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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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Five Circuits, Seven Spins

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

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A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.


Stage: 5 Challenge Level: Challenge Level:1

Why do this problem?

It provides experience of geometrical thinking,applying only the geometry of right angles triangles and the formula for arc length.

Possible approach

Sugggest the learners draw a neat diagram and mark in everything they know and can deduce from the diagram.

Key question

How do we split the belt into sections for which the lengths can be calculated?