Τετάρτη, 11 Οκτωβρίου 2017

2000 JBMO Shortlist 18

A triangle ${ABC}$ is given. Find all the segments ${XY}$ that lie inside the triangle such that ${XY}$ and five of the segments ${XA,XB,XC,YA,YB,YC}$ divide the triangle ${ABC}$ into ${5}$ regions with equal areas. Furthermore, prove that all the segments ${XY}$ have a common point.

proposed in aops here

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