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5 regions of equal area - JBMO Shortlist

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October 30, 2010
geometrygeometry proposed

Problem Statement

A triangle ABCABC is given. Find all the segments XYXY that lie inside the triangle such that XYXY and five of the segments XA,XB,XC,YA,YB,YCXA,XB, XC, YA,YB,YC divide the triangle ABCABC into 55 regions with equal areas. Furthermore, prove that all the segments XYXY have a common point.
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