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No. of Direct and Transverse Common Tang...

No. of Direct and Transverse Common Tangents When `|C_1C_2|lt|r_1-r_2|`

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No of Direct and Transverse Common Tangents When |C_(1)C_(2)|=|r_(1)-r_(2)|

No of Direct and Transverse Common Tangents When |C_(1)C_(2)|=r_(1)+r_(2)

Knowledge Check

  • 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`

  • Statement-1:If the line y=x+c intersects the circle x^2+y^2=r^2 in two real distinct points then -rsqrt2 lt c lt r sqrt2 Statement -2: If two circles intersects at two distinct points then C_1C_2 lt r_1+r_2

    A
    Statement-1 is True , Statement -2 is true , Statement -2 is a correct explanation for Statement-1
    B
    Statement-1 is True , Statement -2 is true , Statement -2 is NOT a correct explanation for Statement-1
    C
    Statement -1 is True , Statement -2 is False
    D
    Statement-1 is False , Statement-2 is True

  • Instruction : Answer the questions given below on the basis following figure. MN is a transverse common tangent. A and B are centres of the circles whose radii are respectively r_1 and r_2 . Length of AB is d. Length of MN is

    A
    `sqrt( d^(2) - ( r_1 + r_2)^2)`
    B
    `sqrt( d^(2) - (r_1 - r_2)^2)`
    C
    `sqrt( d^(2) + ( r_1 + r_2)^2)`
    D
    `sqrt( d^2 + (r_1 + r_2)^2)`

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    Common Tangents of Two Circles - Direct and Transverse Common Tangent

    The line L_(1)-=3x-4y+1=0 touches the circles C_(1) and C_(2) . Centers of C_(1) and C_(2) are A_(1)(1, 2) and A_(2)(3, 1) respectively Then, the length (in units) of the transverse common tangent of C_(1) and C_(2) is equal to

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