Angle in the Centre vs Angle at the Circumference
Select points A, B and C and move them round the circle.
Use the Animate function to set up an animation of point A around the circle.
What do you notice about the size of the two angles? What can you say about the Angle at the Centre of a Circle compared to the Angle at the Circumference? Can you prove the result?
What do you notice about the size of the two angles?
What can you say about the Angle at the Centre of a Circle compared to the Angle at the Circumference?
Can you prove the result?
Use this Activity as a homework, where the students must come up with a conjecture regarding Angles at the Centre vs Angles at the Circumference. Ensuring they are using the correct vocabulary here is essential.
As an extension task, you could ask the students to try and prove this result (this is quite tricky on their own, but a few well placed hints should get the more capable on their way).
An alternative approach, which is even more hands on, is to get them to make this in Autograph themselves. You could do this in two ways: show them this activity, asking them to reproduce it (will develop their understanding of Autograph and circles); use the worksheet provided which gives a step by step approach to creating it.
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A worksheet for students to work through which involves them creating the above activity using Autograph before doing the investigation.