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Subtended Angles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem you can make use of the coloured rubber bands in the interactivity below.

Choose two points on the edge of the circle. Call them $A$ and $B$.

Join these points to the centre, $C$. What is the angle at $C$?

Join $A$ and $B$ to a point on the edge. Call that point $D$. What is the angle at $D$?

What do you notice?


Circle example

Would the same thing happen if $D$ took a different position on the edge of the circle?

Would the same thing happen if you started with a different two points on the edge of the circle?

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Would the same thing happen if you started with any two points on the edge of any circle?
Can you prove it?

For printable sets of circle templates for use with this activity, please see Printable Resources page.

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.

The boards, moulded in crystal clear ABS that can be used on an OHP (185 cm in diameter), together with a teacher's guide, are available from Geoff at Education Initiatives

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.