2010 OIM Problems/Problem 3
Problem
The circle 
inscribed in the scalene triangle 
is tangent to the sides 
, 
and 
at points 
, 
and 
, respectively. The line 
cuts the line at 
. The circumference of diameter 
cuts at 
(
). Let 
and 
(
, 
) the intersections of 
and 
with , respectively. The lines 
and 
intersect at X. The circumscribed circle at 
cuts the 
segment in 
and the circumscribed circle at 
cuts the segment 
at 
. Show that the lines 
and 
are concurrent.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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