Question

A point Q is 13 cm away from the center of a circle and the length PQ of the tangent drawn from P to the circle is 12 cm, then radius of circle is (in cm

(A) 25

(B) \(\sqrt { 313 }\)

(C) 5

(D) 1

Answer 1

Answer is (C) 5

PQ is the tangent on circle drawn from external point Q and OP is radius of circle.

So, ∠OPQ = 90°

From right angled OPQ

OQ² = PQ² + OP² (By Pythagoras theorem)

⇒ 13² = 12² + OP²

⇒ OP² = 13² – 12²

⇒ OP² = (13 + 12) (13 – 12)

⇒ OP² = 25

⇒ OP = \(\sqrt { 25 }\) = 5 cm