**Solution:**

AB is a tangent drawn on this circle from point A.

∴ OB ⊥ AB

OA = 5cm and AB = 4 cm (Given)

In ΔABO,

By Pythagoras theorem in ΔABO,

OA^{2} =^{ }AB^{2 }+ BO^{2}

⇒ 5^{2 }= 4^{2 }+ BO^{2}

⇒ BO^{2} = 25 - 16

⇒ BO^{2} = 9

⇒ BO = 3

**∴ The radius of the circle is 3 cm.**