The radius of two circles are 5cm and 3cm, the distance between their centres is 24 cm. Then the length of the transverse common tangent is

Transverse common tangent

$=\sqrt{d^{2}-\left(r_{1}+r_{2}\right)^{2}}=\sqrt{(24)^{2}-(5+3)^{2}}$

$=\sqrt{576-64}=\sqrt{512}=16 \sqrt{2} \mathrm{~cm} .$