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There circle C1,C2 and C3 with radii r1,...

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

A

`sqrt((r_1r_3))`

B

`(r_1+r_3)//2`

C

`(2r_1r_2)//(r_1+r_2)`

D

`sqrt((r_1+r_3))`

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Knowledge Check

  • 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

    A
    `r_(2)=4`
    B
    `r_(2)=5`
    C
    `r_(2)=10`
    D
    `r_(2)=16`

  • If A=[[1, 2, -1], [3, -2, 5]] , then first R_1 harr R_2 and then C_1 to C_1+2C_3 on A gives

    A
    `[[-1, 2, -1], [13, -2, 5]]`
    B
    `[[3, -2, 5], [1, 2, -1]]`
    C
    `[[-1, 2, -1], [13, -2, 5]]`
    D
    `[[13, -2, 5], [-1, 2, -1]]`

  • 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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