1. Two large, two small
An Investigation

2. The diagram shows two sets of identical circles,
Two large, two small
30cm
The diagram shows two sets of identical circles,
one small set and one large set.
The small circles fit exactly as shown between
the large ones and touch the large circles.
The diameter of the large circles is 30cm.
Calculate the radius of the small circles.

3. Solution Form the triangle with sides 15-r, 15-r and 15+r.
Using Pythagoras gives
On expanding the brackets
and simplifying you obtain
which gives r = 2.57 on using the quadratic formula.