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Two circles with radii a and b respectiv...

Two circles with radii `a` and `b` respectively touch each other externally . Let `c` be the radius of a circle that touches these two circles as well as a common tangent to the circles. Then

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Knowledge Check

  • Two circle with radii r_(1) and r_(2) respectively touch each other externally. Let r_(3) be the radius of a circle that touches these two circle as well as a common tangents to two circles then which of the following relation is true

    A
    `1/(sqrt(r_(3)))=1/(sqrt(r_(1)))+1/(sqrt(r_(2))`
    B
    `1/(sqrt(r_(3)))=|1/(r_(1))-1/(sqrtr_(2))|`
    C
    `sqrt(r_(3))-sqrt(r_(1))+sqrt(r_(2))`
    D
    `sqrt(r_(3))=|sqrt(r_(1))-sqrt(r_(2))|`

  • Two circles of radii 8 cm and 6 cm touch each other externally. The length of the direct common tangent is:

    A
    20
    B
    24
    C
    `13.86`
    D
    `10.12`

  • Two circles with unequal radii,centred at A and B respectively,touch each other externally at T.If BD is tangent to the first circle at D and TC is transverse common tangent meeting BD at C.Also,AT has the length 3 and BT has length 2. Then the length of CD is equal to

    A
    2
    B
    `5/2`
    C
    `3/2`
    D
    `1/2`

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