Question 179
The radii of five concentric circles $\omega_0, \omega_1, \omega_2, \omega_3, \omega_4$ form (in this order) a geometric progression with ratio $q$. Determine the largest value of $q$ for which it is possible to choose a broken line $A_0A_1A_2A_3A_4$ consisting of four segments of equal lengths, such that $A_i \in \omega_i$ for all $i = 0, 1, 2, 3, 4$.