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two circumcenters and one orthocenter, vertices of parallelogram

Source: Greece JBMO TST 2015 p2

April 29, 2019
geometrycircumcircleparallelogramorthocenter

Problem Statement

Let ABCABC be an acute triangle inscribed in a circle of center OO. If the altitudes BD,CEBD,CE intersect at HH and the circumcenter of △BHC\triangle BHC is O1O_1, prove that AHO1OAHO_1O is a parallelogram.
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