Students are able to explore the following circle theorems:
· the angle at the centre is twice the angle at the circumference;
· angles from the same arc in the same segment are equal;
· the angle in a semicircle is a right angle;
· opposite angles in a cyclic quadrilateral add up to 180°;
· the tangent to a circle at a point is perpendicular to the radius
In each case students are encouraged to discover the theorem for themselves before seeing a formal statement . However the activities do not prove the circle theorems. Instead they give students the opportunity to get a sense of how the theorems work, as they move points and lines around and see what happens.
There is .ts file with 14 pages, supported by detailed instructions on a 3-page student handout and teacher notes. The activity forms part of the OxBox, published by Oxford University Press to support their course 'Oxford GCSE Maths'. http://www.oup.com/oxed/secondary/2010gcse/