You might like to have a look at Nine-Pin Triangles
before trying this problem.
How many different triangles can you draw on a circular pegboard which has four equally spaced pegs?
What are the angles of each triangle?
If you have a six-peg circular pegboard, how many different triangles are possible now?
What are their angles?
How many different triangles could you draw on an eight-peg board?
Can you find the angles of each?
You may like to use the interactivity to try out your ideas.
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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 geoboard.
For further ideas about using geoboards in the classroom, please see Geoff's publications available through the Association of Teachers of Mathematics (search for 'geoboards').