Regular polygons and circles

problem
Ford circles

Age

16 to 18

Challenge level

Can you find the link between these beautiful circle patterns and Farey Sequences?
problem
Bicentric quadrilaterals

Age

14 to 16

Challenge level

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
problem
Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Partly circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?
problem
Efficient packing

Age

14 to 16

Challenge level

How efficiently can you pack together disks?
problem
Shaping up

Age

7 to 11

Challenge level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
problem
Lighting up time

Age

7 to 14

Challenge level

A very mathematical light - what can you see?
problem
Overlapping again

Age

7 to 11

Challenge level

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
problem
Angle to chord

Age

14 to 16

Challenge level

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?
problem
Oh so circular

Age

14 to 16

Challenge level

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?