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:

A $3 \times8$ rectangle is cut into two pieces along the dotted line shown. The two pieces are then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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