Circles and Circle Theorems - February 2004, Stage 2&3

Problems

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Overlapping Circles

Stage: 2 Challenge Level: Challenge Level:1

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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A Square in a Circle

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

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Sponge Sections

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Rolling Around

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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Rollin' Rollin' Rollin'

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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Inscribed in a Circle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?