### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

### Rotating Triangle

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

### Pericut

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

# Sticky Tape

##### Stage: 4 Short Challenge Level:

The cross section of the $20 \; \text{m}$ tape has area $\pi(4^2 - 3^2) \text{cm}^2 = 7\pi \text{cm}^2$ Therefore, the $80 \; \text{m}$ tape should have a cross-section area $28\pi \; \text{cm}^2$. Hence, the outer radius of the $80 \;\text{m}$ roll will be approximately $\sqrt{37} \;\text{cm}$

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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