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collinearity wanted, 3 circumcircles related (Kharkiv City XI 2018 - Ukr)

Source:

March 21, 2020
geometrycircumcircleparallelKharkivcollinear

Problem Statement

The line ℓ\ell parallel to the side BCBC of the triangle ABCABC, intersects its sides AB,ACAB,AC at the points D,ED,E, respectively. The circumscribed circle of triangle ABCABC intersects line ℓ\ell at points FF and GG, such that points F,D,E,GF,D,E,G lie on line ℓ\ell in this order. The circumscribed circles of the triangles FEBFEB and DGCDGC intersect at points PP and QQ. Prove that points A,PA, P and QQ are collinear.
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