1. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty1 Isosceles Triangles in Circles Right angle in a Semi-Circle The Circle www.mathsrevision.com 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

2. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty2 Starter Questions Starter Questions www.mathsrevision.com Q1.Calculate Area and perimeter Q4.If a = 1, b = 2 and c = 4 Find Q3. Q2.30% of 200 5cm 2cm 3cm 4cm

3. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty3 www.mathsrevision.com To identify isosceles triangles within a circle. Aim of Today’s Lesson Isosceles triangles in Circles

4. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty4 When two radii are drawn to the ends of a chord, An isosceles triangle is formed. C A B www.mathsrevision.com Isosceles triangles in Circles

5. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty5 Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180 o www.mathsrevision.com Isosceles triangles in Circles

6. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty6 Q.Find the angle x o. A B C Solution Angle at C is equal to: Since the triangle is isosceles we have xoxo 280 o www.mathsrevision.com Isosceles triangles in Circles

7. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty7 Begin Maths in Action Book page 181 www.mathsrevision.com Isosceles triangles in Circles

8. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty8 Starter Questions Starter Questions www.mathsrevision.com

9. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty9 Semi-circle angle 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. Aim of Today’s Lesson www.mathsrevision.com

10. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty10 Semi-circle angle Tool-kit required 1.Protractor 2.Pencil 3.Ruler www.mathsrevision.com

11. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty11 1.Using your pencil trace round the protractor so that you have semi-circle. semi-circle. 2.Mark the centre of the semi-circle. You should have something like this. Semi-circle angle www.mathsrevision.com

12. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty12 Mark three points 1.Outside the circle x x x x x x x x x Semi-circle angle 2. On the circumference 3. Inside the circle www.mathsrevision.com

13. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty13 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 x Semi-circle angle Log your results in a table. InsideCircumferenceOutside www.mathsrevision.com

14. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty14 Inside Circumference Outside x Semi-circle angle x x < 90 o > 90 o = 90 o Begin Maths in Action Book page 182 www.mathsrevision.com

15. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty15 Starter Questions Starter Questions www.mathsrevision.com If a = 7 b = 4 and c = 10 Write down as many equations as you can e.g.a + b = 11

16. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty16 To understand what a tangent line is and its special property with the radius at the point of contact. Aim of Today’s Lesson Tangent line www.mathsrevision.com

17. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty17 Tangent line A tangent line is a line that touches a circle at only one point. Which of the lines are tangent to the circle? www.mathsrevision.com

18. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty18 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. www.mathsrevision.com

19. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty19 Tangent line Q.Find the length of the tangent line between A and B. A and B. A B 8 10 C Solution Right-angled at A since AC is the radius at the point of contact with the Tangent. By Pythagoras Theorem we have www.mathsrevision.com

20. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty20 Tangent line Begin Maths in Action Book page 185 www.mathsrevision.com

21. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty21 Starter Questions Starter Questions www.mathsrevision.com Q1.Calculate Area and perimeter Q4.If x = -1, y = 3 and z = 10 Find Q3. Q2.15% of 280 10cm 3cm 5cm 7cm

22. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty22 To understand some special properties when a diameter bisects a chord. Aim of Today’s Lesson Diameter symmetry www.mathsrevision.com

23. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty23 Diameter symmetry AB C D 1.A line drawn through the centre of a circle through the midpoint a chord will ALWAYS cut the chord at right-angles 2.A line drawn through the centre of a circle at right-angles to a chord will ALWAYS bisect that chord. 3.A line bisecting a chord at right angles will ALWAYS pass through the centre of a circle. O

24. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty24 Q.Find the length of the chord A and B. A B 6 O Solution By Pythagoras Theorem we have Diameter symmetry 4 Since yellow line bisect AB and passes through centre O, triangle is right-angle. Radius of the circle is 4 + 6 = 10. 10 Since AB is bisected The length of AB is www.mathsrevision.com

25. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty25 Begin Maths in Action Book page 187 Diameter symmetry www.mathsrevision.com

26. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty26 Starter Questions Q1. Q2. Q3. Calculate the area of the triangle Q4. 12 8 www.mathsrevision.com

27. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty27 Circumference of a circle Aim of Today’s Lesson To be able to use the formula for calculating the circumference of a circle www.mathsrevision.com

28. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty28 Main parts of the circle radius O Circumference Diameter www.mathsrevision.com Circumference of a circle

29. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty29 Q.Find the circumference of the circle ?Solution 4cm www.mathsrevision.com Circumference of a circle

30. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty30 Q. The circumference of the circle is 60cm ? Find the length of the diameter and radius.Solution www.mathsrevision.com Circumference of a circle

31. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty31 Now it’s your turn ! Begin Maths in Action Book page 190 www.mathsrevision.com Circumference of a circle

32. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty32 Starter Questions Q3. Q1.Calculate Q2. Make D the subject of the equation. Q4. Calculate www.mathsrevision.com

33. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty33 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. www.mathsrevision.com

34. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty34 Q. What is an arc ? A B Answer An arc is a fraction of the circumference. minor arc major arc www.mathsrevision.com length of the arc of a circle

35. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty35 Q. Find the circumference of the circle ?Solution 10cm Maths in Action Book Exercise 1 Questions 1 & 2 www.mathsrevision.com length of the arc of a circle

36. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty36 Q. Find the arc length for the semi-circle ? Solution 180 o www.mathsrevision.com length of the arc of a circle

37. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty37 Q. Given part of the circle below. Find the arc length ? Solution 10cm 90 o www.mathsrevision.com length of the arc of a circle

38. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty38 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. Step 3 Find the arc length. www.mathsrevision.com length of the arc of a circle

39. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty39 Solution 6cm 45 o Q. Part of a circle is given below. Find the arc length. Fraction of circle www.mathsrevision.com length of the arc of a circle

40. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty40 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. Step 3 Find the arc length. www.mathsrevision.com length of the arc of a circle

41. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty41 Q. Find the length of the arc AB below ? 9 cm 60 o A BSolution www.mathsrevision.com length of the arc of a circle

42. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty42 Now it’s your turn ! Begin Maths in Action Book page 193 www.mathsrevision.com length of the arc of a circle

43. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty43 Starter Questions Q1. Find all missing angles Q2. List the prime numbers between 10 and 20. Q3. Solve Q4. Calculate the area of the shape. 52 o 10cm 5cm 4cm www.mathsrevision.com

44. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty44 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 www.mathsrevision.com

45. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty45 2 3 4 1 2 3 4 5 6 7 8 1 5 6 7 8 If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. www.mathsrevision.com The Area of a circle

46. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty46 1 2 3 4 5 6 7 8 thinner and thinner sectors 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. www.mathsrevision.com The Area of a circle

47. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty47 But the area inside this rectangle is also the area of the circle www.mathsrevision.com The Area of a circle

48. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty48 Q.Find the area of the circle ?Solution 4cm www.mathsrevision.com The Area of a circle

49. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty49 The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q1-2 www.mathsrevision.com

50. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty50 Q. The diameter of the circle is 60cm. Find area of the circle?Solution www.mathsrevision.com The Area of a circle

51. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty51 The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q3-4 www.mathsrevision.com

52. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty52 Q. The area of a circle is 12.64 cm 2. Find its radius?Solution www.mathsrevision.com The Area of a circle

53. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty53 The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q5 onwards www.mathsrevision.com

54. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty54 Starter Questions Q3.Calculate Q1.Factorise Q2. Make h the subject of the equation. 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. www.mathsrevision.com

55. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty55 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. www.mathsrevision.com

56. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty56 Q. What is an sector area ? Sector area of a circle A B Answer Sector area is a fraction of the area of the whole circle. minor sector major sector www.mathsrevision.com

57. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty57 Sector area of a circle Q. Find the area of the circle ?Solution 10cm www.mathsrevision.com

58. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty58 Q. Find the sector area for the semi-circle ? Solution Sector area of a circle 180 o 10cm www.mathsrevision.com

59. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty59 Q. Given part of the circle below. Find the sector area ? Solution Sector area of a circle www.mathsrevision.com

60. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty60 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. Step 3 Find the sector area. www.mathsrevision.com

61. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty61 Solution 6cm Sector area of a circle 45 o Q. Part of a circle is given below. Find the sector area. Fraction of circle www.mathsrevision.com

62. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty62 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. Step 3 Find the sector area. www.mathsrevision.com

63. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty63 Q. Find the area of the sector below ? Sector area of a circle Solution www.mathsrevision.com

64. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty64 Sector area of a circle Now it’s your turn ! Begin Maths in Action Book page 196 www.mathsrevision.com

65. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty 65 Starter Questions 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. 115 o www.mathsrevision.com

66. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty66 Area is Summary of Circle Topic Circumference is Sector area Arc length is Diamete r Radius line that bisects a chord 1.Splits the chord into 2 equal halves. 2.Makes right-angle with the chord. 3.Passes through centre of the circle Pythagoras Theorem SOHCAHTOA Semi-circle angle is always 90 o Tangent touches circle at one point and make angle 90 o with point of contact radius www.mathsrevision.com

67. S3 Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Tuesday, 18 August 2015Created by Mr Lafferty67 Summary of Circle Topic Maths in Action Book Page 199 www.mathsrevision.com