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

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `sqrt((3)/(2))`
D. `(sqrt(3))/(2)`

Answer

B

Explanation

Clearly, circles C and T touch each other externally.

`:. C_(1)T`= Sum of the radii
`rArr sqrt((0-1)^(2)+(y-1)^(2))=1+|y| [[:' "Radius of C and T are"],["1 and |y|respectively"]]`
`rArr y^(2)+2y+2=(1+|y|)^(2)`
`rArr y^(2)-2y+2=1+2|y|+y^(2)`
`rArr 2|y|+2y=1 rArr 4y=1 rArr y = (1)/(4)`