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Intersection of A and P is empty

Source: Romanian TST 1998

April 23, 2011
geometrygeometry proposed

Problem Statement

Let ABCABC be an equilateral triangle and n≥2n\ge 2 be an integer. Denote by A\mathcal{A} the set of n−1n-1 straight lines which are parallel to BCBC and divide the surface [ABC][ABC] into nn polygons having the same area and denote by P\mathcal{P} the set of n−1n-1 straight lines parallel to BCBC which divide the surface [ABC][ABC] into nn polygons having the same perimeter. Prove that the intersection A∩P\mathcal{A} \cap \mathcal{P} is empty.
Laurentiu Panaitopol
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