Question

Find the difference of the areas of two segments of a circle formed by a chord of length 7 cm subtending an angle of 60 at the centre.​

Answer 1

Answer:

Let r be the radius of circle and AB be the chord, which makes 90

o

angle at centre.

AB=5cm

In right △OAB, using pythagoras theorem

OA

2

+OB

2

=AB

2

⇒r

2

+r

2

=5

2

⇒2r

2

=25

⇒r=

2

5

Area of circle =πr

2

=

7

22

×

2

5

×

2

5

=39.28cm

2

Area of minor segment =Areaofsector−Areaof△OAB

=

360

o

90

o

×πr

2

−

2

1

×

2

5

×

2

5

=

4

1

×39.28−

4

25

=

4

14.28

=3.57cm

2

Area of major segment =39.28−3.57=35.71cm

2

Required difference =35.71−3.57=32.14cm

2