2009 IMO Problems/Problem 2
Problem
Let be a triangle with circumcentre
. The points
and
are interior points of the sides
and
respectively. Let
and
be the midpoints of the segments
and
, respectively, and let
be the circle passing through
and
. Suppose that the line
is tangent to the circle
. Prove that
.
Author: Sergei Berlov, Russia
--Bugi 10:22, 23 July 2009 (UTC)Bugi