IMO 1992 LL PRK59

Let a regular 7-gon A0A1A2A3A4A5A6 be inscribed in a circle.

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IMO 1992 LL PRK59

Origin: PRK

Problem

Let a regular 7-gon A0A1A2A3A4A5A6 be inscribed in a circle. Prove that for any two points P, Q on the arc A0A6 the following equality holds:  i=0 (−1)iPAi =  i=0 (−1)iQAi.