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Czech-Polish-Slovak Match 2016

Source: Czech-Polish-Slovak Match 2016,P3,day 2

July 12, 2016
geometry proposedgeometrycircumcircleCentroid

Problem Statement

Let ABCABC be an acute-angled triangle with AB<ACAB < AC. Tangent to its circumcircle Ω\Omega at AA intersects the line BCBC at DD. Let GG be the centroid of △ABC\triangle ABC and let AGAG meet Ω\Omega again at H≠AH \neq A. Suppose the line DGDG intersects the lines ABAB and ACAC at EE and FF, respectively. Prove that ∠EHG=∠GHF\angle EHG = \angle GHF.(Slovakia)
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