## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 49 of Multiple Choice Questions (MCQ)

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

49
##### In the given figure, O is the center of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to

In given Figure,

OA AP [Tangent at any point on the circle is perpendicular to the radius through point of contact]

In right - angled OAP,

By Pythagoras Theorem

[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2]

(OP)2 = (OA)2 + (PA)2

Given, PA = 12 cm and OA = radius of outer circle = 5 cm

(OP)2 = (5)2 + (12)2

(OP)2 = 25 + 144 = 136

OP = 13 cm …[1]

Also,

OB BP [Tangent at any point on the circle is perpendicular to the radius through point of contact]

In right - angled OBP,

By Pythagoras Theorem

[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2 ]

(OP)2 = (OB)2 + (PB)2

Now, OB = radius of inner circle = 3 cm

And, from [2] (OP) = 13 cm

(13)2 = (3)2 + (PB)2

(PB)2 = 169 - 9 = 160

PB = 4√10 cm

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55