note math pmr circle
TRANSCRIPT
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Wednesday, May 3, 2023
AIRIL AHMAD
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Wednesday, May 3, 2023
AIRIL AHMAD
CIRCLES
BYMR.AIRIL AHMAD
CIRCLES
BYMR.AIRIL AHMAD
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AIRIL BIN AHMAD
Wednesday, May 3, 2023
CIRCLECIRCUMFERENCE
ARCDIAMETERMINOR SECTOR
RADIUS
AREA OF SECTOR
MAJOR SECTOR
MINOR ARC
MAJOR ARC
CHORD
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AIRIL BIN AHMAD
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Where can you find the arc around you?
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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.
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CHORD AND ARC
CHORD
ARC
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PROPERTIES OF CHORD
1. A radius that is perpendicular to a chord divides the chord into two equal parts.
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PROPERTIES OF CHORD
5cm X cm
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Wednesday, May 3, 2023
PROPERTIES OF CHORD
2. Equal chords in a circle are equidistant from the centre.
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PROPERTIES OF CHORD
14 cm
14 cm
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PROPERTIES OF CHORD
3. Two chords of the same length cut arcs of the same length.
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AIRIL BIN AHMAD
Wednesday, May 3, 2023
PROPERTIES OF CHORD
14 cm
14 cm
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Wednesday, May 3, 2023
PYTHAGORAS’ THEOREM
22 43 x
3cm
4cm
x cm 169 x
25x5x
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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
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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
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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
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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
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Wednesday, May 3, 2023
AIRIL AHMAD
PROPERTIES OF CIRCLE
BYMR.AIRIL AHMAD
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PROPERTIES OF CIRCLE
1. Angle subtended at the circumference by the same arc are equal.
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PROPERTIES OF CIRCLE
ANGLE AT THE CIRCUMFERENCE
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PROPERTIES OF CIRCLE
500
500
500
500
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Example 1:
y0
X0
600
300
Find:
a. x0= ………..
b. y0= ………..
600
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AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 1:
y0
X0
600
300Find:
a. x0= ………..
b. y0= ………..
600
300
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Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X0 500
350
z0
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AIRIL BIN AHMAD
Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X0
500
350
z0
350
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Wednesday, May 3, 2023
Example 2:Find:
a. x0= ………..
b. y0= ………..
c. z0= ………..
y0
X050
0
350
z0
350
500
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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
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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
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ExercisePAGE 48
EXERCISE 3.2A
NO. 1, 2 , 3
ENJOY DOING IT!!!
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Exercise: 1.Find the value of x
320
x0
200
x0
x0
a. b.
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Exercise: 1.Find the value of x
260
x0360
d.
580
x0
c.420
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Exercise: 2.Find the value of x and y
260
x0360
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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.
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PROPERTIES OF CIRCLE
ANGLE AT THE CENTRE
ANGLE AT THE CIRCUMFERENCE
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PROPERTIES OF CIRCLE
350
X0700
X0= x 2 = 700350
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PROPERTIES OF CIRCLE
1040
X0520
X0= ÷ 2 = 5201040
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Example 1:y0
2500
X0
x0= 3600-2500
x0= 1100
y0= 1100 ÷ 2y0= 550
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Example 2:x0= 1800-600
x0= 1200
y0= 1200 ÷ 2y0= 600
y0
300
X0
300
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ExercisePAGE 52
EXERCISE 3.2C
NO. 1, 2 , 3
ENJOY DOING IT!!!
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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
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PROPERTIES OF CIRCLE
3. Angle subtended at the circumference by the diameter of a semicircle = 900
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PROPERTIES OF CIRCLE
1800
900
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Example 1:
250x0
380 y0
X0 = 90 - 25X0 = 650
y0 = 90 - 38y0 = 520
900
900
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ExercisePAGE 53
EXERCISE 3.2D
NO. 1, 2 , 3
ENJOY DOING IT!!!
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CYCLICQUADILATERAL
BYMR.AIRIL AHMAD
CYCLICQUADILATERAL
BYMR.AIRIL AHMAD
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A cyclic quadrilateral is a
quadrilateral
which is inscribed in a circle.P
S
R
Q
PQRS is a cyclic quadrilateral.
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DEFINITION
A cyclic quadrilateral is a quadrilateral with its four vertices located on the
circumference of a circle
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a
c
b
d
a + c = 1800
b + d = 1800
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kj
n mt
s
rq
a
c
b
d g
fe
h
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Exercise pg 58 3.3c 1b , 2 & 4
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Exterior angles and
the corresponding interior angles
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P
S
R
Q
M
If PQ is extended to M, then RQM is an exterior angle.
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P
S
R
Q
If SRM is a straight line, which is the exterior angle?
MQRM is the exterior angle.
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P
S
R
Q
M
For the exterior angle, QRM.
Exterior angleCorresponding interior angle
Corresponding interior
opposite angle
650650
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Homework
Pg 61 Ex.3.3e 1, 2, 3, 4
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Homework
Pg 64 Ex.3.3g 1, 2, 3, 4