Chp 10 Booklet
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Transcript of Chp 10 Booklet
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CHAPTER 10
CIRCLES
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(A) To Identify Parts of a Circle
Centre Circumference
Radius Diameter
Chord Arc
Sector Segment
(B) To Draw a Circle and Parts of a Circle
Draw the circles below:
1. Draw a circle with centerO and radius 2 cm.
2. Draw a circle given its diameter is 6cm.
2
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3. Draw a diameter of 3cm passing through a point Con a circle
with centre O.
4. Draw two chords of length 4cm passing through a pointEon the
circumference of the circle with radius 3cm.
5. Draw the sector of a circle given that the angle at the centre is
60o and its radius is 4cm.
3
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(C) To Determine The Centre Or Radius Of A Circle By
Construction
The perpendicular bisector of chords of a circle intersect at thecentre of the circle.
1. Determine the centre and radius of the circles given below:
(a) (b)
(D) To Understand and Use the Concept of Circumference to Solve
Problems.
Formula : Circumference = 2r
4
==
22
73.142
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(i) To find the circumference of a circle given its diameter or
radius
1. Find the circumference of a circle of
(a) diameter 14 cm (b) radius 2.1 cm
2. Take = 3.142, find the circumference of the circles below:
(a) (b)
3. CirclePhas a radius of 21cm and circle Q has a diameter of5.6cm. Find the difference in the circumference of circlePand
Q.
(Take =7
22)
5
O
3 cm
O
10 cm
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(ii) To find the diameter or radius of a circle given its
circumference
1. Take =722 , find the diameter of the circle with circumference
17.6cm.
2. Take = 3.142, find the radius of a circle given its
circumference is 314.2 cm.
3. A circle and a square with length 5 cm have the same perimeter.Find the radius of the circle, correct to 2 decimal places.
6
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(iii) To solve problems involving the circumference of circles.
1. A circle is inscribed inside a square of length 1.4 cm as shown.
Find
(a) the circumference of the circle.
(b) the difference in the perimeter of the
square and the circle.
2. The tyre of a bicycle rotates 50 times per minutes. Given the
diameter of the tyre is 42 cm, find the distance traveled by the
bicycle in 5 minutes. Give your answer in meters.
3. XYZis a right-angled triangle. Semicircles are drawn on all 3
sides of the triangle. Find the perimeter of the diagram.
(E) Arc of a Circle
7
1.4cm
5 cm
13 cm
cm
Z Y
X
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The length of arc is proportional to the angle at the centre
Formula:
=
360
CentreAtAngle
nceCircumfere
arcofLength
(i) To find the length of the arc given the angle at the centre and
the radius
1. Find the length of the arc of a circle with radius 4.9cm and anangle of 56o at the centre.
2. Find the value ofx for each of the following circles:(a) (b)
3. The figure shows a circle of diameter 12.6cm and and arcAB
that subtends an angle of 80o at the centre. Find the length of arc
AB.
8
Length of Arc
=
Angle at centre
Circumference 360o
O
7 cm
72o x
O3.5cm
cm
300o
x
O80o
A
B
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(ii) To find the angle at the centre given the length of the arcand the radius of the circle
1. Find the angle subtended at the centre of the circle, given
(a) radius = 35mm, length of arc = 143mm(b) radius = 28cm, length of arc = 22cm
(Take =7
22)
2. Find the angle subtended at the centre of a circle by an arc of
length 12.1 cm, given that its radius is 3.5cm. (Take =
7
22)
3. Find the value ofx given that the circle with centre O has aradius of 14m and the minor arcAB is 44m long.
9
O
xAB
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(iii) To find the radius of a circle given the length of thearc and the angle at the centre
1. Find the radius of the circle, given
(a) angle at the centre = 36o, length of arc = 8.8cm(b) angle at the centre = 45o, length of arc = 121mm
(Take =7
22)
2. Find the radius of a circle given that an arc of length 19.8m
subtends an angle of 180o at the centre of the circle.
