### 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?

# Subtended Angles

##### Stage: 3 Challenge Level:

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?

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