Question

Find the area of minor segment of a circle of radius 14 cm, when the angle of corresponding sector is 90°.​

Answer 1

Answer:

Giventhat−

thecentralangle∠AOBofasector=60

o

andtheradius=14cm.

Tofindout−

theareaofthecorrespondingminorsegment.

Solution−

InΔAOBwehaveOA=OB.

∴∠OAB=∠OBA⟹∠OAB+∠OBA=2∠OABor2∠OBA.

Now∠AOB=60

o

.

∴2∠OAB=180

o

−60

o

⟹∠OAB=60

o

=∠OBA.

(theanglesumpropertyoftriangles).

SoΔAOBisequilateralonewithsidea=14cm.

∴ar.ΔAOB=

4

3

×a

2

=

4

3

×14

2

cm

2

=49

3

cm

2

.

Alsoar.sector=

360

o

θ

×π×r

2

whenθisthecentralangleand

r=radiusofthesector

=

360

o

60

o

×

7

22

×14

2

cm

2

=

3

308

cm

2

.

Nowar.minorsegment=ar.sector−ar.Δ

=

3

308

cm

2

−49

3

cm

2

=(

3

308

−49

3

)cm

2

.

Ans−OptionD.