AREAS RELATED
TO CIRCLE
Segment of a circle
A
B
O
Major segment
The part of the circular region enclosed by
a chord and its corresponding arc is called
a Segment of a circle
Area of Segment =
Area of sector –
Area of triangle
Area of Major Segment =
Area of circle –
Area of minor segment
r
r
θ
Let us draw chord AB
Y
90°
10 cm
Q. A chord of a circle of radius 10 cm subtends
a right angle at the centre. Find the area of
the corresponding:
r =
θ =
(ii) Major segment.
Sol.
(Use π = 3.14)
(i) Minor segment
10 cm
Area of minor segment =
A
B
X
O
ar(O – AXB) –
What is formula to find area of sector?
× πr2
θ
360
90
360
×
3.14
×
10
×
10
=
Area of sector (O – AXB) =
=
78.5 cm2
4
2.5
θ
360
×
π
r2
∴ Area of sector (O – AXB)
?
ar(ΔOAB)
10 cm
Area of minor segment =
=
78.5
∴
Area of minor segment is 28.5 cm2
A(O – AXB) –
50
–
A (O – AXB)
=
78.5 cm2
A(ΔAOB)
A
B
X
10 cm
O
10 cm
Q. A chord of a circle of radius 10 cm subtends
a right angle at the centre. Find the area of
the corresponding:
(ii) Major segment.
(Use π = 3.14)
(i) Minor segment
Sol.
Area of minor segment =
ar(O – AXB) –
1
2
×
10
×
10
Area of ΔAOB =
=
=
50 cm2
5
1
2
×
AO
×
OB
?
ar(ΔOAB)
What is formula to find area of triangle?
× base × height
1
2
Area of ΔAOB
=
28.5 cm2
Area of circle =
=
3.14
314 cm2
∴
Area of major segment is
285.5 cm2
Area of circle =
πr2
Area of major segment =
Area of circle
– Area of minor segment
=
314
×
10
×
10
28.5
–
Q. A chord of a circle of radius 10 cm subtends
a right angle at the centre. Find the area of
the corresponding:
(ii) Major segment.
(Use π = 3.14)
(i) Minor segment
Area of major segment =
Area of circle –
Area of minor segment
∴ Area of circle
Sol.
=
285.5 cm2
Area of minor segment
=
28.5cm2
A
B
X
10 cm
O
10 cm
What is formula to find area of circle?
πr2
?