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Let C be the circle with centre at (1,1...

Let C be the circle with centre at (1,1) and radius =1 . If T is the circle centered at (0,y) passing through the origin and touching the circle C externally. Then the radius of T is equal to

A

`(sqrt3)/(sqrt2)`

B

`(sqrt3)/(2)`

C

`(1)/(2)`

D

`(1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
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)`.
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