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yet another geometry

Source: MDA TST 2016 P11!

March 26, 2019
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. Circle with diameter ABAB intersects CACA, CBCB, DADA, and DBDB in EE, FF, GG, and HH, respectively (all different from AA and BB). The lines EFEF and GHGH intersect in II. Prove that the bisector of ∠GIF\angle GIF and the line CDCD are perpendicular.
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