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AUSTRIAN-POLISH 1984 Problem 4

    A regular heptagon A1A2...A7A_1A_2... A_7 is inscribed in circle CC . Point PP is taken on the shorter arc A7A1A_7A_1 . Prove that PA1+PA3+PA5+PA7=PA2+PA4+PA6PA_1+PA_3+PA_5+PA_7 = PA_2+PA_4+PA_6 .

    Dataset text AI-MO AoPS. Quoted with source.

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