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Intersection point on circle

Source: VII Caucasus Olympiad, Senior, Day1 P4.

March 13, 2022
geometry

Problem Statement

Let ω\omega is tangent to the sides of an acute angle with vertex AA at points BB and CC. Let DD be an arbitrary point onn the major arc BCBC of the circle ω\omega. Points EE and FF are chosen inside the angle DACDAC so that quadrilaterals ABDFABDF and ACEDACED are inscribed and the points A,E,FA,E,F lie on the same straight line. Prove that lines BEBE and CFCF intersectat ω\omega.
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