IMO 1989 LL LUX65

A regular n-gon A1A2A3 . . . Ak . . . An inscribed in a circle of

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IMO 1989 LL LUX65

Origin: LUX

Problem

A regular n-gon A1A2A3 . . . Ak . . . An inscribed in a circle of radius R is given. If S is a point on the circle, calculate T = SA2 1 +SA2 2 + \cdot \cdot \cdot + SA2 n.