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Iberoamerican Math Olympiad 2017 problem 2

Source: Iberoamerican Math Olympiad 2017 problem 2

September 20, 2017
geometrycircumcircleinternational competitionsIberoamerican

Problem Statement

Let ABCABC be an acute angled triangle and Γ\Gamma its circumcircle. Led DD be a point on segment BCBC, different from BB and CC, and let MM be the midpoint of ADAD. The line perpendicular to ABAB that passes through DD intersects ABAB in EE and Γ\Gamma in FF, with point DD between EE and FF. Lines FCFC and EMEM intersect at point XX. If ∠DAE=∠AFE\angle DAE = \angle AFE, show that line AXAX is tangent to Γ\Gamma.
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