Circle properties and circle theorems

problem
Tied up

Age

14 to 16

Challenge level

How much of the field can the animals graze?
problem
Sports equipment

Age

7 to 11

Challenge level

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
problem
Perfect eclipse

Age

14 to 16

Challenge level

Use trigonometry to determine whether solar eclipses on earth can be perfect.
problem
Cyclic quadrilaterals

Age

11 to 16

Challenge level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
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
Circles in quadrilaterals

Age

14 to 16

Challenge level

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
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
Right angles

Age

11 to 14

Challenge level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Subtended angles

Age

11 to 14

Challenge level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
problem
Triangles in circles

Age

11 to 14

Challenge level

Can you find triangles on a 9-point circle? Can you work out their angles?