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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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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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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?

Triangles Within Triangles

Stage: 4 Challenge Level: Challenge Level:1

Why not encourage pupils to discover rules of their own?

By using isometric paper the triangular numbers can be represented as equilateral triangles wich give scope to investigating their connection with hexagonal numbers.

This problem links to "Triangles within Squares ".