3. Find the radius of the circle with centre O given that the majorarcPQ is 121cm.
10
O30o
P
Q
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(iv) To solve problems involving arcs of a circle
4. The minute hand of a clock has traveled one quarter ofa revolution. Find the distance traveled by the tip of theminute hand given that the minute hand is 12.1cm.
5. The hour hand of a clock moves from 12am to 8am, covering a
length of7
250 cm. Find the length of the hour hand.
6. The figure shows a right-angled triangle joined to a semicircle.
find the perimeter of the figure.
11
6cm
8cm
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7. The figure given shows a rectanglePQRSoverlapped by twoquadrantsPAD andRCB of radius 7cm. IfPS= 10cm andPQ
= 14cm, calculate the perimeter of the shaded area.
(F) Area of a Circle
Formula:
(i) To find the area of a circle given the radius or diameter
1. Take =7
22, find the area of a circle with radius 7 cm.
2. Take =3.14, find the area of a circle with radius 5.6 cm.
3. Take =7
22, find the area of a circle with diameter 42cm.
(ii) To find the radius or diameter given the area of a circle
12
P A S
B
RC
Q
D
Area of circle = r2
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1. The area of a circle is 154 cm2. Find its radius and diameter.
(Take =7
22)
2. A circle has an area of 78.55cm2. Determine the diameter of the
circle given =3.142.
3. The circumference of a circle is 88cm. Calculate the area of the
circle.
4. Determine the circumference of a circle which has an area of616cm2.
13
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5. The figure shows two concentric circles with centre O. Find thearea of the annulus.
(iii) To solve problems involving area of circles
1. Take = 7
22
, find the area of the shaded regions below.
(a) (b)
14
O
3 cm4 cm
Important!
ConcentricCircles= circles havingthe same centre
Annulus= area betweentwo concentriccircles
O
14cm
24cm
18cm
O P
42cm
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2. The diameter of the circle has the same length as the sides of the
square. Take =3.142, find the area of the figure below.
3. Mr Lingam bought a pizza which is circular in shape. His
daughter ate quarter of the cake. Given the area of the topsurface of the remaining portion is 462 cm2, find the diameter of
the pizza.
15
O
28 cm
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(G) Area of a Sector of a Circle
Formula:
(i) To find the area of a sector given the radius and angle at the
centre
1. Find the area of the sector of a circle, given
(a) Radius = 14cm (b) Radius = 24m
Angle at centre = 45o Angle subtended at
centre = 210o
(Take =7
22)
2. Find the area of each of the shaded regions where O is the centre
of the circle.(a) (b)
16
Area of
Sector
= Angle at centre
Area of Circle 360o
1 circlesemicircle
= circle
A quarter of a circle
= circle
O
72o
7cmO
72o
7cm 4.9mO
=
360
CentreAtAngle
CircleofArea
SectorofArea
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(ii) To find the angle at the centre given the radius and area of a
sector
1. Find the angle at the centre for the circles shown below.
(a) (b)
2. The area of the sector of a circle, with the radius 4.2cm, is
15.28cm2
. Find the angle at the centre.
17
O 21 m
Area of sector = 77 m2
2.8cm
O18.75cm2
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(iii) To find the radius given the area of a sector and the angle at the
centre
1. The area of the sector of a circle, with an angle of 70o at the
centre is 22 m2. Find the radius of the circle. (Take =7
22)
2. The sector of a circle subtends an angle of 60o at the centre of
the circle. Given the area of the sector is 231cm2, find thediameter of the circle.
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(iv) To solve problems involving area of sectors and area of circles
1. The diagram below shows a circle with centre O and a radius of
14mm. OAB is a right-angled triangle. Find the area of the
shaded part.
2. Find the area of the shaded part for the diagram below. (Take
=7
22)
19
36o
6cm10cm
O
A
B
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PMR Past Year Questions (Chapter 10 Circles)
2004 Paper 1 Question 19
Diagram 12 shows a circle with centre O.
