### 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?

##### Stage: 3 Challenge Level:

This problem invited students to consider the relationship between opposite angles of cyclic quadrilaterals. Often, with these types of problems, it is helpful to draw diagrams; several students submitted diagrams as part of their solution - well done.

The problem is divided into two parts: the first part contains questions that form "building blocks" to help meet the final challenge in the second part.

Nick, from St Stephen's at Carramar summed up his solution:

The sum of the angles at opposite vertices of a cyclic quadrilateral is $180^\circ$. This is the same for all cyclic quadrilaterals, regardless of the positioning of the centre dot.