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Three circles with centres C1, C2 and C3...

Three circles with centres `C_1, C_2 and C_3` and radii `r_1, r_2 and r_3` where `r_1

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There circle C_1,C_2 and C_3 with radii r_1 , r_2 and r_3 (where r_1 तीन वृत्त C_1,C_2 तथा C_3 जिनको त्रिज्याएँ r_1 , r_2 तथा r_3 है, (जहाँ r_1

Three circle C_(1),C_(2)andC_(3) with radii r_(1),r_(2) and r_(3) (where r_(1)ltr_(2)ltr_(3) ) are placed as shown in the given figure. What is the value of r_(2) ?

Knowledge Check

  • Two circles with centres at C_(1) , C_(2) and having radii r_(1) , r_(2) will intersect each in two real distinct points if , and only if :

    A
    `l (C_(1) C_(2)) lt r_(1) + r_(2)`
    B
    `l (C_(1) C_(2)) - |r_(1) - r_(2)|`
    C
    `|r_(1) - r_(2)| lt l (C_(1) C_(2) ) lt r_(1) + r_(2)`
    D
    none of these

  • There are two circles C_1 and C_2 of radii r_1 and r_2 , respectively. They are mutually tangent to each other and to a line as well. There is one more circle of radius r_3 which is tangent to this line and first two circles C_1 and C_2 . What is the relation between the three radii r_1, r_2 and r_3 ?

    A
    `1/sqrtr_1+1/sqrtr_2=1/sqrtr_3`
    B
    `sqrtr_1/sqrtr_2+sqrtr_2/sqrtr_1=1/sqrtr_3`
    C
    `1/sqrtr_3+1/sqrtr_1+1/sqrtr_2`
    D
    none of these

  • 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`

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    Three circles C_(1),C_(2),C_(3) with radii r_(1),r_(2),r_(3)(r_(1)ltr_(2)ltr_(3)) respectively are given as r_(1)=2 , and r_(3)=8 they are placed such that C_(2) lines to the right of C_(1) and touches it externally C_(3) lies ot the right of C_(2) and touches it externally. There exist two stratight lines each of whic is a direct common tangent simultaneously to all the three circles then r_(2) is equal to

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