Question

In a circle with center P, draw two radii PA and PB such that they make an acute angle with each other. What is the region bounded by the two radii drawn and the corresponding arc AB known as? Please give step by step explanation
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Answer 1

Answer:

Here, r=5cm and θ=90

o

⇒ Area of sector OABO=

360

θ

πr

2

=

360

o

90

o

×3.14×(5)

2

∴ Area of sector OABO=

4

3.14×25

=19.62cm

2

⇒ Area of △AOB=

2

1

×AO×BO=

2

1

×5×5

∴ Area of △AOB=

2

25

=12.5cm

2

∴ Area of minor segment made bye the chord AB = Area of sector OABO - Area of △AOB

∴ Area of minor segment made bye the chord AB =19.62−12.5=7.12cm

2

⇒ Area of circle =πr

2

=3.14×(5)

2

∴ Area of circle =78.5cm

2

⇒ Area of major segment made by chord AB = Area of a circle - Area of minor segment.

∴ Area of major segment made by chord AB=78.5−7.12=71.38cm

2