The radius of the circle is2
110 cm. Calculate the length, in cm, of the
minor arcMN. (Use7
22= )
A2
55B
2
77C
8
1155D
81617
2004 Paper 1 Question 20
In Diagram 13,POR is the diameter of circlePQR.
Given thatPQ = QR andPR = 14cm, calculate the area, in cm2
, of theshaded region. (Use
7
22= )
20
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A 56 B 93 C 105 D 142
2004 Paper 1 Question 39
In Diagram 25,PQR is an arc of a circle with centre O andPRO is an
equilateral triangle.
The perimeter, in cm, of the whole diagram is
(Use7
22= )
A 42 B 63 C 64 D 85
2005 Paper 1 Question 23In Diagram 18,PQR is a straight line andPQSis a quadrant of a circle
with centre Q.
The area if triangle QRSis 21cm2. Calculate the area, in cm2, of
quadrantPQS. (Use7
22= )
A 11 B 19.25 C 38.5 D 154
21
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2005 Paper 1 Question 24
In Diagram 19,PQR is an arc of a circle with centre O.
The radius of the circle is 14 cm andPT= 2 TS. Calculate the perimeter,
in cm, of the whole diagram. (Use7
22= )
A 66 B 94 C 98 D 126
2005 Paper 1 Question 40
Diagram 25 shows a circle with centre O. The length of the minor arc
PQ is 3.3 cm.
Calculate the radius, in cm, of the circle. (Use7
22= )
A 2.42 B 4.50 C 14.85 D 29.70
22
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2006 Paper 1 Question 20
Diagram 15 shows a circle with centre O.
Calculate the length, in cm, of the minor arcPQ. (Use7
22= )
A 22 B 44 C 88 D 176
2006 Paper 1 Question 21Diagram 16 shows the surface of a tablePQRSTU.PQSTis a rectangle.
PUTand QRSare semicircles with centresXand Yrespectively.
It is given thatPT= 1.4 m andPQ = 3 m. Calculate the perimeter, in m,
of the surface of the table. (Use7
22= )
23
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A 10.4 B 13.2 C 14.8 D 17.6
2006 Paper 1 Question 22
Diagram 17 shows two sectors, QSR and UST, with the common centre
S.RSUand QSTare straight lines.
It is given that ST= 2QS. Calculate the area, in cm2, of the sectorUST.
(Use7
22= )
A 11 B 19.25 C 38.50 D 77
2007 Paper 1 Question 23
Diagram 16 shows a circle with centre O.PT, QU,RVand SWare
diameters of the circle.
Which of the following minor arcs is the longest?A TU B UV C WP D RS
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2007 Paper 1 Question 24
Diagram 17 shows a circle with centre O and radius 6 cm.
Calculate the area, in cm2, of the shaded region.
A 18 B 5.4 C 10.2 D 30.6
2007 Paper 1 Question 31
Diagram 22 shows a square OPQR and an arcRSPwith centre O.
Calculate the perimeter, in cm, of the whole diagram.A 61 B 58 C 47 D 33
25
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2008 Paper 1 Question 21
Diagram 12 shows a circle with centre O.
Calculate the area, in cm2, of the coloured region. (Use7
22= )
A 105 B 116 C 539 D 616
2008 Paper 1 Question 22
Diagram 13, O is the centre of the circle andPOR is a diameter of the
circle.PQRSis a rectangle.
26
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It is given thatPR = 10 cm andPQ = 6 cm. Find the area, in cm2, of thecoloured region.
A 25 48 B 25 96 C 100 48 D 100 96
2008 Paper 1 Question 30
In Diagram 19,PQRSis a square and STUis an arc of a circle with
centreP.
The area ofPQRSis 576 cm2. Calculate the length, in cm, of the arc
STU.
A 16 B 28 C 32 D 48
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