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Convex polygon distances

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November 26, 2016
geometry

Problem Statement

We have a convex polygon PP in the plane and two points S,TS,T in the boundary of PP, dividing the perimeter in a proportion 1:21:2. Three distinct points in the boundary, denoted by A,B,CA,B,C start to move simultaneously along the boundary, in the same direction and with the same speed. Prove that there will be a moment in which one of the segments AB,BC,CAAB, BC, CA will have a length smaller or equal than STST.