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AC, BF, DE concurrent

Source: APMO 2020 Problem 1

June 9, 2020
geometryconcurrency

Problem Statement

Let Γ\Gamma be the circumcircle of △ABC\triangle ABC. Let DD be a point on the side BCBC. The tangent to Γ\Gamma at AA intersects the parallel line to BABA through DD at point EE. The segment CECE intersects Γ\Gamma again at FF. Suppose BB, DD, FF, EE are concyclic. Prove that ACAC, BFBF, DEDE are concurrent.
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