2014 OIM Problems/Problem 5
Problem
Let 
be an acute triangle and 
be the point of intersection of the heights. The height from 
cuts 
in 
. Let 
and 
be the midpoints of 
and 
, respectively. 
and 
intersect 
and 
at 
and 
, respectively. If 
intersects at 
and in 
, show that 
, and are on the same circle.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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