### 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?

### Coins on a Plate

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

### AP Rectangles

An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?

# L-emental

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Two identical rectangular cards are glued together as shown, to form an 'L' shape.
The perimeter of this 'L' shape is 40 cm.
What can you say about the length and width of the original rectangles?

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.