Regular polygons and circles

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

What fractions of the largest circle are the two shaded regions?

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?

Weekly Problem 1 - 2006
The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?

Investigate these hexagons drawn from different sized equilateral triangles.

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?