Junior Balkan MO 2017 - Problem 3
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Avg: 4,0Let be an acute triangle such that
, with circumcircle
and circumcenter
. Let
be the midpoint of
and
be a point on
such that
. let
be a point such that
is a parallelogram and
a point on the same side of
as
such that
and
. Let the line
intersect
at
and let the circumcircle of
intersect
at point
. Prove that the point
and
are collinear.
Izvor: Juniorska balkanska matematička olimpijada 2017.