Circle Theorems

Age 14 to 16
Challenge Level

This page contains a geoboard environment that can be used for circle work as well as well as other problems (such as Pick's Theorem ). There are also a number of problems that introduce circle theorems, all of which have a special version of the interactivity to support them. By working on the problems learners will develop a better understanding of some of the angle properties of circles.

Virtual Geoboard
A generic environment for supporting work on geometry and area can be found here .

Triangles in Circles
This problem offers a good preparation for the problems Subtended angles and Right angles which lead towards the circle theorems.
Students will only need to know that the angles round a point add up to 360 ° and how to calculate angles in isosceles triangles.
"How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?"

Subtended Angles
This problem asks:
"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? "

Right Angles
This problem focusses on the angle subtended by a semicircle.
"Can you make a right-angled triangle on this peg-board by joining up three points round the edge?What do you notice and can you explain it?"

Pegboard Quads
This problem asks:
"Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?"