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Some(?) of the Parts

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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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Pericut

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?

Circle Packing

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

Equal circles can be arranged in regular square or hexagonal packings to fill space as shown in the diagram so that each circle touches four or six others.

Square and hexagonal packings

What percentage of the plane is covered by circles in each packing pattern? How is this of use in packing cylindrical cans and what are the advantages and disadvantages of the two packing systems?

 

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