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circumcentres and orthocentres

Source: 2014 China Tst 3 Day1 Q1

March 26, 2014
geometrycircumcirclegeometric transformationhomothetytrigonometrycyclic quadrilateralgeometry proposed

Problem Statement

Let the circumcenter of triangle ABCABC be OO. HAH_A is the projection of AA onto BCBC. The extension of AOAO intersects the circumcircle of BOCBOC at A′A'. The projections of A′A' onto AB,ACAB, AC are D,ED,E, and OAO_A is the circumcentre of triangle DHAEDH_AE. Define HB,OB,HC,OCH_B, O_B, H_C, O_C similarly. Prove: HAOA,HBOB,HCOCH_AO_A, H_BO_B, H_CO_C are concurrent
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