Question

The length of tangent from a point A at a distance of 5 cm from the center of the circle is 4 cm. What is the radius of the circle?

Answer 1

Given:

OA (say) = 5 cm

AB = 4 cm

Let AC be the tangent which meets the circle at the point B and O be the center of circle.

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆AOB is right-angled at ∠OBA.

Therefore, by Pythagoras Theorem,

AB² + OB² =AO²

⇒ OB² = AO² – AB²

⇒ OB = √(AO² – AB²)

⇒ OB= √(5² – 4²) 

⇒ OB= √(25 – 16) 

⇒ OB = √9 

⇒ OB = 3 cm

Hence, Radius = 3 cm