GCSE: Circles Dr J Frost Last modified: 6 th October 2013

12 Area = 18 π Perimeter = π 4 Area = 4 π Perimeter = π Give your answers in terms of π ? ? ? ? Area of shaded region = 4 – π 4 ? Starter

Edexcel March 2012 What is the perimeter of the shape? P = 3x + pi x / 2 ? Typical GCSE example

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) 3x 2x ? ? ? ? ? ? ? ? ? ?

θ r Arc Sector Area of circle:= π r 2 Circumference of circle: = 2 π r Proportion of circle shaded: = _θ_ 360 Area of sector = π r 2 × _θ_ 360 Length of arc = 2 π r × _θ_ 360 ? ? ? ? ? (Write down) Arcs and Sectors

5 Sector area = Arc length = 4.36 Area = 20 Radius = cm Sector area = 4.04cm 2 Arc length = 3.85cm ? ? ? ? ? 50 ° 105 ° 135 ° (Hint: Plug values into your formula and rearrange) Practice Questions

A* GCSE questions Area of triangle = 3 √ 27 Area of sector = 1.5 π Area of shaded region = 3 √ π = 10.9cm 2 ? ? ? Helpful formula: Area of triangle = ½ ab sin C

The shape PQR is a minor sector. The area of a sector is 100cm 2. The length of the arc QR is 20cm. a)Determine the length PQ. Answer: 10cm b)Determine the angle QPR Answer: ° P Q R Bonus super hard question: Can you produce an inequality that relates the area A of a sector to its arc length L? L < 4πA Hint: Find an expression for θ. What constraint is on this variable? ? ? ? Difficult A* Style Question

Exercises Rayner GCSE Pg 191 Exercise 17C: Q2, 3, 10, 11, 12 Exercise 18C: Q9, 10, 13, 17, 19, 22