A Circle Theorem

The Resource

This worksheet encourages pupils to practice the deductive reasoning required to solve problems involving angles in circles.  At the same time, they develop the theorem that ‘the angle at the centre is twice the angle at the circumference’, either by spotting the pattern, or by generalising in question 5.  I would usually go through the general case the class afterwards.

The back of the worksheet contains lots of hints and tips for pupils who are finding it difficult, allowing those who can to create the arguments for themselves.

One weakness of this worksheet is that it requires pupils to be familiar with the AOB (three points) method of describing angles.  I should really make a version with a simpler notation for pupils who are less familiar with that.

Although this general case proves it for all angles, it’s important to follow this up with a demonstration (I like geogebra, but I’m sure there are alternatives) to show that this rule works even upon moving around the points on the circle, in particular demonstrating the alternative cases such as this…