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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Half a Triangle

Age 14 to 16 Challenge Level:

If the area ratio has to be $1:2$ , what would the line ratio need to be?

What constructions do you know that create such a ratio?

Can you see how to create such a construction on the given triangle?