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HMMT Geometry 2019/8: Nine-point center on BC

Source:

February 17, 2019
HMMTgeometry

Problem Statement

In triangle ABCABC with AB<ACAB < AC, let HH be the orthocenter and OO be the circumcenter. Given that the midpoint of OHOH lies on BCBC, BC=1BC = 1, and the perimeter of ABCABC is 6, find the area of ABCABC.
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