 ## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 33 of Multiple Choice Questions (MCQ)

Listen NCERT Audio Books - Kitabein Ab Bolengi

33
##### In the given figure, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the perimeter of ΔEDF is Given : In the given figure, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively and EK = 9 cm

To Find : Perimeter of EDF

As we know that, Tangents drawn from an external point to a circle are equal.

So, we have

KD = DH …

[Tangents from point D]

HF = FM …

[Tangents from point F]

Now Perimeter of Triangle PCD

= ED + DF + EF

= ED + DH + HF + EF

= ED + KD + FM + EF [From 1 and 2]

= EK + EM

Now,

EK = EM = 9 cm as tangents drawn from an external point to a circle are equal

So, we have

Perimeter = EK + EM = 9 + 9 = 18 cm

33

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