Length of direct common tangent is 24 cm for two circles whose radii are 16 cm and 6 cm. What is the distance between their centres ?

26 cm 

Using the length of the direct tangent, l = √\( {d }^{ 2} \) - \( {(r1\; - \; r2) }^{2 } \)

⇒ 24 = √(\( {d }^{ 2} \) - \( {(16\; - \; 6) }^{2 } \))

⇒ 576 = \( {d }^{ 2} \) - 100

⇒ \( {d }^{ 2} \) = 576 + 100

⇒ d = 26

Therefore, the distance between their centres is 26 cm.