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Source: Swiss Imo Selection 2006

May 25, 2006
geometrycircumcircletrigonometryIMO ShortlistSpiral SimilarityMiquel point

Problem Statement

Let △ABC\triangle ABC be an acute-angled triangle with AB≠ACAB \not= AC. Let HH be the orthocenter of triangle ABCABC, and let MM be the midpoint of the side BCBC. Let DD be a point on the side ABAB and EE a point on the side ACAC such that AE=ADAE=AD and the points DD, HH, EE are on the same line. Prove that the line HMHM is perpendicular to the common chord of the circumscribed circles of triangle △ABC\triangle ABC and triangle △ADE\triangle ADE.
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