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angle chasing, in terms of angles (Greece junior 2019 p2)

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February 23, 2020
geometryanglesaltitudes

Problem Statement

Let ABCABC be an acute-angled triangle with AB<ACAB<AC. Let DD be the midpoint of side BCBC and BE,CZBE,CZ be the altitudes of the triangle ABCABC. Line ZEZE intersects line BCBC at point OO. (i) Find all the angles of the triangle ZDEZDE in terms of angle ∠A\angle A of the triangle ABCABC (ii) Find the angle ∠BOZ\angle BOZ in terms of angles ∠B\angle B and ∠C\angle C of the triangle ABCABC
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