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Prove the existence and uniqueness of three points

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September 20, 2010
geometryTriangleIMO Shortlist

Problem Statement

We consider three distinct half-lines Ox,Oy,OzOx, Oy, Oz in a plane. Prove the existence and uniqueness of three points A∈Ox,B∈Oy,C∈OzA \in Ox, B \in Oy, C \in Oz such that the perimeters of the triangles OAB,OBC,OCAOAB,OBC,OCA are all equal to a given number 2p>0.2p > 0.
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