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Wednesday, May 3, 2023
AIRIL AHMAD
Wednesday, May 3, 2023
AIRIL AHMAD
CIRCLES
BYMR.AIRIL AHMAD
CIRCLES
BYMR.AIRIL AHMAD
AIRIL BIN AHMAD
Wednesday, May 3, 2023
CIRCLECIRCUMFERENCE
ARCDIAMETERMINOR SECTOR
RADIUS
AREA OF SECTOR
MAJOR SECTOR
MINOR ARC
MAJOR ARC
CHORD
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Where can you find the arc around you?
AIRIL BIN AHMAD
Wednesday, May 3, 2023
CHORD AND ARC
1. A chord is a straight line that joins any two points on the circumference of a circle.
2. An arc is a curved line that joins any two points on the circumference of a circle.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
CHORD AND ARC
CHORD
ARC
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
1. A radius that is perpendicular to a chord divides the chord into two equal parts.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
5cm X cm
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
2. Equal chords in a circle are equidistant from the centre.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
14 cm
14 cm
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
3. Two chords of the same length cut arcs of the same length.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
14 cm
14 cm
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PYTHAGORAS’ THEOREM
22 43 x
3cm
4cm
x cm 169 x
25x5x
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Trigonometry
3 4 5 5 12 13 6 8 10 7 24 25
8 15 17 9 12 15 10 24 26 12 16 20
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 1:From the figure find:
a. AQ= …………cm
b. OA= …………cm
c. OR= …………cm
d. OP= …………cm
e. QR= …………cmB4 cmQ
O
A
R
P
3 cm
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2: Given that AB=16cm and OQ=6cm from the figure find:
a. AQ= …………cm
b. OS= …………cm
c. OP= …………cm
d. OA= …………cm
e. OR= …………cm
f. QR= …………cmB
Q
O
A
R
S
6 cm
P
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 3: Given that AB=30cm and OC=8cm from the figure find:
a. AC= …………cm
b. CB= …………cm
c. OA= …………cm
d. OD= …………cm
e. OB= …………cm
f. DC= …………cmBC
O
A
8 cm
D
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Wednesday, May 3, 2023
AIRIL AHMAD
PROPERTIES OF CIRCLE
BYMR.AIRIL AHMAD
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
1. Angle subtended at the circumference by the same arc are equal.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
ANGLE AT THE CIRCUMFERENCE
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
500
500
500
500
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 1:
y0
X0
600
300
Find:
a. x0= ………..
b. y0= ………..
600
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 1:
y0
X0
600
300Find:
a. x0= ………..
b. y0= ………..
600
300
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X0 500
350
z0
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X0
500
350
z0
350
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X050
0
350
z0
350
500
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X0 500
350
Z0
350
500
X0
Z0
500
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
350
500X0
Z0
500
350
Z0 = 1800 – 350 - 500
Z0 = 950
AIRIL BIN AHMAD
Wednesday, May 3, 2023
ExercisePAGE 48
EXERCISE 3.2A
NO. 1, 2 , 3
ENJOY DOING IT!!!
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Exercise: 1.Find the value of x
320
x0
200
x0
x0
a. b.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Exercise: 1.Find the value of x
260
x0360
d.
580
x0
c.420
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Exercise: 2.Find the value of x and y
260
x0360
AIRIL BIN AHMAD
Wednesday, May 3, 2023
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
2. An angle subtended at the centre of a circle by an arc is TWICE the angle subtended by the arc at the circumference.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
ANGLE AT THE CENTRE
ANGLE AT THE CIRCUMFERENCE
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
350
X0700
X0= x 2 = 700350
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
1040
X0520
X0= ÷ 2 = 5201040
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 1:y0
2500
X0
x0= 3600-2500
x0= 1100
y0= 1100 ÷ 2y0= 550
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:x0= 1800-600
x0= 1200
y0= 1200 ÷ 2y0= 600
y0
300
X0
300
AIRIL BIN AHMAD
Wednesday, May 3, 2023
ExercisePAGE 52
EXERCISE 3.2C
NO. 1, 2 , 3
ENJOY DOING IT!!!
AIRIL BIN AHMAD
Wednesday, May 3, 2023
A A B B C C D D E E
16 24 8 24 4 20 2 18 1 17
17 25 9 25 5 21 3 19 3 19
18 26 10 26 6 22 6 22 5 21
19 27 11 27 7 23 7 23 7 23
20 28 12 28 12 28 10 26 9 25
21 29 13 29 13 29 11 27 11 27
22 30 14 30 14 30 14 30 13 29
23 31 15 31 15 31 15 31 15 31
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
3. Angle subtended at the circumference by the diameter of a semicircle = 900
AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CIRCLE
1800
900
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 1:
250x0
380 y0
X0 = 90 - 25X0 = 650
y0 = 90 - 38y0 = 520
900
900
AIRIL BIN AHMAD
Wednesday, May 3, 2023
ExercisePAGE 53
EXERCISE 3.2D
NO. 1, 2 , 3
ENJOY DOING IT!!!
Wednesday, May 3, 2023
AIRIL AHMAD
CYCLICQUADILATERAL
BYMR.AIRIL AHMAD
CYCLICQUADILATERAL
BYMR.AIRIL AHMAD
AIRIL BIN AHMAD
Wednesday, May 3, 2023
A cyclic quadrilateral is a
quadrilateral
which is inscribed in a circle.P
S
R
Q
PQRS is a cyclic quadrilateral.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
AIRIL BIN AHMAD
Wednesday, May 3, 2023
DEFINITION
A cyclic quadrilateral is a quadrilateral with its four vertices located on the
circumference of a circle
AIRIL BIN AHMAD
Wednesday, May 3, 2023
a
c
b
d
a + c = 1800
b + d = 1800
AIRIL BIN AHMAD
Wednesday, May 3, 2023
kj
n mt
s
rq
a
c
b
d g
fe
h
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Exercise pg 58 3.3c 1b , 2 & 4
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Exterior angles and
the corresponding interior angles
AIRIL BIN AHMAD
Wednesday, May 3, 2023
P
S
R
Q
M
If PQ is extended to M, then RQM is an exterior angle.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
P
S
R
Q
If SRM is a straight line, which is the exterior angle?
MQRM is the exterior angle.
AIRIL BIN AHMAD
Wednesday, May 3, 2023
P
S
R
Q
M
For the exterior angle, QRM.
Exterior angleCorresponding interior angle
Corresponding interior
opposite angle
650650
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Homework
Pg 61 Ex.3.3e 1, 2, 3, 4
AIRIL BIN AHMAD
Wednesday, May 3, 2023
Homework
Pg 64 Ex.3.3g 1, 2, 3, 4
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