MathDB

Let

C_1, C_2

be circles of radius

1/2

tangent to each other and both tangent internally to a circle

C

of radius

1

. The circles

C_1

and

C_2

are the first two terms of an infinite sequence of distinct circles

C_n

defined as follows:

C_{n+2}

is tangent externally to

C_n

and

C_{n+1}

and internally to

C

. Show that the radius of each

C_n

is the reciprocal of an integer.

Problem Statement