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:

49

24+25

=49

Step-by-step explanation:

Answer 2

Answer:

First, draw a perpendicular from the center O of the triangle to a point P on the circle which is touching the tangent. This line will be perpendicular to the tangent of the circle.

So, OP is perpendicular to PQ i.e. OP ⊥ PQ

From the above figure, it is also seen that △OPQ is a right angled triangle.

It is given that

OQ = 25 cm and PQ = 24 cm

By using Pythagoras theorem in △OPQ,

OQ2 = OP² +PQ²

(25)2 = OP²+(24)²

OP2 = 625-576

OP2 = 49

OP = 7 cm

So, option A i.e. 7 cm is the radius of the given circle.