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Grade -10 (SEE) Math

Find the area of the corresponding segment of the circle

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

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CTEVT > Diploma/PCL > PCL In Medical Lab Technology Revised 2019

Solution:

Radius, r = 12 cm

Now, draw a perpendicular OD on chord AB and it will bisect chord AB.

So, AD =DB

 

                  Circle- class 10 mathmatics

 

Now, the area of the minor sector = (θ/360°) × π r2

= (120/360) × (22/7) × 122

= 150.72 cm2

Consider the ΔAOB

Area of ΔAOB =

∠OAB = 180° – (90° + 60°) = 30°

Now, cos 30° = AD/OA

=> √3/2 = AD/12

Or, AD = 6√3 cm

We know OD bisects AB. So,

AB = 2 × AD = 12√3 cm

Now, sin 30° = OD/OA

Or, ½ = OD/12

∴ OD = 6 cm

So, the area of ΔAOB = ½ × base × height

Here, base = AB = 12√3 and

Height = OD = 6

area of ΔAOB = ½ × 12√3 × 6 = 36√3 cm = 62.28 cm2

∴ Area of the corresponding Minor segment = Area of the Minor sector – Area of ΔAOB

= 150.72 cm2 – 62.28 cm2 = 88.44 cm2

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