Question

A chord of a circle of the radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73).

Instructions:- ❎ No Spamming ❎
✔️ Verified Answers ✔️
Spam answers reported+ Websites answers Reported..
Full Explanation..

Important Notice:- Answers will be shown to Moderators..
​

Answer 1

Answer:

, the area of the corresponding segment of the circle is 88.44 cm²

Answer 2

Answer:

Heya,

In a given circle,

Radius (r) = 12 cm

And, 0 = 120°

Area of segment APB Area of sector OAPB - Area of AOAB

Area of sector OAPB =

360

120 = x 3.14 x (12)² 360

x 3.14 x 12 x 12

= 1 x 3.14 x 4×12

= 150.72 cm²

Finding area of triangle AOB

Area A AOB = Base x Height

We draw OM 1 AB

LOMB = 2 OMA = 90°

In triangle OMA & OMB

OA = OB. (Both radius)

angle OMB = angle OMA (Both 90°)

··ΔΟΜΑ Ξ ΔΟΜΕ

→ ANGLE AOM = BOM

angle AOM= BOM= 1/2 BOA

→ angle AOM= BOM = 1/2 * 120° = 60°

Also, since triangle OMB is congruent OMA

BM = AM (CPCT)

⇒BM = AM = 1/2 AB

In right triangle OMA

sin O = side opposite to angle 0/Hypotenuse

sin 60° AM / AO

√3/2 AM/12

√3/2 x 12 = AM

In right triangle OMA

Cos 0 = side adjacent to angle /Hypotenuse

cos 60°= OM / AO

1/2 = OM/12

12/2 = OM

6= OM

OM = 6

From (1)

AM = 1/2 AB

2AM = AB

AB= 2AM

Putting value of AM

AB=2× 6√3

AB=12√3

Now,

Area of triangle AOB = 1/2 x Base x Height

=1/2 x AB x OM

=×1/2 * 12√3x6

= 36√3

= 36 × 1.73

= 62.28 cm²

Area of segment APB

= Area of sector OAPB Area of AOAB

= 150.72-62.28

= 88.44 cm²

Hope it helps