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tangent circles wanted, cyclic pentagon related (Kharkiv City X 2013 - Ukr)

Source:

March 13, 2020
tangent circlesgeometrycirclesCyclicpentagonKharkiv

Problem Statement

The pentagon ABCDEABCDE is inscribed in the circle ω\omega. Let TT be the intersection point of the diagonals BEBE and ADAD. A line is drawn through the point TT parallel to CDCD, which intersects ABAB and CECE at points XX and YY, respectively. Prove that the circumscribed circle of the triangle AXYAXY is tangent to ω\omega.
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