Question

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is 

A. 7 cm 

B. 12 cm 

C. 15 cm 

D. 24.5 cm

Answer 1

Answer is A. 7 cm

Given: 

OQ = 25 cm

PQ = 24 cm

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, ∆POQ is right-angled at ∠OPQ. 

Therefore, 

By Pythagoras Theorem in ∆POQ, 

OP² + PQ² =OQ² 

⇒ OP² = OQ² – PQ² 

⇒ OP= √( OQ² – PQ²) 

⇒ OP= √(25² – 24²) 

⇒ OP= √(625 – 576) 

⇒ OP = √49 cm 

⇒ OP = 7 cm 

Hence, OP = 7 cm