### Absurdity Again

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

### Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

### Incircles

The incircles of 3, 4, 5 and of 5, 12, 13 right angled triangles have radii 1 and 2 units respectively. What about triangles with an inradius of 3, 4 or 5 or ...?

# Look Before You Leap

##### Stage: 5 Challenge Level:

The first hint is to think of fractions. Make the fractions by dividing by $abc$.

The second hint is in the diagram. Find $a^2+b^2+c^2$ using the algebra that comes from the diagram.