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Perimeter does not exceed 2 * Pi

Source: China Team Selection Test 2004, Day 2, Problem 3

October 14, 2005
geometryperimetertrigonometrygeometry solved

Problem Statement

Let a,b,ca, b, c be sides of a triangle whose perimeter does not exceed 2⋅π.2 \cdot \pi., Prove that sin⁡a,sin⁡b,sin⁡c\sin a, \sin b, \sin c are sides of a triangle.
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