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

Let us consider a circle centered at point O.

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

Given that,

OA = 5 cm and AB = 4 cm

In ΔABO,

OB ⊥ AB (Radius ⊥ tangent at the point of contact)

Applying Pythagoras theorem in ΔABO, we obtain

AB² + BO² = OA²

4² + BO² = 5²

16 + BO² = 25

BO² = 9

BO = 3

Hence, the radius of the circle is 3 cm.