Question

from a point q the length of the tangent to a circle is 24cm and the distance of q from the centre is 25cm .The radius of the circle is A.7cm B.12cm C.15cm D.24.5cm

Answer 1

Let O be the centre of the circle.

Given that,

OQ = 25cm and PQ = 24 cm

As the radius is perpendicular to the tangent at the point of contact,

Therefore, OP ⊥ PQ

Applying Pythagoras theorem in ΔOPQ, we obtain

OP2 + PQ2 = OQ2

OP2 + 242 = 252

OP2 = 625 − 576

OP2 = 49

OP = 7

Therefore, the radius of the circle is 7 cm.

Hence, alternative (A) is correct.

Answer 2

hello users 

solution
In triangle OPQ
OP is the Radius of circle 
PQ is the length of tangent drawn
And
OQ is the distance of the point from centre .

Using Pythagoras theorem 
H² = B² + P² 

Here
OQ² = OP² + PQ²

=> OP= √ (OQ² - PQ²)

=> OP = √ 25² - 24²
= √ 625 - 576
= √49 
= 7 cm 

Hence
 the radius of circle = 7 cm 
option A. is correct

# hope it helps :)