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.

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.