Ex 10.2,1
Choose the correct option and give justification.
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
Given:
Tangent = XY
Point of contact = B
Length of the tangent to a circle = 24 cm
i.e. PQ = 24 cm
& OQ = 25 cm
To find: Radius of circle i.e. OP
Solution:
Since XY is tangent,
OP XY
So, OPQ = 90
So, OPQ is a right angled triangle
Using Pythagoras theorem
(Hypotenuse)2 = (Height)2 + (Base)2
OQ2 = OP2 + PQ2
(25)2 = OP2 + (24)2
OP2 = (25)2 (24)2
OP2 = 625 576
OP2 = 49
OP = 49
OP= (7^2 )
OP = 7cm
Hence, radius = OP = 7 cm
Option (A) is correct .

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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