2017 OIM Problems/Problem 4
Problem
Let 
be an acute triangle with 
and 
its circumcenter. Let 
be a point on the segment 
such that is inside the triangle 
and 
. We call 
and 
the circumcenters of the triangles 
and 
, respectively, and 
the point of intersection of the lines 
and 
. Show that the lines 
and are
concurrent.
Note. The circumcenter of a triangle is the center of the circle that passes through the three vertices of the triangle.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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