Two large, two small An Investigation

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.

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.