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Trapezoid angle chase

Source: Tuymaada 2021 Senior P2

July 28, 2021
geometry

Problem Statement

In trapezoid ABCDABCD,MM is the midpoint of the base ADAD.Point EE lies on the segment BMBM.It is known that ∠ADB=∠MAE=∠BMC\angle ADB=\angle MAE=\angle BMC.Prove that the triangle BCEBCE is isosceles.
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