## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 23 of Multiple Choice Questions (MCQ)

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

23
##### In the given figure, PA and PB are two tangents drawn from an external point P to a circle with center C and radius 4 cm. If PA ⏊ PB, then the length of each tangent is

Join AC, BC and CP

To Find: Length of tangents

Now,

PA = PB…[1]

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

In ACP and BCP

PA = PB [By 1]

CP = CP [Common]

CA = CB [radii of same circle]

ACP ≅△BCP [By Side - Side - Side Criterion]

CPA = CPB

[Corresponding parts of congruent triangles are congruent]

Now,

APB = 90°

[Given that PA PB]

CPA + CPB = 90°

CPA + CPA = 90°

2 CPA = 90°

CPA = 45°

In ACP

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

ACP is a right - angled triangle.

So, we have

PA = 4 cm

From [1]

PA = PB = 4 cm

i.e. length of each tangent is 4 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