2001 IMO Shortlist Problems/G7
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Problem
Let 
be an interior point of acute triangle 
. Let 
lie on 
with 
perpendicular to . Define 
on 
and 
on 
similarly. Prove that is the circumcenter of if and only if the perimeter of 
is not less than any one of the perimeters of 
, and 
.
Solution
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