1. CIRCLE
Prepared by : Pang Kai Yun, Sam Wei Yin,
Ng Huoy Miin, Trace Gew Yee,
Liew Poh Ka, Chong Jia Yi

2. CIRCLE
A circle is a plain figure enclosed by a curved line,
every point on which is equidistant from a point
within, called the centre.

3. DEFINITION
Circumference - The circumference of a
circle is the perimeter
Diameter - The diameter of a circle is longest
distance across a circle.
Radius - The radius of a circle is the distance
from the center of the circle to the outside
edge.

4. CIRCUMFERENCE
C = 2πrC = πd
* Where π = 3.142

5. EXAMPLE (CIRCUMFERENCE)
C = πd
= 3.142 x 6 cm
= 18.85 cm
C = 2πr
= 2 x 3.142 x 4 cm
= 25.14 cm

6. AREA OF CIRCLE
* Where π = 3.142
A = πr2

7. EXAMPLE 1 (AREA OF CIRCLE)
A = πr2
= 3.142 x 62
= 3.142 x 36
= 113.11 cm2

8. EXAMPLE 2 (AREA OF CIRCLE)
A = πr2
= 3.142 x 42
= 3.142 x 16
= 50.27 cm2
r =
𝑑
2
=
8
2
= 4cm

9. ARC
A portion of the circumference of a circle.

10. ARC LENGTH (DEGREE)
𝑙 𝑎=
𝑛
360 𝑜 2𝜋r
* A circle is 360 𝑜

11. EXAMPLE 1 (ARC LENGTH)
𝑙 𝑎 =
𝑛
360 𝑜 2𝜋r
=
45 𝑜
360 𝑜 x 2 x 3.142 x 12
=
1
8
x 75.41
= 9.43 cm

12. RADIAN
The angle made by taking the radius and
wrapping it along the edge of the circle.

13. FROM RADIAN TO DEGREE
Degree =
180 𝑜
π
x Radians
Radians =
π
180 𝑜 x Degree
FROM DEGREE TO RADIAN

14. EXAMPLE (FROM DEGREE TO RADIAN)
1. 30 𝑜
=
π
180 𝑜 x 30 𝑜
=
π
6
rad
3. 270 𝑜
=
π
180 𝑜 x 270 𝑜
=
3π
2
rad
2. 150 𝑜
=
π
180 𝑜 x 150 𝑜
=
5π
6
rad

15. EXAMPLE (FROM RADIAN TO DEGREE)
1.
π
3
rad =
180 𝑜
π
x
π
3
rad = 60 𝑜
2.
2π
3
rad =
180 𝑜
π
x
2π
3
rad = 120 𝑜
3.
5π
4
rad =
180 𝑜
π
x
5π
4
rad = 225 𝑜

16. ARC LENGTH (RADIAN)
𝑙 𝑎 = r θ
* Where θ is radians

17. EXAMPLE 2 (ARC LENGTH)
𝑙 𝑎 = r θ
= 4.16 cm x 2.5 rad
= 10.4 cm

18. EXAMPLE 3 (ARC LENGTH)
𝑙 𝑎 = r θ
= 10 cm x
π
4
rad
= 7.86 cm
𝑙 𝑎 = r θ
= 25 cm x 0.8 rad
= 20 cm

19. SECTOR
A sector is the part of a circle enclosed by two
radii of a circle and their intercepted arc.

20. AREA OF SECTOR (DEGREE)
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐶𝑖𝑟𝑐𝑙𝑒
=
𝐶𝑒𝑛𝑡𝑟𝑎𝑙 𝐴𝑛𝑔𝑙𝑒
360 𝑜
𝐴
𝜋𝑟2 =
𝑛
360 𝑜
A =
𝑛
360 𝑜 𝜋𝑟2
By propotion,

21. EXAMPLE 1 (AREA OF SECTOR)
Area =
𝑛
360 𝑜 𝜋𝑟2
=
45 𝑜
360 𝑜 x 3.142 x 62
=
1
8
x 3.142 x 36
= 14.14 cm2

22. AREA OF SECTOR (RADIAN)
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟
𝐴𝑟𝑒𝑎 𝑜𝑓 𝐶𝑖𝑟𝑐𝑙𝑒
=
𝐶𝑒𝑛𝑡𝑟𝑎𝑙 𝐴𝑛𝑔𝑙𝑒
2𝜋
𝐴
𝜋𝑟2 =
θ
2𝜋
A =
θ
2𝜋
𝑥 𝜋𝑟2
A =
1
2
𝑟2
θ
By propotion,

23. EXAMPLE 2 (AREA OF SECTOR)
Area
5 cm
O
1.4 rad
2
2
1
r
   
2
2
5.17
4.15
2
1
cm


24. SEGMENT
The segment of a circle is the region bounded by
a chord and the arc subtended by the chord.

25. AREA OF SEGMENT
2
2
1
r sin
2
1 2
r
)sin(
2
1 2
  r
  
sin
2
1
0
180
2
r
or

26. EXAMPLE (AREA OF SEGMENT)
Solution:
(i) 𝑙 𝑎 = 8 cm
𝑙 𝑎 = r θ
8 = r θ
8 = 6 θ
θ = 1.333 radians
Ð AOB = 1.333 radians
The above diagram shows a sector of a
circle, with centre O and a radius 6 cm.
The length of the arc AB is 8 cm. Find
(i) Ð AOB
(ii) the area of the shaded segment.
(ii) the area of the shaded segment
1
2
𝑟2(θ - sin θ)
=
1
2
(6)2(1.333 - sin (1.333 x
180 𝑜
ϴ
))
=
1
2
(36)(1.333 – sin 76.38 𝑜
)
= 6.501 cm2

27. CHORD
Chord of a circle is a line segment whose ends
lie on the circle.

28. GIVEN THE RADIUS AND CENTRAL ANGLE
Chord length = 2r sin
θ
2

29. EXAMPLE 1
Chord length = 2r sin
θ
2
= 2(6) sin
90
2
= 12 x sin 45
= 8.49 cm

30. GIVEN THE RADIUS AND DISTANCE TO CENTER
This is a simple application of Pythagoras'
Theorem.
Chord length = 2 𝑟2 − 𝑑2

31. EXAMPLE 2
Find the chord of the circle where the radius
measurement is about 8 cm that is 6 units from the
middle.
Solution:
Chord length = 2 𝑟2 − 𝑑2
= 2 82 − 62
= 2 64 − 36
= 2 28
= 10.58 cm

32. SEMICIRCLE

33. PERIMETER OF A SEMICIRCLE
 Remember that the perimeter is the distance
round the outside. A semicircle has two edges.
One is half of a circumference and the other is
a diameter
 So, the formula for the perimeter of a semicircle
is:
Perimeter = πr + 2r

34. EXAMPLE (PERIMETER)
Perimeter = πr + 2r
= (3.142)
8
2
+ 8
= 20.56 cm

35. AREA OF A SEMICIRCLE
 A semicircle is just half of a circle. To find the
area of a semicircle we just take half of the
area of a circle.
 So, the formula for the area of a semicircle is:
Area =
1
2
π𝑟2

36. EXAMPLE (AREA)
Area =
1
2
π𝑟2
=
1
2
x 3.142 x 42
= 25.14 cm2

37. SUMMARY

38. THANK YOU !