# Understanding Convex Octagons

Geometry Level 4

Let $$A_1A_2\dots A_8$$ be a convex octagon such that its opposite sides are parallel. Define $$B_i$$ as the intersection between $$A_{i-1}A_{i+1}$$ and $$A_iA_{i+4},$$ where $$A_{j+8} = A_j$$ for all $$j$$.

Let $$x$$ be the minimum value of $$\frac{A_iA_{i+4}}{B_iB_{i+4}}$$. Over all convex octagons, find the maximum possible value of $$x$$ (to 3 decimal places).

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