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3 circles of radii a,b,c (a<b<c) touch e...

3 circles of radii `a,b,c (a

A

`(1)(sqrt(a))=(1)/(sqrt(b))+(1)/(sqrt(c ))`

B

a, b, c are in A.P.

C

`sqrt(a), sqrt(b), sqrt(c )` are in A. P.

D

`(1)/(sqrt(b))=(1)/(sqrt(a))+(1)/(sqrt(c ))`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The locus of a point, which moves such that the lengths of the tangents from it two concentric circles of radii a and b are inversely proportional to their radii is a circle with radius

    A
    `a +b`
    B
    `sqrt (| a ^(2) -b ^(2) |)`
    C
    `sqrt (a ^(2) +b ^(2))`
    D
    none of these

  • Two concentric circles of radii a and b(a gt b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

    A
    `2sqrt(a^(2)+b^(2))`
    B
    `2sqrt(b^(2)-a^(2))`
    C
    `2sqrt(a^(2)-b^(2))`
    D
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  • 3 circle of radii 1, 2 and 3 and centres at A, B and C respectively, touch each other. Another circle whose centre is P touches all these 3 circles externally. and has radius r. Also anglePAB = theta & anglePAC = alpha .

    A
    `cos theta = (3-r)/(3(1-r))`
    B
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    C
    `r = (6)/(23)`
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