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

Data: OB is the radius, BA is the tangent.

∴ ∠OBA = 90°, OA = 5 cm. (data)

Length of tangent, AB = 4 cm.

∴ Radius, OB = ?

In ⊥∆OBA, ∠OBA = 90°

∴ OB² + BA² = OA². OB² + (4)² = (5)²

OB² + 16 = 25

OB² = 25 – 16

OB² = 9

∴ OB = 3 cm.

∴ Radius of circle, OB = 3cm.