Junior Balkan MO 2005 - Problem 2
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Avg: 4,0Let be an acute-angled triangle inscribed in a circle
. It is given that the tangent from
to the circle meets the line
at point
. Let
be the midpoint of the line segment
and
be the second intersection point of the circle
with the line
. The line
meets again the circle
at point
different from
.
Prove that the lines and
are parallel.
Izvor: Juniorska balkanska matematička olimpijada 2005.