1. The Circle www.mathsrevision.com Isosceles Triangles in Circles
Right angle in a Semi-Circle
Tangent Line to a Circle
Diameter Symmetry in a Circle
Circumference of a Circle
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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2. Starter Questions www.mathsrevision.com
Q1. Calculate Area and perimeter
5cm
2cm
3cm
4cm
Q2. 30% of 200
Q3.
Q4. If a = 1 , b = 2 and c = 4
Find
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3. Isosceles triangles in Circles
Aim of Today’s Lesson
To identify isosceles triangles
within a circle.
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4. Isosceles triangles in Circles
When two radii are drawn to the ends of a chord,
An isosceles triangle is formed. A B C
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5. Isosceles triangles in Circles
Special Properties of Isosceles Triangles
Two equal lengths
Two equal angles
Angles in any triangle sum to 180o
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6. Isosceles triangles in Circles
Q. Find the angle xo.
Solution
Angle at C is equal to: B xo C
Since the triangle is isosceles
we have A
280o
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7. Isosceles triangles in Circles
Begin Maths in Action Book page 181
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8. Starter Questions www.mathsrevision.com
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9. Semi-circle angle Aim of Today’s 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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10. Semi-circle angle www.mathsrevision.com Tool-kit required
1. Protractor
2. Pencil
3. Ruler
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11. Semi-circle angle www.mathsrevision.com
1. Using your pencil trace round
the protractor so that you have
semi-circle.
2. Mark the centre of the semi-circle.
You should have
something like this.
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12. Semi-circle angle x x x www.mathsrevision.com x x 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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13. Semi-circle angle Log your results in a table. www.mathsrevision.com 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
Log your results in a table.
Inside
Circumference
Outside
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14. Begin Maths in Action Book page 182
Semi-circle angle x x x
Inside
Circumference
Outside
< 90o
= 90o
> 90o
Begin Maths in Action Book page 182
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15. Write down as many equations as you can
Starter Questions
If a = 7 b = 4 and c = 10
Write down as many equations as you can
e.g. a + b = 11
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16. Tangent line Aim of Today’s Lesson
To understand what a tangent line is
and its special property with the
radius at the point of contact.
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17. Tangent line www.mathsrevision.com A tangent line is a line that
touches a circle at only one point.
Which of the
lines are
tangent to
the circle?
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18. Tangent line www.mathsrevision.com
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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19. Tangent line www.mathsrevision.com
Q. Find the length of the tangent line between
A and B.
Solution
Right-angled at A since
AC is the radius at the point
of contact with the
Tangent. B 10
By Pythagoras Theorem we have A C 8
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20. Begin Maths in Action Book page 185
Tangent line
Begin Maths in Action Book page 185
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21. Starter Questions www.mathsrevision.com
Q1. Calculate Area and perimeter
10cm
3cm
5cm
7cm
Q2. 15% of 280
Q3.
Q4. If x = -1 , y = 3 and z = 10
Find
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22. Diameter symmetry Aim of Today’s Lesson To understand
some special properties
when a diameter bisects a chord.
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23. Diameter symmetry C D O A B
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 B
A line bisecting a chord at right angles
will ALWAYS pass through the centre of a circle.
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24. Diameter symmetry www.mathsrevision.com
Q. Find the length of the chord A and B.
Solution
Radius of the circle is = 10. B
Since yellow line bisect AB and passes
through centre O, triangle is right-angle. 10 O
By Pythagoras Theorem we have 4 6
Since AB is bisected
The length of AB is A
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25. Begin Maths in Action Book page 187
Diameter symmetry
Begin Maths in Action Book page 187
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26. Starter Questions www.mathsrevision.com Q1. Q2.12 8
Q3. Calculate the area of the triangle
Q4.
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27. Circumference of a circle
Aim of Today’s Lesson
To be able to use the formula
for calculating
the circumference of a circle
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28. Circumference of a circle
Main parts of the circle
radius O
Diameter
Circumference
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29. Circumference of a circle
Q. Find the circumference of the circle ?
Solution
4cm
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30. Circumference of a circle
The circumference of the circle is 60cm ?
Find the length of the diameter and radius.
Solution
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31. Circumference of a circle
Now it’s your turn !
Begin Maths in Action Book page 190
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32. Starter Questions www.mathsrevision.com Q1. Calculate
Q2. Make D the subject of the equation.
Q3.
Q4. Calculate
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33. length of the arc of a circle
Aim of Today’s Lesson
To find and be able to use the formula
for calculating the length of an arc.
