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through the midpoint of $OH$

Source: 2012 CWMO P5

September 30, 2012
geometrycircumcircletrapezoidratioparallelogram

Problem Statement

OO is the circumcenter of acute ΔABC\Delta ABC, HH is the Orthocenter. ADBCAD \bot BC, EFEF is the perpendicular bisector of AOAO,D,ED,E on the BCBC. Prove that the circumcircle of ΔADE\Delta ADE through the midpoint of OHOH.