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...

Just Opposite

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?

Fermat's Poser

Age 14 to 16 Challenge Level:

Fermat was an amateur mathematician of great intellect. He wrote this problem:

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.