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A-angle bisector and B-foot of altitude

Source: 2021 Thailand Online MO P4 (Mock TMO contest)

April 6, 2021
geometry

Problem Statement

Let ABCABC be an acute triangle such that ∠B>∠C\angle B > \angle C. Let DD and EE be the points on the segments BCBC and CACA, respectively, such that ADAD bisects ∠A\angle A and BE⊥ACBE\perp AC. Finally, let MM be the midpoint of the side BCBC. Suppose that the circumcircle of △CDE\triangle CDE intersects ADAD again at a point XX different from DD. Prove that ∠XME=90∘−∠BAC\angle XME = 90^{\circ} - \angle BAC.
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