Question

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.

Answer 1

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,
OA² = AB² + BO²
⇒ 5² = 4² + BO²
⇒ BO² = 25 - 16
⇒ BO² = 9
⇒ BO = 3
∴ The radius of the circle is 3 cm.