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34. length of the arc of a circle
Q. What is an arc ?
Answer
An arc is a fraction
of the circumference. A
minor arc
major arc B
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35. length of the arc of a circle
Q. Find the circumference of the circle ?
Solution
10cm
Maths in Action Book Exercise 1 Questions 1 & 2
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36. length of the arc of a circle
Q. Find the arc length for the semi-circle ?
Solution
180o
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37. length of the arc of a circle
Q. Given part of the circle below. Find the arc length ?
Solution
10cm
90o
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38. length of the arc of a circle
3 step process to calculating the length of an arc.
Step Find the circumference of the circle.
Step 2 Find fraction of the whole circle.
Step 3 Find the arc length.
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39. length of the arc of a circle
Q. Part of a circle is given below. Find the arc length.
Fraction of circle
6cm
45o
Solution
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40. length of the arc of a circle
3 step process to calculating the length of an arc.
Step Find the circumference of the circle.
Step 2 Find fraction of the whole circle.
Step 3 Find the arc length.
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41. length of the arc of a circle
Q. Find the length of the arc AB below ?
Solution A
9 cm
60o B
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42. length of the arc of a circle
Now it’s your turn !
Begin Maths in Action Book page 193
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43. Starter Questions www.mathsrevision.com Q1. Find all missing angles
Q2. List the prime numbers
between 10 and 20.
Q3. Solve
4cm
Q4. Calculate the area of the shape.
5cm
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10cm

44. The Area of a circle Aim of Today’s Lesson
To come up with and be able to use
the formula for calculating
the area of a circle
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45. And lay them out side by side
The Area of a circle
If we break the circle
into equal sectors
And lay them out side by side
We get very close
to a rectangle. 1 2 3 4 5 6 7 8 5 6 7 8 2 4 3 1
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46. The Area of a circle www.mathsrevision.com 8 2 4 6 3 1 5 7
If we cut the sectors
Thinner and thinner then
we get closer and closer
to a rectangle. Hence we can represent the area of a circle
by a rectangle. 1 2 3 4 5 6 7 8
thinner and thinner
sectors
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47. The Area of a circle www.mathsrevision.com
But the area inside this rectangle is also the area of the circle
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48. The Area of a circle www.mathsrevision.com
Q. Find the area of the circle ?
Solution
4cm
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49. Begin Maths in Action Book
The Area of a circle
Now it’s your turn !
Begin Maths in Action Book
Ex9.1 page 194 Q1-2
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50. The Area of a circle www.mathsrevision.com Find area of the circle?
The diameter of the circle is 60cm.
Find area of the circle?
Solution
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51. Begin Maths in Action Book
The Area of a circle
Now it’s your turn !
Begin Maths in Action Book
Ex9.1 page 194 Q3-4
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52. The Area of a circle www.mathsrevision.com Find its radius?
The area of a circle is cm2.
Find its radius?
Solution
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53. Begin Maths in Action Book
The Area of a circle
Now it’s your turn !
Begin Maths in Action Book
Ex9.1 page 194 Q5 onwards
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54. Starter Questions www.mathsrevision.com Q1. Factorise
Q2. Make h the subject of the equation.
Q3. Calculate
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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55. Sector area of a circle Aim of Today’s Lesson
To find and be able to use the formula
for calculating the sector of an circle.
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56. Sector area is a fraction
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
minor sector
major sector B
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57. Sector area of a circle www.mathsrevision.com
Q. Find the area of the circle ?
Solution
10cm
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58. Sector area of a circle www.mathsrevision.com
Q. Find the sector area for the semi-circle ?
Solution
10cm
180o
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59. Sector area of a circle www.mathsrevision.com
Q. Given part of the circle below. Find the sector area ?
Solution
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60. Sector area of a circle www.mathsrevision.com
3 step process to calculating sector area of a circle.
Step Find the area of the circle.
Step 2 Find fraction of the whole circle.
Step 3 Find the sector area.
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61. Sector area of a circle www.mathsrevision.com
Q. Part of a circle is given below. Find the sector area.
Fraction of circle
6cm
45o
Solution
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62. Sector area of a circle www.mathsrevision.com
3 step process for calculating the sector area.
Step Find the area of the circle.
Step 2 Find fraction of the whole circle.
Step 3 Find the sector area.
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63. Sector area of a circle www.mathsrevision.com
Q. Find the area of the sector below ?
Solution
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64. Begin Maths in Action Book page 196
Sector area of a circle
Now it’s your turn !
Begin Maths in Action Book page 196
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65. Starter Questions www.mathsrevision.com 115o
Q1. Find all the missing angles
Q2. Calculate
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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66. Summary of Circle Topic
Arc length is
Pythagoras Theorem
SOHCAHTOA
line that bisects a chord
Splits the chord into 2 equal halves.
Makes right-angle with the chord.
Passes through centre of the circle
Circumference is
Semi-circle angle is
always 90o
Area is
Tangent touches circle at one point
and make angle 90o with point of contact radius
Radius
Diameter
Sector area
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67. Summary of Circle Topic
Maths in Action Book Page 199
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