JEE Math Practice Question

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 :

1. A.$${1 \over 2}$$
2. B.$${1 \over 4}$$
3. C.$${{\sqrt 3 } \over {\sqrt 2 }}$$
4. D.$${{\sqrt 3 } \over 2}$$