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### The Circle

### Starter Questions

### Starter Questions

### Semi-circle angle

### Starter Questions

### Starter Questions

### Starter Questions

### Circumference of a circle

### Circumference of a circle

### Circumference of a circle

### Circumference of a circle

### Circumference of a circle

### Starter Questions

### length of the arc of a circle

### Arc length of a circle

### Arc length of a circle

### Arc length of a circle

### Arc length of a circle

### Arc length of a circle

### length of the arc of a circle

### Starter Questions

### The Area of a circle

### The Area of a circle

### The Area of a circle

### The Area of a circle

### The Area of a circle

### The Area of a circle

### Starter Questions

### Sector area of a circle

### Area of Sector in a circle

### Area of Sector in a circle

### Area of Sector in a circle

### Area of Sector in a circle

### Starter Questions

Isosceles Triangles in Circles

Right angle in a Semi-Circle

Tangent Line to a Circle

Diameter Symmetry in a Circle

Circumference of a Circle

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Length of an ARC of a Circle

Area of a Circle

Area of a SECTOR of a Circle

Summary of Circle Chapter

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Q1. True or false

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Q2. How many degrees in one eighth of a circle.

Q3.

Q4. After a discount of 20% an iPod is £160.

How much was it originally.

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Isosceles Triangles in Circles

Aim of Today’s Lesson

We are learning to identify

isosceles triangles

within a circle.

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Isosceles triangles in Circles

When two radii are drawn to the ends of a chord,

an isosceles triangle is formed.

DEMO

A

B

xo

xo

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C

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Isosceles triangles in Circles

Special Properties of Isosceles Triangles

Two equal lengths

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Two equal angles

Angles in any triangle sum to 180o

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Angle at C is equal to:

Isosceles triangles in Circles

Q. Find the angle xo.

B

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C

xo

A

Since the triangle is isosceles

we have

280o

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Isosceles triangles in Circles

Maths in Action Ex 2.1 page 181

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Q1. Explain how we solve

Q2. How many degrees in one tenth of a circle.

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Q3.

Q4. After a discount of 40% a Digital Radio is £120.

Explain why the originally price was £200.

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Aim of Today’s Lesson

We are learning to

find the angle in a semi-circle made

by a triangle with hypotenuse equal to

the diameter and the two smaller

lengths meeting at the circumference.

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Tool-kit required

1. Protractor

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2. Pencil

3. Ruler

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something like this.

Semi-circle angle

1. Using your pencil trace round

the protractor so that you have

semi-circle.

2. Mark the centre of the semi-circle.

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x

x

x

x

- Mark three points
- Outside the circle

x

x

x

2. On the circumference

x

x

3. Inside the circle

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Outside

Circumference

Inside

Semi-circle angle

x

For each of the points

Form a triangle by drawing a

line from each end of the

diameter to the point.

Measure the angle at the

various points.

x

x

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DEMO

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Circumference

Inside

Semi-circle angle

DEMO

x

x

x

= 90o

> 90o

< 90o

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Begin Maths in Action Book page 182

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If a = 7 b = 4 and c = 10

Write down as many equations as you can

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e.g. a + b = 11

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Aim of Today’s Lesson

We are learning to understand

what a tangent line is and its

special property with the

radius at the point of contact.

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lines are

tangent to

the circle?

Tangent line

A tangent line is a line that

touches a circle at only one point.

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The radius of the circle that touches the tangent

line is called the point of contact radius.

DEMO

Special Property

The point of contact radius

is always perpendicular

(right-angled)

to the tangent line.

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Right-angled at A since

AC is the radius at the point

of contact with the

Tangent.

Tangent line

Q. Find the length of the tangent line between

A and B.

B

10

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By Pythagoras Theorem we have

C

A

8

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Q1. Using FOIL multiply out (x2 + 4x - 3)(x + 1)

Using a multiplication table

expand out (x2 + 4x - 3)(x + 1)

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Q2.

Q3. I want to make 15% profit on a computer

I bought for £980. How much must I sell it for.

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Aim of Today’s Lesson

We are learning to understand

some special properties

when a diameter bisects a chord.

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A

B

D

Diameter symmetry

- A line drawn through the centre of a circle
- through the midpoint a chord will ALWAYS cut
- the chord at right-angles

O

- A line drawn through the centre of a circle
- at right-angles to a chord will
- ALWAYS bisect that chord.

