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If a circle of radius 3 units is touchin...

If a circle of radius `3` units is touching the lines `sqrt3y^2-4xy+ sqrt3x^2=0` in the first quadrant then the length of chord of contact to this circle, is:

A

`(sqrt3 +1)/(2)`

B

`(sqrt3+1)/(sqrt2)`

C

`3((sqrt3+1)/(sqrt2))`

D

`(3(sqrt3+1))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C

Given equation of lines `sqrt3 y^2 - 4xy +sqrt3 x^2 = 0`
`sqrt3 y^2 - 3xy - xy + sqrt3 x^2 = 0`
`rArr (sqrt3 y- x)(y-sqrt3 x) = 0 rArr y = (x)/(sqrt3) , y = sqrt3x`
`angle APO = 75^@`
Length of chord of contact AB
` = 2.3 sin 75^@ = 6(sin 45^@ cos 30^@ + sin 30^@ cos 45^@)`
`6((1)/(sqrt2) .(sqrt3)/(2) + 1/2 . (1)/(sqrt2)) = (6(sqrt3+1))/(2sqrt2) = (3(sqrt3 + 1))/(sqrt2)`
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