Ng Huoy Miin, Trace Gew Yee,
“ Prepared by : Pang Kai Yun, Sam Wei Yin,
. Liew Poh Ka, Chong Jia Yi
A circle is a plain figure enclosed by a curved line,
every point on which is equidistant from a point
within, called the centre.
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
AREA OF SECTOR (RADIAN)
Area of Sector _ Central Angle
Area of Circle _ Zn
A _ 1
E _ 21t
= — X 71'7"
A = lr20
EXAMPLE 2 (AREA OF SECTOR)
Area = 1 r26’
The segment of a circle is the region bounded by
a chord and the arc subtended by the chord.
Chord Minor Segment
Major Segment D
AREA OF SEGMENT
E 6 M 4
E . m n
S } .1
1 2 g S
AI V H _
m 6 z_. w
. .~l. 6 ( (1
a 2 2 _2I_
EXAMPLE (AREA OF SEGMENT)
The above diagram shows a sector of a
circle, with centre Oand a radius 6 cm.
The length of the arc AB is 8 cm. Find
(i) 0 A06’
(ii) the area of the shaded segment.
(i) la = 8 cm (ii) the area Ofthe shaded segment
8 = r0 0
1 2 . 180
8:69 = 5(6) (1.333-s1n(1.333X G ))
9 = 1-333 radians = §(36)(1.333 — sin 76.380) .
B AOB= 1.333 radians
= 6.501 cm2
Chord of a circle is a line segment whose ends
lie on the circle.
GIVEN THE RADIUS AND CENTRAL ANGLE
Chord length = 2r sin (3) D
Chord length = 2r sin (3)
= 2(6) sin (7)
= 12 X sin 45
0 ,2 Cm C = 8.49 cm
GIVEN THE RADIUS AND DISTANCE TO CENTER
This is a simple application of Pythagoras‘
Chord length = 2/ r2 — d2 D
Find the chord of the circle where the radius
measurement is about 8 cm that is 6 units from the
Chord length = 2/ T
=2/ E .
= 10.58 cm
PERIMETER OF A SEMICIRCLE
o 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
0 So, the formula for the perimeter of a semicircle
Perimeter = nr + 2r Q
Perimeter = 1Tr + 2r
= (3.142)(§) + 8
= 20.56 cm Q
AREA OF A SEMICIRCLE
OA semicircle is just half of a circle. To find the
area of a semicircle we just take half of the
area of a circle.
0 So, the formula for the area of a semicircle is:
Area = Enrz
_ . n
Area = - TE? ‘
= X 3.142 X 42
— 25.14 cm2
Length of Arc: Area of Segment:
s = r 0 1 .
Length of Chord: A T 5 V2 (9 T Sme )
I = 2r sin —
Area of Triangle:
I 2 .
Areaofsectorz 3. A T Er Slug
A = —r20
A” Length Area of Triangle Area of Segment