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IL-GILLIS 2020 Problem 5

    Two triangles ACE,BDFACE, BDF are given which intersect at six points: G,H,I,J,K,LG, H, I, J, K, L as in the picture. It is known that in each of the quadrilaterals ABIK,BCJL,CDKG,DELH,EFGIABIK ,BCJL ,CDKG ,DELH ,EFGI it is possible to inscribe a circle. Is it possible for the quadrilateral FAHJFAHJ is also circumscribed around a circle?

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    2020gillisP5.jpg

    Dataset text AI-MO AoPS. Quoted with source.

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