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2011 Japan Mathematical Olympiad Finals Problem 1

Source: Japanese MO Finals 2011

February 11, 2011
geometryanalytic geometrycircumcircletrigonometrypower of a pointradical axishumpty point

Problem Statement

Given an acute triangle ABCABC with the midpoint MM of BCBC. Draw the perpendicular HPHP from the orthocenter HH of ABCABC to AMAM. Show that AMā‹…PM=BM2AM\cdot PM=BM^2.
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