The Circle www mathsrevision com Isosceles Triangles in

The Circle www. mathsrevision. com Isosceles Triangles in Circles Right angle in a Semi-Circle Tangent Line to a Circle The Tangent Kite Finding an ARC length Finding the area of a SECTOR Mixed questions Finding the centre angle given ARC length Finding the centre angle given SECTOR area Exam questions Monday, November 30, 2020 Created by Mr Lafferty 1

Starter Questions www. mathsrevision. com Level 4 Q 1. True or false Q 2. How many degrees in one eighth of a circle. Q 3. After a discount of 20% an i. Pod is £ 160. How much was it originally. Monday, November 30, 2020 Created by Mr Lafferty 2

www. mathsrevision. com Level 4 Isosceles triangles in Circles Aim of Today’s Lesson To identify isosceles triangles within a circle. Monday, November 30, 2020 Created by Mr Lafferty 3

www. mathsrevision. com Level 4 Isosceles triangles in Circles When two radii are drawn to the ends of a chord, An isosceles triangle is formed. Demo A xo xo B C Monday, November 30, 2020 Created by Mr Lafferty 4

www. mathsrevision. com Level 4 Isosceles triangles in Circles Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180 Monday, November 30, 2020 Created by Mr Lafferty o 5

Isosceles triangles in Circles www. mathsrevision. com Level 4 Q. o Find the angle x. Solution Angle at C is equal to: B Since the triangle is isosceles A x we have Monday, November 30, 2020 Created by Mr Lafferty o C 280 o 6

www. mathsrevision. com Level 4 Isosceles triangles in Circles Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180 Monday, November 30, 2020 Created by Mr Lafferty o 7

Isosceles triangles in Circles www. mathsrevision. com Level 4 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 10 through centre O, triangle is right-angle. O By Pythagoras Theorem we have 6 4 Since AB is bisected The length of AB is Monday, November 30, 2020 Created by Mr Lafferty A 8

Isosceles triangles in Circles www. mathsrevision. com Level 4 Now try N 4+ TJ Ex 18. 1 Ch 18 (page 139) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com Level 4 Q 1. Explain how we solve Q 2. How many degrees in one tenth of a circle. Q 3. After a discount of 40% a Digital Radio is £ 120. Explain why the originally price was £ 200. Monday, November 30, 2020 Created by Mr Lafferty 10

Semi-circle angle www. mathsrevision. com Level 4 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. Monday, November 30, 2020 Created by Mr Lafferty 11

Semi-circle angle www. mathsrevision. com National 5 Tool-kit required 1. Protractor 2. Pencil 3. Ruler Monday, November 30, 2020 Created by Mr Lafferty 12

Semi-circle angle www. mathsrevision. com Level 4 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. Monday, November 30, 2020 Created by Mr Lafferty 13

Semi-Circle Angle www. mathsrevision. com Level 4 x Mark three points 1. 2. Outside the circle On the circumference 3. Inside the circle Monday, November 30, 2020 x x x Created by Mr Lafferty x x 14

Semi-Circle Angle www. mathsrevision. com Level 4 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 Demo Log your results in a table. Outside Monday, November 30, 2020 Circumference Created by Mr Lafferty Inside 15

Semi-Circle Angle www. mathsrevision. com Level 4 x Demo Outside < 90 o Circumference o = 90 Monday, November 30, 2020 x x Inside > 90 o Created by Mr Lafferty 16

Outer Circumference Circle 1 Circle 2 Circle 3 Circle Circumference Angle - Investigation Worksheet Inner

Semi-Circle Angle www. mathsrevision. com Level 4 Now try N 4+ TJ Ex 18. 2 Ch 18 (page 141) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com Level 4 If a = 7 b = 4 and c = 10 Write down as many equations as you can e. g. a + b = 11 Monday, November 30, 2020 Created by Mr Lafferty 19

Tangent line www. mathsrevision. com Level 4 Aim of Today’s Lesson To understand what a tangent line is and its special property with the radius at the point of contact. Monday, November 30, 2020 Created by Mr Lafferty 20

Tangent line www. mathsrevision. com Level 4 A tangent line is a line that touches a circle at only one point. Which of the lines are tangent to the circle? Monday, November 30, 2020 Created by Mr Lafferty 21

Tangent line www. mathsrevision. com Level 4 The radius of the circle that touches the tangent line is called the point of contact radius. Demo Special Property The point of contact radius is always perpendicular (right-angled) to the tangent line. Monday, November 30, 2020 Created by Mr Lafferty 22

Tangent line www. mathsrevision. com Level 4 Q. Find the length of the tangent line between A and B. Solution B Right-angled at A since AC is the radius at the point 10 of contact with the Tangent. By Pythagoras Theorem we have A C 8 Monday, November 30, 2020 Created by Mr Lafferty 25

Tangent Line www. mathsrevision. com Level 4 Now try N 4+ TJ Ex 18. 3 Ch 18. 3 (page 143) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 5 Q 1. True or false Q 2. Expand out (x + 3)(x – 2) Monday, November 30, 2020 Created by Mr Lafferty 28

Tangent Kite www. mathsrevision. com National 5 Learning Intention We are learning properties of a tangent kite. Success Criteria 1. Know the properties of tangent kites. 2. Be able to calculate lengths and angles related to a tangent kite. 30 -Nov-20 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 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Tangent Kite A 90 o 138 o 42 o 90 o B Find all angles in the tangent kite. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept. C

Tangent Kite r Using Pythagoras Theorem r 2 = 502 - 402 r 2 = 2500 - 1600 √ 30 -Nov-20 r 2 = 900 r = 30 cm A = πr 2 A = π(30)2 A = 2827 cm 2 Compiled by Mr. Lafferty Maths Dept. 50 cm Find the area of the circle. 40 cm

