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cyclic hexagon wanted with opposite sides // and not equal

Source: 2023 Croatia MO p3 HMO https://artofproblemsolving.com/community/c1251476_croatia_mo_hmo___geometry

May 5, 2024
geometryhexagonCyclic

Problem Statement

A convex hexagon ABCDEFABCDEF is given, with each two opposite sides of different lengths and parallel (AB∥DEAB \parallel DE, BC∥EFBC \parallel EF and CD∥FACD \parallel FA). If ∣AE∣=∣BD∣|AE| = |BD| and ∣BF∣=∣CE∣|BF| = |CE|, prove that the hexagon ABCDEFABCDEF is cyclic.
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