MathNet 2026 — Part 09 Question 124

Let $A_{1} A_{2} \cdots A_{2 n}$ be a convex $2 n$-gon. Prove that there is an $i$ ($1 \leq i \leq n$) and a pair of parallel lines, each intersecting the $2 n$-gon only once, one at $A_{i}$ and one at $A_{n+i}$.