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incenters are concyclic, started with a cyclic ABCD, vietnamese IGO proposal

Source: Iranian Geometry Olympiad 2018 IGO Advanced p5

September 19, 2018
geometryincenterConcycliccyclic quadrilateral

Problem Statement

ABCDABCD is a cyclic quadrilateral. A circle passing through A,BA,B is tangent to segment CDCD at point EE. Another circle passing through C,DC,D is tangent to ABAB at point FF. Point GG is the intersection point of AE,DFAE,DF, and point HH is the intersection point of BEBE, CFCF. Prove that the incenters of triangles AGFAGF, BHFBHF, CHECHE, DGEDGE lie on a circle.
Proposed by Le Viet An (Vietnam)
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