 GCSE: Circles Dr J Frost ([email protected]) Last modified: 6th October 2013 Starter Give your answers in terms of 4 Area of shaded region = 4 ? 12 Area = 4 ? Perimeter = 8 +?2 4

Area = 18 ? Perimeter = 12 +? 6 Typical GCSE example Edexcel March 2012 What is the perimeter of the shape? P = 3x +? pi x / 2 Exercises Find the perimeter and area of the following shapes in terms of the given variable(s) and in terms of . (Copy the diagram first) 3 2 1

2x 2x 5 3x 2x ? ? Perimeter: Area: 4 Perimeter: Area: ? ? 5

2 Perimeter: Area: 8 6 Perimeter: Area: ? ? 2 ? ? Perimeter: Area: ? ?

Arcs and Sectors Arc Area of circle: = r2 ? Circumference of circle: = 2r ? r (Write down) Proportion of circle shaded: __ = ?

360 Sector __ Area of sector = r ? 360 2 __ Length of arc = 2r ? 360 Practice Questions Sector area = 10.91 ? 50 Area = 20 5

Arc length = 4.36 ? Sector area = 4.04cm ? 2 105 2.1cm ? Arc length = 3.85cm 135 (Hint: Plug values into your formula and rearrange) Radius = 4.12 ? A* GCSE questions ?

Area of triangle = 327 Area of sector = 1.5 ? Area of shaded region = 327 - 1.5 ? = 10.9cm2 Helpful formula: Area of triangle = ab sin C Difficult A* Style Question The shape PQR is a minor sector. The area of a sector is 100cm2. The length of the arc QR is 20cm. Q a) Determine the length PQ. P ? Answer: 10cm R

b) Determine the angle QPR Answer: 114.6 ? Bonus super hard question: Can you produce an inequality that relates the area A of a sector to its arc length L? L < ?4AA Hint: Find an expression for . What constraint is on this variable? Exercises Rayner GCSE Pg 191 Exercise 17C: Q2, 3, 10, 11, 12 Exercise 18C: Q9, 10, 13, 17, 19, 22