NOTE MATH PMR CIRCLE

Wednesday, May 3, 2023

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CIRCLES

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CIRCLES

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CIRCLECIRCUMFERENCE

ARCDIAMETERMINOR SECTOR

RADIUS

AREA OF SECTOR

MAJOR SECTOR

MINOR ARC

MAJOR ARC

CHORD

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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

C:\Documents and Settings\MOE\Desktop\KMK MathsT3\3 Circles\Property of chords.gsp

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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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PROPERTIES OF CHORD

14 cm

14 cm

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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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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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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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PROPERTIES OF CIRCLE

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1. Angle subtended at the circumference by the same arc are equal.

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ANGLE AT THE CIRCUMFERENCE

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500

500

500

500

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Example 1:

y0

X0

600

300

Find:

a. x0= ………..

b. y0= ………..

600

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Example 1:

y0

X0

600

300Find:

a. x0= ………..

b. y0= ………..

600

300

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Example 2:Find:

a. x0= ………..

b. y0= ………..

c. z0= ………..

y0

X0 500

350

z0

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Example 2:Find:

a. x0= ………..

b. y0= ………..

c. z0= ………..

y0

X0

500

350

z0

350

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Example 2:Find:

a. x0= ………..

b. y0= ………..

c. z0= ………..

y0

X050

0

350

z0

350

500

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Example 2:Find:

a. x0= ………..

b. y0= ………..

c. z0= ………..

y0

X0 500

350

Z0

350

500

X0

Z0

500

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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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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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ANGLE AT THE CENTRE

ANGLE AT THE CIRCUMFERENCE

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350

X0700

X0= x 2 = 700350

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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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3. Angle subtended at the circumference by the diameter of a semicircle = 900

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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

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CYCLICQUADILATERAL

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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

NOTE MATH PMR CIRCLE

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