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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-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 `sqrt3y^(2)-4xy+sqrt3x^(2)=0`
`sqrt3y^(2)-3xy-xy+sqrt3x^(2)=0`
`rArr(sqrt3y-x)(y-sqrtx)=0rArry=x/(sqrt3),y=sqrt3x`
`angleAPO=75^(@)`
Length of chord of contact AB
`=2.3sin75^(@)=6(sin45^(@)cos30^(@)+sin30^(@)cos45^(@))`
`=6(1/(sqrt2).(sqrt3)/2+1/2.1/(sqrt2))=(6(sqrt3+1))/(2sqrt2)=(3(sqrt3+1))/(sqrt2)`
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