2006 Romanian NMO Problems/Grade 7/Problem 3
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Problem
In the acute-angle triangle 
we have 
. The points 
and 
are the feet of the altitudes from 
and 
, and 
is the orthocenter of the triangle. We consider the points 
and 
on the segments 
and 
such that 
. Prove that
a) 
;
b) 
.
Solution
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