IMO Shortlist 2005 problem G5

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Dodao/la: arhiva
April 2, 2012
Let \triangle ABC be an acute-angled triangle with AB \not= AC. Let H be the orthocenter of triangle ABC, and let M be the midpoint of the side BC. Let D be a point on the side AB and E a point on the side AC such that AE=AD and the points D, H, E are on the same line. Prove that the line HM is perpendicular to the common chord of the circumscribed circles of triangle \triangle ABC and triangle \triangle ADE.
Source: Međunarodna matematička olimpijada, shortlist 2005