MathDB

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}

6