### 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?

### Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

### Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

# Where Am I?

##### Age 11 to 16Challenge Level

On a weekend break a short while ago I saw this market cross.

On the side perhaps you can see that it has a plaque with distances to local and more distant towns:

Where was I?
What is the minimum amount of information you need to know where I was? Is some of the information redundant?
Is some of the information more useful than other parts?
How accurate can you be about exactly where I was from the distances that are given?

#### Then why not think about the following questions:

Why has someone bothered to include so much information?