Angles, Angles in Circles
Key Stage: 3 ★★
What is the angle at the centre of the circle? What is the angle on the circumference? Does it matter where the point on the circumference is?
This problem leads towards the theorem about the relationship between the angle subtended by an arc at the centre of a circle and the angle subtended by the same arc at the circumference. Students will then be able to deduce that angles subtended by an arc at the circumference are all equal. The nine-peg circle allows students to concentrate on the geometrical structure without having to worry about the arithmetic.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
Key Stage: 3 ★★
What is the angle at the centre of the circle? What is the angle on the circumference? Does it matter where the point on the circumference is?
This problem leads towards the theorem about the relationship between the angle subtended by an arc at the centre of a circle and the angle subtended by the same arc at the circumference. Students will then be able to deduce that angles subtended by an arc at the circumference are all equal. The nine-peg circle allows students to concentrate on the geometrical structure without having to worry about the arithmetic.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
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A nice task which would ideally be used as a starter activity to get pupils thinking about subtended angles. I particularly like how open-ended the task is and the freedom it allows to discuss/follow whatever the pupils suggest.
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