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Equal angles in trapezoid where sum of the bases = diagonal

Source: XIV Rioplatense Mathematical Olympiad (2005), Level 3

July 26, 2011
geometrytrapezoidgeometric transformationreflectiongreatest common divisorparallelogramcircumcircle

Problem Statement

In trapezoid ABCDABCD, the sum of the lengths of the bases ABAB and CDCD is equal to the length of the diagonal BDBD. Let MM denote the midpoint of BCBC, and let EE denote the reflection of CC about the line DMDM. Prove that ∠AEB=∠ACD\angle AEB=\angle ACD.
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