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angles inequalities given sides inequalities in regular polygon

Source: Spanish Mathematical Olympiad 1969 P7

December 4, 2022
geometric inequalitygeometryregular polygon

Problem Statement

A convex polygon A1A2...AnA_1A_2 . . .A_n of nn sides and inscribed in a circle, has its sides that satisfy the inequalities AnA1>A1A2>A2A3>...>An−1AnA_nA_1 > A_1A_2 > A_2A_3 >...> A_{n-1}A_n Show that its interior angles satisfy the inequalities ∠A1<∠A2<∠A3<...<∠An−1,∠An−1>∠An>∠A1.\angle A_1 < \angle A_2 < \angle A_3 < ... < \angle A_{n-1}, \angle A_{n-1} > \angle A_n> \angle A_1.
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