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Resources tagged with Circles similar to Two Points Plus One Line:

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

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Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

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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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Arclets Explained

Stage: 3 and 4

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

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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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Roaming Rhombus

Stage: 4 Challenge Level: Challenge Level:1

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .

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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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Tricircle

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

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

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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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Circle Packing

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

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...

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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.

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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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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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What Is the Circle Scribe Disk Compass?

Stage: 3 and 4

Introducing a geometrical instrument with 3 basic capabilities.

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Three Four Five

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

Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.

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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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LOGO Challenge 10 - Circles

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

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

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Not So Little X

Stage: 3 Challenge Level: Challenge Level:1

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

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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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Circumspection

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

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

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Some(?) of the Parts

Stage: 4 Challenge Level: Challenge Level:1

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

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Squaring the Circle and Circling the Square

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

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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Squaring the Circle

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

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

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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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Coins on a Plate

Stage: 3 Challenge Level: Challenge Level:1

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

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Fitting In

Stage: 4 Challenge Level: Challenge Level:1

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .

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Get Cross

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

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

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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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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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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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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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Square Pegs

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

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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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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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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Floored

Stage: 3 Challenge Level: Challenge Level:1

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

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Illusion

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

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

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Bull's Eye

Stage: 3 Challenge Level: Challenge Level:1

What fractions of the largest circle are the two shaded regions?

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F'arc'tion

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

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

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Holly

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

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.

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The Pillar of Chios

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

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

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Pie Cuts

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

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

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A Chordingly

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

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.

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Blue and White

Stage: 3 Challenge Level: Challenge Level:1

In the four examples below identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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Round and Round

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

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

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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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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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Semi-square

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

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

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Angle A

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

The three corners of a triangle are sitting on a circle. The angles are called Angle A, Angle B and Angle C. The dot in the middle of the circle shows the centre. The counter is measuring the size. . . .

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Crescents and Triangles

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

Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'. Show that the sum of the areas of the two crescents equals the area of triangle ABC.

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Polycircles

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

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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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?