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Another cyclic quadrilateral in CGMO

Source: China Girls Math Olympiad 2019 Day 2 P3

August 13, 2019
geometrycyclic quadrilateral

Problem Statement

Let DFGEDFGE be a cyclic quadrilateral. Line DFDF intersects EGEG at C,C, and line FEFE intersects DGDG at H.H. JJ is the midpoint of FG.FG. The line ℓ\ell is the reflection of the line DEDE in CH,CH, and it intersects line GFGF at I.I. Prove that C,J,H,IC,J,H,I are concyclic.
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