Question

The length of a tangent drawn from a point 10 cm away from the centre of the circle of radius 5 cm is

(a) 5 cm

(b) \(5\sqrt3\) cm

(c) \(2\sqrt3\) cm

(d) \(\sqrt{15}\) cm

Answer 1

(b) \(5\sqrt3\) cm

Given, OP = 10 cm and OA = 5 cm Since, the tangent to a circle at a point is perpendicular to the radius through the point of contact

OA ⊥ PA ⇒ ∠OAP = 90° 

∴ In ΔOAP, PA² = OP² – OA²

⇒ PA² = 100 – 25 = 75 

⇒ PA = \(\sqrt{75}\) = \(5\sqrt3\) cm.