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A circle of radius 2 has its centre at (...

A circle of radius 2 has its centre at (2, 0) and another circle of radius 1 has its centre at (5, 0). A line is tangent to the two circles at point in the first quadrant. The y-intercept of the tangent line is

A

A. `sqrt(2)`

B

B. `2sqrt(2)`

C

C. `3sqrt(2)`

D

D. `4sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(1)/(2) =(a-5)/(a-2) rArr a =8`
Thus, equation of line is `y = m(x-8)`
Now, this line touches the circle.

`:. |(6m)/(sqrt(1+m^(2)))| =2`
`rArr 9m^(2) = 1+m^(2)`
`:. m =- (1)/(sqrt(8))`
`rArr` y-intercept `= sqrt(8) =2sqrt(2)`.
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