- A line bisecting a chord at right angles
- will ALWAYS pass through the centre of a circle.

DEMO

Created by Mr Lafferty

Q. Find the length of the chord A and B.

Solution

Radius of the circle is 4 + 6 = 10.

B

Since yellow line bisect AB and passes

through centre O, triangle is right-angle.

10

O

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By Pythagoras Theorem we have

4

6

Since AB is bisected

The length of AB is

A

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12m

Q1.

Q2.

Q3. Explain why

the area of the triangle is 48m2

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Q4.

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Aim of Today’s Lesson

We are learning to use the formula

for calculating

the circumference of a circle

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Diameter

Circumference

Main parts of the circle

O

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Q.Find the circumference of the circle ?

4cm

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- The circumference of the circle is 60cm ?
- Find the length of the diameter and radius.

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Now it’s your turn !

Maths in Action Ex 7.1 page 191

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Q1. True or false

Q2. Using the balancing method rearrange into D =

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Q3.

Q4. Calculate

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Aim of Today’s Lesson

We are learning to use the formula

for calculating the length of an arc.

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major arc

Q. What is an arc ?

Answer

An arc is a fraction

of the circumference.

A

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B

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Q. Find the circumference of the circle ?

10cm

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Q. Find the length of the minor arc XY below ?

x

Arc length

Arc angle

=

connection

πD

360o

y

6 cm

45o

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360o

DEMO

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Q. Find the length of the minor arc AB below ?

Arc length

Arc angle

=

connection

A

πD

360o

9 cm

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60o

B

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Q. Find the length of the major arc PQ below ?

Arc length

Arc angle

=

connection

P

πD

360o

10 m

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260o

100o

Q

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Now it’s your turn !

Maths in Action Ex 8.1 page 193

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Q1. True or false

Q2. Expand out (x + 3)(x2 + 40 – 9)

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Q3.

Q4. I want to make 30% profit on a DVD player I

bought for £80. How much must I sell it for.

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Aim of Today’s Lesson

We are learning to use

the formula for calculating

the area of a circle

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into equal sectors

And lay them out side by side

We get very close

to a rectangle.

1

8

2

2

7

1

3

6

5

8

6

4

4

3

7

5

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Thinner and thinner then

we get closer and closer

to a rectangle. Hence we can represent the area of a circle

by a rectangle.

8

6

4

2

3

7

1

5

thinner and thinner

sectors

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But the area inside this rectangle is also the area of the circle

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Now it’s your turn !

Begin Maths in Action Book

Ex9.1 page 194 Q1-2

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- The diameter of the circle is 60cm.
- Find area of the circle?

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Now it’s your turn !

Maths in Action

Ex9.1 page 194

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- The area of a circle is 12.64 cm2.
- Find its radius?

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Now it’s your turn !

Begin Maths in Action Book

Ex9.1 page 194 Q5 onwards

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Q1. Find the missing numbers

Q2. Using the balancing method rearrange into x =

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Q3. Calculate

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Aim of Today’s Lesson

We are learning to use the formula

for calculating the sector of an circle.

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Q. Find the area of the circle ?

10cm

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Find the area of the minor sector XY below ?

x

connection

Area Sector

Sector angle

=

y

πr2

360o

6 cm

45o

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360o

DEMO

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Q. Find the area of the minor sector AB below ?

connection

Area Sector

Sector angle

=

A

πr2

360o

9 cm

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60o

B

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Q. Find the area of the major sector PQ below ?

connection

Sector Area

Sector angle

=

P

πr2

360o

10 m

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260o

100o

Q

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Now it’s your turn !

Maths in Action Ex 10.1 page 196

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Q1. Using the balancing method rearrange into x =

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Q2. True or false 2(x - 3) + 3x = 5x - 6

Q3.

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Pythagoras Theorem

SOHCAHTOA

Circumference is

Area is

Radius

Diameter

Sector area

Summary of Circle Topic

- line that bisects a chord
- Splits the chord into 2 equal halves.
- Makes right-angle with the chord.
- Passes through centre of the circle

Semi-circle angle is

always 90o

Tangent touches circle at one point

and make angle 90o with point of contact radius

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Created by Mr Lafferty

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