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Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty 1 The Circle www.mathsrevision.com Finding an ARC length.

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Presentation on theme: "Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty 1 The Circle www.mathsrevision.com Finding an ARC length."— Presentation transcript:

1 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty 1 The Circle Finding an ARC length Finding the area of a SECTOR Finding the centre angle given ARC length Finding the centre angle given SECTOR area Mixed questions Exam questions Isosceles Triangles in Circles Right angle in a Semi-Circle Tangent Line to a Circle The Tangent Kite

2 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty2 Starter Questions Q1. True or false Q2. How many degrees in one eighth of a circle. Q3. After a discount of 20% an iPod is £160. How much was it originally.

3 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty3 To identify isosceles triangles within a circle. Aim of Today’s Lesson Isosceles triangles in Circles

4 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty4 When two radii are drawn to the ends of a chord, An isosceles triangle is formed. C AB Isosceles triangles in Circles x o x o DEMO

5 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty5 Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180 o Isosceles triangles in Circles

6 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 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 Isosceles triangles in Circles

7 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty7 Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180 o Isosceles triangles in Circles

8 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty8 Q.Find the length of the chord A and B. A B 6 O Solution By Pythagoras Theorem we have Isosceles triangles in Circles 4 Since yellow line bisect AB and passes through centre O, triangle is right-angle. Radius of the circle is = Since AB is bisected The length of AB is

9 Level 4 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N4+ TJ Ex18.1 Ch18 (page 139) Isosceles triangles in Circles

10 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty10 Starter Questions Q1. Explain how we solve Q2. How many degrees in one tenth of a circle. Q3. After a discount of 40% a Digital Radio is £120. Explain why the originally price was £200.

11 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty11 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

12 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty12 Semi-circle angle Tool-kit required 1.Protractor 2.Pencil 3.Ruler

13 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty13 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

14 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty14 Mark three points 1.Outside the circle x x x x x x x x x 2. On the circumference 3. Inside the circle Semi-Circle Angle

15 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty15 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 Log your results in a table. InsideCircumferenceOutside DEMO Semi-Circle Angle

16 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty16 Inside Circumference Outside x x x < 90 o > 90 o = 90 o Begin Maths in Action Book page 182 DEMO Semi-Circle Angle

17 Level 4 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N4+ TJ Ex18.2 Ch18 (page 141) Semi-Circle Angle

18 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty18 Starter Questions Starter Questions If a = 7 b = 4 and c = 10 Write down as many equations as you can e.g.a + b = 11

19 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty19 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

20 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty20 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?

21 Level 4 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty21 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. DDDD EEEE MMMM OOOO

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24 Level 4 Right-angled at A since AC is the radius at the point of contact with the Tangent. Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty24 Tangent line Q.Find the length of the tangent line between A and B. A and B. A B 8 10 C Solution By Pythagoras Theorem we have

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26 Level 4 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N4+ TJ Ex18.3 Ch18.3 (page 143) Tangent Line

27 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty27 Starter Questions Q1. True or false Q2. Expand out (x + 3)(x – 2)

28 National 5 Tangent Kite 1-May-15Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know the properties of tangent kites. We are learning properties of a tangent kite. 2.Be able to calculate lengths and angles related to a tangent kite.

29 1-May-15 Compiled by Mr. Lafferty Maths Dept. Tangent Kite A tangent kite has two right-angles A tangent kite is made up of two congruent triangles

30 1-May-15 Compiled by Mr. Lafferty Maths Dept. Tangent Kite Find all angles in the tangent kite. 42 o 90 o 90 o 138 o A B C

31 1-May-15 Compiled by Mr. Lafferty Maths Dept. Tangent Kite Find the area of the circle. 40cm 50cm Using Pythagoras Theorem r r 2 = r 2 = r 2 = 900 r = 30cm √ A = πr 2 A = π(30) 2 A = 2827cm 2

32 Level 4 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N4+ TJ Ex18.4 Ch18.3 (page 145) Tangent Line

33 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty33 Starter Questions Q1. True or false Q2. Expand out (x + 3)(x – 9) Q3. I want to make 30% profit on a DVD player I bought for £80. How much must I sell it for.

