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find the size of angle AME

Source: China south east mathematical Olympiad 2012 day2 problem 7

July 17, 2013
trigonometrygeometrycircumcirclegeometry unsolved

Problem Statement

In △ABC\triangle ABC, point DD lies on side ACAC such that ∠ABD=∠C\angle ABD=\angle C. Point EE lies on side ABAB such that BE=DEBE=DE. MM is the midpoint of segment CDCD. Point HH is the foot of the perpendicular from AA to DEDE. Given AH=2−3AH=2-\sqrt{3} and AB=1AB=1, find the size of ∠AME\angle AME.
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