in a circle radius 21 cm the length of minor arc is 33 cm find the measure of the angle subtended at the centre by this arc also find the area of the minor sector and the major sector formed in it
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Answers
Answer:
Solution
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In the mentioned figure,
O is the centre of circle,
AB is a chord
AXB is a major arc,
OA=OB= radius =21 cm
Arc AXB subtends an angle 60
o
at O.
i) Length of an arc AXB =
360
60
×2π×r
=
6
1
×2×
7
22
×21
=22cm
ii) Area of sector AOB =
360
60
×π×r
2
=
6
1
×
7
22
×(21)
2
=231cm
2
iii) Area of segment (Area of Shaded region) = Area of sector AOB− Area of △AOB
By trigonometry,
AC=21sin30
OC=21cos30
And, AB=2AC
∴ AB=42sin30=41×
2
1
=21 cm
∴ OC=21cos30=
2
21
3
cm
∴ Area of △ AOB =
2
1
×AB×OC
=
2
1
×21×
2
21
3
=
4
441
3
cm
2
∴ Area of segment (Area of Shaded region) =(231−
4
441
3
) cm
2