NCERT Solutions for Class 10 Science Chapter 12

Important NCERT Questions

Areas Related To Circles Class,

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 12.2

Page No:230

Questions No:7

# A chord of a circle of 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)

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The perpendicular OV drown form O to chord ST bisects ST.

Therefore, SV = VT

In △OVS,

OV/OS = cos 60° ⇒ OV/12 = 1/2 ⇒ OV = 6 cm

SV/OS = sin 60° ⇒ SV/12 = √3/2 ⇒ OV = 6√3 cm

ST = 2 x SV = 2 x 6√3 = 12√3

Area of △OST

= 1/2 × ST × OV = 1/2 × 12√3 × 6 = 36√3 = 36 x 1.73 = 62.28 cm²

Area of sector OSUT

= 120°/360° x πr² = 1/3 x π(12)²

= 1/3 x 3.14 x 12 x 12 = 150.72 cm²

Area of minor segment

= Area of sector OSUT – Area of △OST

= (150.72 – 62.28) cm²

= 88.44 cm²

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