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?
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).
How can you make an angle of 60 degrees by folding a sheet of paper
What is the relationship between the angle at the centre and the
angle at the circumference?
What do we know already that might be useful here?
What are the implications of our findings? (How can other circle
theorems be deduced from this one?)
Would the same thing happen if you started with an arc between
any two points on the circumference of any circle?
Can you prove it?