Challenge Level

*Triangles in Circles printable sheet
9 dot circles printable sheet*

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

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.*