Two circles of radii 8 cm and 3 cm, respectively, are 13 cm apart. AB is a direct common tangent touch to both the circles at A and B respectively then the length of AB is
Answer & explanation
Correct answer: option 2
Formula Used
Length of the direct common tangent =
√ (\( {d }^{2 } \) - \( {(r1 - r2) }^{ 2} \))
Where, d = distance between the circles
r1 and r2 are the radii of the two circles respectively
Calculation
Here, we have to find the length of the direct common tangent
Now, d = 13 cm, r1 = 8 cm, r2 = 3 cm
Length of the direct common tangent =
√ (\( {d }^{2 } \) - \( {(r1 - r2) }^{ 2} \))
= √ (\( {13 }^{2 } \) - \( {(8 - 3) }^{ 2} \)) = \(\sqrt {144 }\) = 12 cm
Therefore, length of the direct common tangent is 12 cm.