\\(D)\;\large\frac{1}{4}\end{array}$