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

12 cm

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.