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?
What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
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?