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.

Since tangent to a circle is perpendicular to the radius through the point of contact,

\(\therefore \) \( ∠ \ OTA \ = \ 90° \)

In \( ∆ \ OTA \), we have

\(\Rightarrow OA^2 \ = \ OT^2 \ + \ AT^2 \ \)
\( \Rightarrow \ 5^2 \ = \ OT^2 \ + \ 4^2 \)
\( \Rightarrow \ OT^2 \ = \ 5^2 \ - \ 4^2 \ = \ 25 \ - \ 16 \ = \ 9 \)

\( OT \ = \ \sqrt{9} \ = \ 3 \)

\(\therefore \) Radius of the circle is 3 cm.