MathDB

2023.3

Part of Croatia MO (HMO) - geometry

Problems(1)

cyclic hexagon wanted with opposite sides // and not equal

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

5/5/2024
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.
geometryhexagonCyclic