### Matter of Scale

Prove Pythagoras' Theorem using enlargements and scale factors.

### Conical Bottle

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

### Arrh!

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

# Fit for Photocopying

##### Stage: 4 Challenge Level:
Start by looking at the relationship between the even numbered paper sizes ($A4$ to $A2$, $A0$ and so on).