Circle properties and circle theorems
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?