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## 'Triangles in Circles' printed from http://nrich.maths.org/

*If you prefer to work on paper, you may wish to print out some 9 dot circles*
In the GeoGebra interactivity below there is

**a circle with 9 equally spaced points on the edge**, and one in the centre.

**Draw as many different triangles as you can, by joining the centre dot and any two of the dots on the edge.**
Can you work out the angles in your triangles?

You should have found four different triangles with angles of:

40, 70, 70

80, 50, 50

120, 30, 30,

160, 10, 10

**Here is a triangle formed by joining three dots on the edge of the nine-point circle:**
**Can you work out the angles of this triangle?**
*Click to reveal a diagram that might help you work out the angles.*
Create some more triangles by joining three dots on the edge of the nine point circle.

**How many different triangles can you make?**

Can you work out the angles each time?
When the centre dot isn't inside your triangle, you might find it a little trickier to work out the angles. Click below for a diagram that might help:

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