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 = 25-16
BO² = 9
BO = 3

Hence, the radius of the circle is 3 cm.