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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

Diagram of problem A length of thin wire ($L$ ) binds together two cylindrical welding rods, whose radii are $R$ and $r$ , by passing all the way around them both.

Find $L$ in terms of $R$ and $r$.