# National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty1 Isosceles Triangles.

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National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty2 Starter Questions Q3. Q1. True or false Q2. How many degrees in one eighth of a circle. Q4. After a discount of 20% an iPod is £160. How much was it originally. www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty3 www.mathsrevision.com We are learning to identify isosceles triangles within a circle. Aim of Today’s Lesson Isosceles Triangles in Circles

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty4 When two radii are drawn to the ends of a chord, an isosceles triangle is formed. C AB www.mathsrevision.com Isosceles triangles in Circles x o x o DEMO

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty7 Maths in Action Ex 2.1 page 181 www.mathsrevision.com Isosceles triangles in Circles

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty8 Starter Questions Q3. Q1. Explain how we solve Q2. How many degrees in one tenth of a circle. Q4. After a discount of 40% a Digital Radio is £120. Explain why the originally price was £200. www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty9 Semi-circle angle 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. Aim of Today’s Lesson www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty10 Semi-circle angle Tool-kit required 1.Protractor 2.Pencil 3.Ruler www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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 DEMO

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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 DEMO

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty16 We are learning 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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 DDDD EEEE MMMM OOOO

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty20 Tangent line Maths in Action Ex 4.1 page 185 www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty21 Starter Questions Q2. Q1. Using FOIL multiply out (x 2 + 4x - 3)(x + 1) Q3. I want to make 15% profit on a computer I bought for £980. How much must I sell it for. www.mathsrevision.com Using a multiplication table expand out (x 2 + 4x - 3)(x + 1)

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty22 We are learning to understand some special properties when a diameter bisects a chord. Aim of Today’s Lesson Diameter symmetry www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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 DEMO

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty25 Maths in Action Ex 5.1 & Ex 5.2 page 187 Diameter symmetry www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty26 Starter Questions Q1. Q2. Q3. Explain why the area of the triangle is 48m 2 Q4. 12m 8m www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty27 Circumference of a circle Aim of Today’s Lesson We are learning to use the formula for calculating the circumference of a circle www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty28 Main parts of the circle radius O Circumference Diameter www.mathsrevision.com Circumference of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty29 Q.Find the circumference of the circle ?Solution 4cm www.mathsrevision.com Circumference of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty31 Now it’s your turn ! Maths in Action Ex 7.1 page 191 www.mathsrevision.com Circumference of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty32 Starter Questions Q3. Q1.True or false Q2. Using the balancing method rearrange into D = Q4. Calculate www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty33 length of the arc of a circle Aim of Today’s Lesson We are learning to use the formula for calculating the length of an arc. www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created 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 Arc length of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty35 Q. Find the circumference of the circle ?Solution 10cm www.mathsrevision.com Arc length of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty36 www.mathsrevision.com 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty37 www.mathsrevision.com 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty38 www.mathsrevision.com 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty39 Now it’s your turn ! Maths in Action Ex 8.1 page 193 www.mathsrevision.com length of the arc of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty40 Starter Questions Q3. Q1. True or false Q2. Expand out (x + 3)(x 2 + 40 – 9) Q4. I want to make 30% profit on a DVD player I bought for £80. How much must I sell it for. www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty41 The Area of a circle Aim of Today’s Lesson We are learning to use the formula for calculating the area of a circle www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty42 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty43 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty44 But the area inside this rectangle is also the area of the circle www.mathsrevision.com The Area of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty45 Q.Find the area of the circle ?Solution 4cm www.mathsrevision.com The Area of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty46 The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q1-2 www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty47 Q. The diameter of the circle is 60cm. Find area of the circle?Solution www.mathsrevision.com The Area of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty48 The Area of a circle Now it’s your turn ! Maths in Action Ex9.1 page 194 www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty49 Q. The area of a circle is 12.64 cm 2. Find its radius?Solution www.mathsrevision.com The Area of a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty50 The Area of a circle Now it’s your turn ! Begin Maths in Action Book Ex9.1 page 194 Q5 onwards www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty51 Starter Questions Q3.Calculate Q1.Find the missing numbers Q2. Using the balancing method rearrange into x = www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty52 Sector area of a circle Aim of Today’s Lesson We are learning to use the formula for calculating the sector of an circle. www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty53 A B major sector www.mathsrevision.com Area of Sector in a circle minor sector

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty54 Q. Find the area of the circle ?Solution 10cm www.mathsrevision.com Area of Sector in a circle

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty55 www.mathsrevision.com 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty56 www.mathsrevision.com 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty57 www.mathsrevision.com 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty58 Sector area of a circle Now it’s your turn ! Maths in Action Ex 10.1 page 196 www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty59 Starter Questions Q3. Q1. Using the balancing method rearrange into x = Q2. True or false 2(x - 3) + 3x = 5x - 6 www.mathsrevision.com

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty60 Area is Summary of Circle Topic Circumference is Sector area Arc length is Diameter 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

National 5 Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Thursday, 11 December 2014Created by Mr Lafferty61 Summary of Circle Topic Maths in Action Book Page 199 www.mathsrevision.com

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