The Circle

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The Circle
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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Starter Questions
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 Todays 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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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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Starter Questions
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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Semi-circle angle
Aim of Todays 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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Semi-circle angle
Tool-kit required
1. Protractor
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2. Pencil
3. Ruler
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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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Semi-circle angle
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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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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Semi-circle angle
DEMO
x
x
x
90o
gt 90o
lt 90o
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Begin Maths in Action Book page 182
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Starter Questions
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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Tangent line
Aim of Todays 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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Tangent line
A tangent line is a line that touches a circle
at only one point.
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Tangent line
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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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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Tangent line
Maths in Action Ex 4.1 page 185
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Starter Questions
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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Diameter symmetry
Aim of Todays Lesson
We are learning to understand some special
properties when a diameter bisects a chord.
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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
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Diameter symmetry
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
6
4
Since AB is bisected The length of AB is
A
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Diameter symmetry
Maths in Action Ex 5.1 Ex 5.2 page 187
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Starter Questions
Q1.
Q2.
Q3. Explain why the area of the triangle
is 48m2
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Q4.
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Circumference of a circle
Aim of Todays Lesson We are learning to use the
formula for calculating the circumference of a
circle
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Circumference of a circle
Main parts of the circle
O
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Circumference of a circle
Q. Find the circumference of the circle ?
4cm
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Circumference of a circle

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

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Circumference of a circle
Now its your turn ! Maths in Action Ex 7.1 page
191
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Starter Questions
Q1. True or false
Q2. Using the balancing method rearrange into D

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Q3.
Q4. Calculate
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length of the arc of a circle
Aim of Todays Lesson We are learning to use the
formula for calculating the length of an arc.
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Arc length of a circle
Q. What is an arc ?
Answer An arc is a fraction of the circumference.
A
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B
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Arc length of a circle
Q. Find the circumference of the circle ?
10cm
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Arc length of a circle
Q. Find the length of the minor arc XY below ?
x
Arc length
Arc angle

connection
pD
360o
y
6 cm
45o
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360o
DEMO
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Arc length of a circle
Q. Find the length of the minor arc AB below ?
connection
A
9 cm
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60o
B
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Arc length of a circle
Q. Find the length of the major arc PQ below ?
connection
P
10 m
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100o
260o
Q
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length of the arc of a circle
Now its your turn ! Maths in Action Ex 8.1 page
193
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Starter Questions
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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The Area of a circle
Aim of Todays Lesson We are learning to use
the formula for calculating the area of a circle
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The Area of a circle
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The Area of a circle
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The Area of a circle
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But the area inside this rectangle is also the
area of the circle
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The Area of a circle
Q. Find the area of the circle ?
4cm
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The Area of a circle
Now its your turn ! Begin Maths in Action Book
Ex9.1 page 194 Q1-2
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The Area of a circle

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

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The Area of a circle
Now its your turn ! Maths in Action Ex9.1
page 194
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The Area of a circle

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

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The Area of a circle
Now its your turn ! Begin Maths in Action Book
Ex9.1 page 194 Q5 onwards
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Starter Questions
Q1. Find the missing numbers
Q2. Using the balancing method rearrange into x
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Q3. Calculate
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Sector area of a circle
Aim of Todays Lesson We are learning to use the
formula for calculating the sector of an circle.
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Area of Sector in a circle
A
B
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Area of Sector in a circle
Q. Find the area of the circle ?
10cm
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Area of Sector in a circle
Find the area of the minor sector XY below ?
x
connection
Area Sector
Sector angle

y
pr2
360o
6 cm
45o
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360o
DEMO
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Area of Sector in a circle
Q. Find the area of the minor sector AB below ?
connection
A
9 cm
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60o
B
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Area of Sector in a circle
Q. Find the area of the major sector PQ below ?
connection
P
10 m
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260o
100o
Q
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Sector area of a circle
Now its your turn ! Maths in Action Ex 10.1
page 196
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Starter Questions
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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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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Summary of Circle Topic
Maths in Action Book Page 199
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