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. Calculate Area and perimeter
Q2. 30 of 200
Q3.
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Q4. If a 1 , b 2 and c 4 Find
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Isosceles triangles in Circles
Aim of Todays Lesson
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.
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C
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Isosceles triangles in Circles
Special Properties of Isosceles Triangles
Two equal lengths
Two equal angles
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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
Since the triangle is isosceles we have
A
280o
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Isosceles triangles in Circles
Begin Maths in Action Book page 181
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Starter Questions
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Semi-circle angle
Aim of Todays Lesson
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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Semi-circle angle
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
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.
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
Begin Maths in Action Book page 185
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Starter Questions
Q1. Calculate Area and perimeter
Q2. 15 of 280
Q3.
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Q4. If x -1 , y 3 and z 10 Find
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Diameter symmetry
Aim of Todays Lesson
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.

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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
Begin Maths in Action Book page 187
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Starter Questions
Q1.
Q2.
Q3. Calculate the area of the triangle
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Q4.
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Circumference of a circle
Aim of Todays Lesson To be able 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 ! Begin Maths in Action Book
page 190
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Starter Questions
Q1. Calculate
Q2. Make D the subject of the equation.
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Q3.
Q4. Calculate
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length of the arc of a circle
Aim of Todays Lesson To find and be able to use
the formula for calculating the length of an arc.
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length of the arc 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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length of the arc of a circle
Q. Find the circumference of the circle ?
10cm
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Maths in Action Book Exercise 1 Questions 1 2
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length of the arc of a circle
Q. Find the arc length for the semi-circle ?
Solution
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180o
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length of the arc of a circle
Q. Given part of the circle below. Find the arc
length ?
10cm
90o
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length of the arc of a circle
3 step process to calculating the length of an
arc.
Step 1 Find the circumference of the circle.
Step 2 Find fraction of the whole circle.
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Step 3 Find the arc length.
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length of the arc of a circle
Q. Part of a circle is given below. Find the arc
length.
Fraction of circle
6cm
45o
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length of the arc of a circle
3 step process to calculating the length of an
arc.
Step 1 Find the circumference of the circle.
Step 2 Find fraction of the whole circle.
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Step 3 Find the arc length.
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length of the arc of a circle
Q. Find the length of the arc AB below ?
A
9 cm
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60o
B
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length of the arc of a circle
Now its your turn ! Begin Maths in Action Book
page 193
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Starter Questions
52o
Q1. Find all missing angles
Q2. List the prime numbers between 10 and
20.
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Q3. Solve
4cm
Q4. Calculate the area of the shape.
5cm
10cm
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The Area of a circle
Aim of Todays Lesson To come up with and be
able 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 ! Begin Maths in Action Book
Ex9.1 page 194 Q3-4
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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. Factorise
Q2. Make h the subject of the equation.
Q3. Calculate
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Q4. The value of the standard deviation for
petrol prices in Glasgow is 2.1 and 1.9 for
Edinburgh. Comparing the two values write down a
valid statement.
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Sector area of a circle
Aim of Todays Lesson To find and be able to use
the formula for calculating the sector of an
circle.
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Sector area of a circle
Q. What is an sector area ?
Answer Sector area is a fraction of the area of
the whole circle.
A
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B
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Sector area of a circle
Q. Find the area of the circle ?
10cm
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Sector area of a circle
Q. Find the sector area for the semi-circle ?
Solution
10cm
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180o
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Sector area of a circle
Q. Given part of the circle below. Find the
sector area ?
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Sector area of a circle
3 step process to calculating sector area of a
circle.
Step 1 Find the area of the circle.
Step 2 Find fraction of the whole circle.
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Step 3 Find the sector area.
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Sector area of a circle
Q. Part of a circle is given below. Find the
sector area.
Fraction of circle
6cm
45o
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Sector area of a circle
3 step process for calculating the sector area.
Step 1 Find the area of the circle.
Step 2 Find fraction of the whole circle.
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Step 3 Find the sector area.
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Sector area of a circle
Q. Find the area of the sector below ?
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Sector area of a circle
Now its your turn ! Begin Maths in Action Book
page 196
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Starter Questions
Q1. Find all the missing angles
Q2. Calculate
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Q3. The cost of a new computer is 1000 vat. If
the vat is charged at 12 what is the total cost.
Q4. The cost of a bag of sugar is 1.12. How
much 50 bags cost.
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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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