Junior Balkan MO 2013 - Problem 3


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Dodao: strujabog
22. ožujka 2014.
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Let ABC be an acute-angled triangle with AB<AC and let O be the centre of its circumcircle \omega. Let D be a point on the line segment BC such that \angle BAD = \angle CAO. Let E be the second point of intersection of \omega and the line AD. If M, N and P are the midpoints of the line segments BE, OD and AC, respectively, show that the points M, N and P are collinear.