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concyclic wanted, AC=AD, orthocenter Puerto Rico Ibero TST 2010.4

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September 16, 2021
geometryConcyclicorthocenter

Problem Statement

Let ABCABC be an acute triangle such that AB>BC>ACAB>BC>AC. Let DD be a point different from CC on the segment BCBC, such that AC=ADAC=AD. Let HH be the orthocenter of triangle ABCABC and let A1A_1 and B1B_1 be the intersections of the heights from AA and BB to the opposite sides, respectively. Let EE be the intersection of the lines A1B1A_1B_1 and DHDH. Prove that BB, DD, B1B_1, EE are concyclic.
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