1997 OIM Problems/Problem 5
Problem
In an acute triangle 
, let 
and 
be two heights, and let 
be the orthocenter. The symmetrical line of with respect to the (interior) bisector of the angle at 
and the symmetrical line of with respect to the (interior) bisector of the angle at 
intersect at a point 
. The lines and 
intersect a second time the circumference circumscribes triangle at points 
and 
, respectively.
Let 
be the intersection of 
with 
; 
, the intersection of with 
; and 
the intersection of 
with 
.
Prove that 
is a parallelogram.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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