Question

the chord AB of circle with radius =28cm subtends angle AOB=45° at center of the circle ,0 .Find the area of minor segment.​

Answer 1

Answer:

Given radius=28cm, θ=45

∘

Area of minor segment = Area of sector OAB - Area of ΔOAB

Area of sector OAB =

360

πr

2

×θ=(

7

22

×

360

1

×(28)

2

×45)cm

2

=308cm

2

Area of ΔOAB=

2

1

×OA×OB×sin45

∘

[∵AreaofΔABC=

2

1

AB×AC×sinA]

=

2

1

×28×28×

2

1

cm

2

=14×14×

2

cm

2

=196×1.414cm

2

=277.144cm

2

∴ Area of minor segment =(308−277.144)cm

2

=30.856cm

2