Tangent Line www. mathsrevision. com Level 4 Now try N 4+ TJ Ex 18. 4 Ch 18. 3 (page 145) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 5 Q 1. True or false Q 2. Expand out (x + 3)(x 2 + 40 – 9) Q 3. I want to make 30% profit on a DVD player I bought for £ 80. How much must I sell it for. Monday, November 30, 2020 Created by Mr Lafferty 34

Arc length of a circle www. mathsrevision. com National 5 Learning Intention We are learning to use the arc length formula. Success Criteria 1. Know the arc length formula. 2. Be able to calculate arc length showing appropriate work. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Arc length of a circle www. mathsrevision. com National 5 Q. What is an arc ? Answer A An arc is a fraction of the circumference. minor arc B major arc Monday, November 30, 2020 Created by Mr Lafferty 36

Arc length of a circle www. mathsrevision. com National 5 Q. Find the circumference of the circle ? Solution 10 cm Monday, November 30, 2020 Created by Mr Lafferty 37

Arc length of a circle www. mathsrevision. com National 5 Q. Find the length of the minor arc XY below ? x y 45 o 6 cm 360 Arc length Arc angle = connection πD 360 o o DEMO Monday, November 30, 2020 Created by Mr Lafferty 38

Arc length of a circle www. mathsrevision. com National 5 Q. Find the length of the minor arc AB below ? Arc length Arc angle = connection A πD 360 o 9 cm 60 o B Monday, November 30, 2020 Created by Mr Lafferty 39

Arc length of a circle www. mathsrevision. com National 5 Q. Find the length of the major arc PQ below ? Arc length Arc angle = connection P πD 360 o 10 m o 260 100 o Q Monday, November 30, 2020 Created by Mr Lafferty 40

Arc length of a circle www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 13. 1 Ch 13 (page 126) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 5 Q 1. True or false Q 2. Expand out (x + 3)(x 2 + 40 – 9) Q 3. I want to make 30% profit on a DVD player I bought for £ 80. How much must I sell it for. Monday, November 30, 2020 Created by Mr Lafferty 42

Sector area of a circle www. mathsrevision. com Nat 54 Level Learning Intention Success Criteria We are learning how to find the area of a sector. 1. Know the sector formula. 2. Be able to calculate sector area showing appropriate work. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Area of Sector in a circle www. mathsrevision. com National 5 A B minor sector major sector Monday, November 30, 2020 Created by Mr Lafferty 44

Area of Sector in a circle www. mathsrevision. com National 5 Q. Find the area of the circle ? Solution 10 cm Monday, November 30, 2020 Created by Mr Lafferty 45

Area of Sector in a circle www. mathsrevision. com National 5 Find the area of the minor sector XY below ? x connection Area Sector = Sector angle y 2 πr 360 o o 6 cm 45 360 o DEMO Monday, November 30, 2020 Created by Mr Lafferty 46

Area of Sector in a circle www. mathsrevision. com National 5 Q. Find the area of the minor sector AB below ? connection A 9 cm 60 Area Sector angle = πr 2 360 o o B Monday, November 30, 2020 Created by Mr Lafferty 47

Area of Sector in a circle www. mathsrevision. com National 5 Q. Find the area of the major sector PQ below ? connection Sector Area Sector angle = P πr 2 360 o 10 m o 260 100 o Q Monday, November 30, 2020 Created by Mr Lafferty 48

Arc length of a circle www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 13. 2 Ch 13 (page 127) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 5 Q 1. Using the balancing method rearrange into x = Q 2. True or false 2(x - 3) + 3 x = 5 x - 6 Q 3. Monday, November 30, 2020 Created by Mr Lafferty 50

Mixed Question www. mathsrevision. com Nat 54 Level Learning Intention We are doing mixed questions on the circle. Success Criteria 1. Identify appropriate formula to use. 2. Be able to calculate sector / arc showing appropriate work. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Arc length of a circle www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 13. 3 Ch 13 (page 128) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 5 Rearrange the formula below into xo = Monday, November 30, 2020 Created by Mr Lafferty 57

Centre Angle (Arc length) www. mathsrevision. com Nat 54 Level Learning Intention We are learning how to find the centre angle given the arc length. Success Criteria 1. Know formula. 2. Be able to calculate centre angle showing appropriate work. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Centre Angle (Arc length) www. mathsrevision. com National 5 Find the centre angle xo given the arc length is 4. 71 cm 2. x y 45 o 6 cm Monday, November 30, 2020 Arc length Arc angle = connection πD 360 o Created by Mr Lafferty 59

Centre Angle (Arc length) www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 13. 4 Ch 13 (page 129) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 5 Rearrange the formula below into xo = Monday, November 30, 2020 Created by Mr Lafferty 62

Centre Angle (Ao. S) www. mathsrevision. com Nat 54 Level Learning Intention We are learning how to find the centre angle given the sector area. Success Criteria 1. Know formula. 2. Be able to calculate centre angle showing appropriate work. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Centre Angle (Ao. S) www. mathsrevision. com National 5 Find the angle xo given that the sector area is 42. 41 cm 2. connection A 9 cm x Area Sector angle = πr 2 360 o o B Monday, November 30, 2020 Created by Mr Lafferty 64

Centre Angle (Ao. S) www. mathsrevision. com National 5 Find the angle xo given that the sector area is 51. 3 mm 2. connection A 7 mm x Area Sector angle = πr 2 360 o o B Monday, November 30, 2020 Created by Mr Lafferty 65

Centre Angle (Ao. S) www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 13. 5 Ch 13 (page 130) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

3 marks