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Broad Topics > 2D Geometry, Shape and Space > Circles

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Circles in Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:1

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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Curvy Areas

Stage: 4 Challenge Level: Challenge Level:1

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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Partly Circles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the same and what is different about these circle questions? What connections can you make?

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2 Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

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Spokes

Stage: 5 Challenge Level: Challenge Level:1

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

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Efficient Cutting

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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Salinon

Stage: 4 Challenge Level: Challenge Level:1

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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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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Semi-detached

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

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Approximating Pi

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

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Quadarc

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .

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Orthogonal Circle

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

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Logosquares

Stage: 5 Challenge Level: Challenge Level:1

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

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Pericut

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Baby Circle

Stage: 5 Challenge Level: Challenge Level:1

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

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Chain of Changes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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Gym Bag

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Curve Spotting

Stage: 1 Challenge Level: Challenge Level:1

Can you spot circles, spirals and other types of curves in these photos?

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A Rational Search

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate constructible images which contain rational areas.

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Olympic Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is intended to get children to look really hard at something they will see many times in the next few months.

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Sports Equipment

Stage: 2 Challenge Level: Challenge Level:1

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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Track Design

Stage: 4 Challenge Level: Challenge Level:1

Where should runners start the 200m race so that they have all run the same distance by the finish?

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Sorting Logic Blocks

Stage: 1 and 2 Challenge Level: Challenge Level:1

This interactivity allows you to sort logic blocks by dragging their images.

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Jig Shapes

Stage: 1 Challenge Level: Challenge Level:1

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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Ford Circles

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.

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Bicentric Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

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Efficient Packing

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can you pack together disks?

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Link Puzzle

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A metal puzzle which led to some mathematical questions.

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Logic Block Collections

Stage: 1 Challenge Level: Challenge Level:1

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

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Sorting Shapes

Stage: 1 Challenge Level: Challenge Level:1

This activity challenges you to make collections of shapes. Can you give your collection a name?

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Shaping Up

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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Overlapping Again

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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Like a Circle in a Spiral

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

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Spirostars

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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LOGO Challenge 12 - Concentric Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.

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LOGO Challenge 11 - More on Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

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First Forward Into Logo 4: Circles

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

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Circle Panes

Stage: 2 Challenge Level: Challenge Level:1

Look at the mathematics that is all around us - this circular window is a wonderful example.

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Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

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Yin Yang

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

Can you reproduce the Yin Yang symbol using a pair of compasses?

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Circles, Circles Everywhere

Stage: 2 and 3

This article for pupils gives some examples of how circles have featured in people's lives for centuries.

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Pi, a Very Special Number

Stage: 2 and 3

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

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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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Lunar Angles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

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Circles in Circles

Stage: 5 Challenge Level: Challenge Level:1

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.

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The Pi Are Square

Stage: 3 Challenge Level: Challenge Level:1

A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?

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Rolling Coins

Stage: 4 Challenge Level: Challenge Level:1

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

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Circumnavigation

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.