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Triangle with perimeter 2p inscribed and circumscribed on circles

Source: Poland Math Olympiad 1993 Round 1 #11

June 4, 2023
geometryperimeter

Problem Statement

A triangle with perimeter 2p2p is inscribed in a circle of radius RR and also circumscribed on a circle of radius rr. Prove that p<2(R+r)p < 2(R+r).
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