OMM 2013 Problem 6

Let $A_1A_2 ... A_8$ be a convex octagon such that all of its sides are equal and its opposite sides are parallel. For each $i = 1, ... , 8$ , define $B_i$ as the intersection between segments $A_iA_{i+4}$ and $A_{i-1}A_{i+1}$ , where $A_{j+8} = A_j$ and $B_{j+8} = B_j$ for all $j$ . Show some number $i$ , amongst 1, 2, 3, and 4 satisfies $$\frac{A_iA_{i+4}}{B_iB_{i+4}} \leq \frac{3}{2}$$