### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# Tilting Triangles

##### Stage: 4 Challenge Level:

A right-angled isosceles triangle whose two equal sides are 2 units in length is attached at its right-angled vertex to the centre of a square of side 2 units and rotated about this centre point.

This text is usually replaced by the Flash movie.

What can you say about the area of the part of the square covered by the triangle as it rotates?

What happens to this area if the triangle is reduced in size so that its two equal sides are $\sqrt 2$ units?

What happens if the triangle is further reduced in size?