4

Part of 1973 Spain Mathematical Olympiad

Problems(1)

8 circles each tangent to 2, in an annulus between concentric circles

Source: Spanish Mathematical Olympiad 1973 P4

C

C'

be two concentric circles of radii

r

r'

respectively. Determine how much the quotient

r'/r

must be worth so that in the limited crown (annulus) through

C

C'

there are eight circles

C_i

i = 1, . . . , 8

, which are tangent to

C

C'

, and also that

C_i

C_{i+1}

i = 1, . . . ,7

C_8

C_1

geometryconcentricconcentric circles