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ASU 261 All Soviet Union MO 1978 perimeter of cyclic polygon >=2S/R

Source:

July 6, 2019
geometric inequalitygeometryperimeterpolygonCyclic

Problem Statement

Given a circle with radius RR and inscribed nn-gon with area SS. We mark one point on every side of the given polygon. Prove that the perimeter of the polygon with the vertices in the marked points is not less than 2S/R2S/R.
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