2009 OIM Problems/Problem 3
Problem
Let 
and 
be two circles with centers 
and 
with the same radius, which intersect at 
and 
. Let 
be a point on the arc 
of that is inside . Line 
intersects at 
, line 
intersects at 
and the bisector of 
intersects at 
and at 
. Let 
be the point symmetrical to with respect to the midpoint of 
. Show that there exists a point 
satisfying 
and 
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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