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Problem 4, Iberoamerican Olympiad 2011

Source:

October 2, 2011
geometryvectorparallelogramcircumcirclerhombustrigonometryperpendicular bisector

Problem Statement

Let ABCABC be an acute-angled triangle, with AC≠BCAC \neq BC and let OO be its circumcenter. Let PP and QQ be points such that BOAPBOAP and COPQCOPQ are parallelograms. Show that QQ is the orthocenter of ABCABC.
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