www mathsrevision com The Circle Isosceles Triangles in

www. mathsrevision. com The Circle Isosceles Triangles in Circles Right angle in a Semi-Circle Tangent Line to a Circle The Tangent Kite Exam questions Wednesday, February 24, 2021 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. Wednesday, February 24, 2021 Created by Mr Lafferty 2

The Circle www. mathsrevision. com Level 4 Learning Intention 1. We are learning how to recognise isosceles triangles in a circle. Success Criteria 1. Be able to recognise isosceles triangles in a circle. 2. Calculate missing angles.

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 Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 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) 24 -Feb-21 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. Wednesday, February 24, 2021 Created by Mr Lafferty 10

The Circle www. mathsrevision. com Level 4 Learning Intention 1. We are learning the property of a triangle with hypotenuse equal to the diameter of the circle and the two smaller sides meeting at the circumference of the cirlce. Success Criteria 1. Be able to recognise property.

Semi-circle angle www. mathsrevision. com National 5 Tool-kit required 1. Protractor 2. Pencil 3. Ruler Wednesday, February 24, 2021 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. Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 Circumference Created by Mr Lafferty Inside 15

Semi-Circle Angle www. mathsrevision. com Level 4 x Demo Outside < 90 o Circumference o = 90 Wednesday, February 24, 2021 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) 24 -Feb-21 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 Wednesday, February 24, 2021 Created by Mr Lafferty 19

The Circle www. mathsrevision. com Level 4 Learning Intention 1. We are learning the property of a tangent line to the circle. Success Criteria 1. Be able to recognise tangent line. 2. Work with property of a tangent line to solve circle problems.

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? Wednesday, February 24, 2021 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. Wednesday, February 24, 2021 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 Wednesday, February 24, 2021 Created by Mr Lafferty 25

Tangent Line www. mathsrevision. com Level 4 Now try N 4+ TJ Ex 18. 3 Ch 18 (page 143) 24 -Feb-21 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) Wednesday, February 24, 2021 Created by Mr Lafferty 28

Tangent Kite www. mathsrevision. com Level 4 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. 24 -Feb-21 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 24 -Feb-21 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. 24 -Feb-21 Compiled by Mr. Lafferty Maths Dept. C

Tangent Kite r Using Pythagoras Theorem r 2 = 502 - 402 r 2 = 2500 - 1600 √ 24 -Feb-21 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 (page 145) 24 -Feb-21 Compiled by Mr. Lafferty Maths Dept.

3 marks