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. `(sqrt3)/(sqrt2)`
B. `(sqrt3)/(2)`
C. `(1)/(2)`
D. `(1)/(4)`

Answer

D

Explanation

Plan Use the property, when two circles touch each other externally, then distance between the centre I s equal to sum of their radii, to get required radius.
Let the coordinate of the centre of T be (0, k).
Distance between their centre
`k+1 = sqrt(1+(k-1)^(2)) " " [thereforeC_(1)C_(2)=k+1]`
`rArr K+1=sqrt(1+k^(2)+1-2k)`

`rArr k+1=sqrt(k^(2)+2-2k)`
`rArrk^(2)+1+2k=k^(2)+2-2k`
`rArr k=(1)/(4)`
So, the radius of circle T is K, i. e.`(1)/(4)`.