34 National 5 Arc length of a circle 1-May-15Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know the arc length formula. We are learning to use the arc length formula. 2.Be able to calculate arc length showing appropriate work.

35 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty35 Q. What is an arc ? A B Answer An arc is a fraction of the circumference. minor arc major arc Arc length of a circle

36 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty36 Q. Find the circumference of the circle ?Solution 10cm Arc length of a circle

37 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty37 Arc length of a circle Arc length πD Arc angle 360 o = Q. Find the length of the minor arc XY below ? 6 cm 45 o x y 360 o connection DEMO

38 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty38 Arc length of a circle Arc length πDπD Arc angle 360 o = Q. Find the length of the minor arc AB below ? 9 cm 60 o A B connection

39 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty39 Arc length of a circle Arc length πDπD Arc angle 360 o = Q. Find the length of the major arc PQ below ? 10 m 100 o P Q connection 260 o

40 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N5 TJ Ex13.1 Ch13 (page 126) Nat 5 Arc length of a circle

41 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty41 Starter Questions Q1. True or false Q2. Expand out (x + 3)(x – 9) Q3. I want to make 30% profit on a DVD player I bought for £80. How much must I sell it for.

42 Sector area of a circle 1-May-15 Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know the sector formula. We are learning how to find the area of a sector. 2.Be able to calculate sector area showing appropriate work. Nat 5

43 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty43 A B major sector Area of Sector in a circle minor sector

44 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty44 Q. Find the area of the circle ?Solution 10cm Area of Sector in a circle

45 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty45 Area Sector πr 2 Sector angle 360 o = Find the area of the minor sector XY below ? 6 cm 45 o x y 360 o connection Area of Sector in a circle DEMO

46 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty46 Area Sector πr2πr2 Sector angle 360 o = Q. Find the area of the minor sector AB below ? 9 cm A B connection Area of Sector in a circle 60 o

47 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty47 Area of Sector in a circle Sector Area πr2πr2 Sector angle 360 o = Q. Find the area of the major sector PQ below ? 10 m 100 o P Q connection 260 o

48 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N5 TJ Ex13.2 Ch13 (page 127) Nat 5 Arc length of a circle

49 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty49 Starter Questions Q3. Q1. Using the balancing method rearrange into x = Q2. True or false 2(x - 3) + 3x = 5x - 6

50 Mixed Question 1-May-15 Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Identify appropriate formula to use. We are doing mixed questions on the circle. 2.Be able to calculate sector / arc showing appropriate work. Nat 5

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55 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N5 TJ Ex13.3 Ch13 (page 128) Nat 5 Arc length of a circle

56 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty56 Starter Questions Rearrange the formula below into x o =

57 1-May-15 Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know formula. We are learning how to find the centre angle given the arc length. 2.Be able to calculate centre angle showing appropriate work. Nat 5 Centre Angle (Arc length)

58 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty58 Arc length πD Arc angle 360 o = Find the centre angle x o given the arc length is 4.71cm 2. 6 cm 45 o x y connection Centre Angle (Arc length)

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60 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N5 TJ Ex13.4 Ch13 (page 129) Nat 5 Centre Angle (Arc length)

61 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty61 Starter Questions Rearrange the formula below into x o =

62 Centre Angle (A o S) 1-May-15 Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know formula. We are learning how to find the centre angle given the sector area. 2.Be able to calculate centre angle showing appropriate work. Nat 5

63 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty63 Area Sector πr2πr2 Sector angle 360 o = Find the angle x o given that the sector area is 42.41cm 2. 9 cm A B connection Centre Angle (A o S) xoxo

64 National 5 Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Friday, 01 May 2015Created by Mr Lafferty64 Area Sector πr2πr2 Sector angle 360 o = Find the angle x o given that the sector area is 51.3mm 2. 7 mm A B connection Centre Angle (A o S) xoxo

65 1-May-15Compiled by Mr. Lafferty Maths Dept. Now try N5 TJ Ex13.5 Ch13 (page 130) Nat 5 Centre Angle (A o S)

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