IMO Shortlist 2001 problem G1
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Avg: 6.0 Let
be the center of the square inscribed in acute triangle
with two vertices of the square on side
. Thus one of the two remaining vertices of the square is on side
and the other is on
. Points
are defined in a similar way for inscribed squares with two vertices on sides
and
, respectively. Prove that lines
are concurrent.









Source: Međunarodna matematička olimpijada, shortlist 2001