2006 OIM Problems/Problem 1
Problem
In the scalene triangle 
, with 
, the inscribed and circumscribed circles are considered. The tangent line at 
to the circumcircle intersects the line 
at 
. Let 
and 
be the points of tangency of the circle inscribed with the lines 
and 
,
respectively. Line 
intersects line at 
. Lines 
and 
meet at 
. Show that the triangle 
is isosceles.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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