**A. 507.** The circles *K*_{1},...,*K*_{6} are externally tangent to the circle *K*_{0} in this order. For each 1*i*5, the circles *K*_{i} and *K*_{i+1} are externally tangent to each other, and *K*_{1} and *K*_{6} are externally tangent to each other as well, according to the *Figure.* Denote by *r*_{i} the radius of *K*_{i} (0*i*6). Prove that if *r*_{1}*r*_{4}=*r*_{2}*r*_{5}=*r*_{3}*r*_{6}=1 then *r*_{0}1.

(Proposed by: *Balázs Strenner,* Székesfehérvár)

(5 points)