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There are two circles C(1) and C2 whose ...

There are two circles `C_(1)` and `C_2` whose radii are `r_(1), r_(2)`, respectively. If distance between their centre is `3r_(1) - r_(2)` and length of direct common tangent is twice of the length of transverse common tangent. Then `r_(1): r_(2)` is:

A

`5:4`

B

`6:5`

C

`7:6`

D

`8:7`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • R and r are the radius of two circles (R gt r) . If the distance between the centre of the two circles be d , then length of common tangent of two circles is

    A
    `sqrt( d^(2) - (R- r) ^2)`
    B
    `sqrt( ( R - r)^(2) - d^(2) )`
    C
    `sqrt( R^(2) - d^(2) )`
    D
    `sqrt( r^(2) - d^(2) )`

  • IF two circles of radii r_1 and r_2 (r_2gtr_1) touch internally , then the distance between their centres will be

    A
    `r_1-r_2`
    B
    `r_2-r_1`
    C
    `r_1^2-r_2^2`
    D
    `r_2^2-r_1^2`

  • R and r are the radii of two circles (R > r). If the distance between the centres of the two circles be d, then length of common tangent of two circles is

    A
    `sqrt(r^2 - d^2)`
    B
    `sqrt(d^2-(R-r^2))`
    C
    `sqrt((R - r)^2-d^2)`
    D
    `sqrt(R^2-d^2)`

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