MathDB

The cross-section of a ball bearing consists of two concentric circles

C

and

C_1

, between which there are

n

small circles

k_1, k_2, \ldots, k_n

, each of which is tangent to the two adjacent circles and to both circles

C

and

C_1

. Given the radius

r

of the inner circle

C

and a natural number

n

, calculate the radius

x

of circle

C_2

passing through the points of tangency of circles

k_1, k_2, \ldots, k_n

and the sum

s

of the lengths of the arcs of circles

k_1, k_2, \ldots, k_n

that lie outside circle

C_2

1