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...

Rotating Triangle

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

Rectangle Rearrangement

Stage: 4 Short Challenge Level:

The diagram shows the two pieces will fit together to form a right-angled triangle which has a base $8$ and height $6$. The length of the hypotenuse = $\sqrt{(6^2+8^2)}$, that is $10$, so the perimeter of the triangle is $24$.

This problem is taken from the UKMT Mathematical Challenges.