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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 :

$(a)\;\large\frac{1}{2} \qquad(b)\;\large\frac{1}{4}\qquad(c)\;\large\frac{\sqrt{3}}{\sqrt{2}}\qquad(d)\;\large\frac{\sqrt{3}}{2}$

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