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ASU 045 All Russian MO 1964 8.5a 10.3ab hexagon

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June 18, 2019
geometryhexagon

Problem Statement

a) Given a convex hexagon ABCDEFABCDEF with all the equal angles. Prove that ∣AB∣−∣DE∣=∣EF∣−∣BC∣=∣CD∣−∣FA∣|AB|-|DE| = |EF|-|BC| = |CD|-|FA| b) The opposite problem: Prove that it is possible to construct a convex hexagon with equal angles of six segments a1,a2,...,a6a_1,a_2,...,a_6, whose lengths satisfy the condition a1−a4=a5−a2=a3−a6a_1-a_4 = a_5-a_2 = a_3-a_6
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