The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Let P be the point of contact of tangent to the circle with center O.

We know that,

Tangent at any point of a circle is perpendicular to the radius through the point of contact.

In right angle triangle OPA,

By pythagoras theorem,

⇒ OA² = OP² + AP²

⇒ 5² = OP² + 4²

⇒ OP² = 25 - 16

⇒ OP² = 9

⇒ OP = $\sqrt{9}$ = 3 cm.

Hence, radius of circle = 3 cm.