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Source: KöMaL A. 771

March 20, 2022
geometrykomal

Problem Statement

Let ω\omega denote the incircle of triangle ABC,ABC, which is tangent to side BCBC at point D.D. Let GG denote the second intersection of line ADAD and circle ω.\omega. The tangent to ω\omega at point GG intersects sides ABAB and ACAC at points EE and FF respectively. The circumscribed circle of DEFDEF intersects ω\omega at points DD and M.M. The circumscribed circle of BCGBCG intersects ω\omega at points GG and N.N. Prove that lines ADAD and MNMN are parallel.
Proposed by Ágoston Győrffy, Remeteszőlős
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