## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 30 of Multiple Choice Questions (MCQ)

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

30
##### In the given figure, PQR is a tangent to the circle at Q, whose center is O and AB is a chord parallel to PR such that ∠BQR = 70°. Then, ∠AQB =?

In given figure, as PR is a tangent

OQ PR

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

LQ PR

LQ AB

[As, AB || PR]

AL = LB

[Perpendicular from center to the chord bisects the chord]

Now,

LQR = 90°

LQB + BQR = 90°

LQB + 70° = 90°

LQB = 20°…[1]

In AQL and BQL

ALQ = BLQ [Both 90° as LQ AB]

AL = LB [Proved above]

QL = QL [Common]

AQL BQL

[Side - Angle - Side Criterion]

LQA = LQB

[Corresponding parts of congruent triangles are congruent]

AQB = LQA + LQB = LQB + LQB

= 2LQB = 2(20) = 40° [By 1]

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