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

( A ) $\frac{1}{4}$
( B ) $\frac{1}{2}$
( C ) $\frac{\sqrt{3}}{\sqrt{2}}$
( D ) $\frac{\sqrt{3}}{2}$