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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:

This problem will need solving in stages by most students.

Perhaps beginning by establishing the required line ratio.

Then by remembering a familiar figure where that particular ratio can be found.

Deciding how that figure can be constructed on the given triangle to locate a useful point.

Finally creating the required line, parallel to the base, across the triangle.