Question

A chord of a circle of radius 5cm subtends an angle of
45° at the centre. Find the area of minor segments of circle.​

Answer 1

Step-by-step explanation:

• In the mentioned figure,
• O is the centre of circle,
• AB is a chord
• AXB is a major arc,
• OA=OB= radius = 15 cm
• Arc AXB subtends an angle 60o at O.
• Area of sector AOB=36060×π×r2
•                                     =36060×3.14×(15)2
•                                     =117.75cm2
• Area of minor segment (Area of Shaded region) = Area of sector AOB− Area of △ AOB
• By trigonometry,
• AC=15sin30
• OC=15cos30
• And, AB=2AC
• ∴ AB=2×15sin30=15 cm
• ∴ OC=15cos30=1523=15×21.73=12.975 cm
• ∴ Area of △AOB=0.5×15×12.975=97.3125cm2
• ∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm2
• Area of major segment = Area of circle − Area of minor segment
•                                        =(3.14×15×15)−20.4375

                                        =686.0625cm2

Answer 2

${\huge{\bold{\underline{Answer:-}}}}$

In the mentioned figure,

O is the centre of circle,

AB is a chord

AXB is a major arc,

OA=OB= radius = 15 cm

Arc AXB subtends an angle 60o at O.

Area of sector AOB=36060×π×r2

                                    =36060×3.14×(15)2

                                    =117.75cm2

Area of minor segment (Area of Shaded region) = Area of sector AOB− Area of △ AOB

By trigonometry,

AC=15sin30

OC=15cos30

And, AB=2AC

∴ AB=2×15sin30=15 cm

∴ OC=15cos30=1523=15×21.73=12.975 cm

∴ Area of △AOB=0.5×15×12.975=97.3125cm2

∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm2

Area of major segment = Area of circle −Area of minor segment

                                       =(3.14×15×15)−20.4375

                                        =686.0625cm2

Hope it helps faiz :)