### Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

### Pie Cuts

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

### Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice?

# Triangles in Circles

##### Stage: 3 Challenge Level:
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.