Difference between revisions of "2006 Romanian NMO Problems/Grade 7/Problem 3"
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b) <math>CH=DE</math>. | b) <math>CH=DE</math>. | ||
==Solution== | ==Solution== | ||
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==See also== | ==See also== | ||
*[[2006 Romanian NMO Problems]] | *[[2006 Romanian NMO Problems]] | ||
[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 08:33, 27 August 2008
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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