The length of a tangent from point A at a distance of 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Question: The length of a tangent from point A at a distance of 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Solution:
Let O be the centre of the circle and AB is the tangent.


OB ⊥ AB then ∆OAB is a right-angled triangle.

OA² = AB² + OB² (by Pythagoras Theorem)
⇒ 5² = 4² + OB²
⇒ OB² = 5² – 4²
⇒ OB² = 25 – 16
⇒ OB² = 9
⇒ OB = √9 = 3

Hence, the radius of the circle = 3 cm.