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trapezoid AD//BC, AB = BC = BD, altitude BK cuts AC at M, <CDM?

Source: 2012 Oral Moscow Geometry Olympiad grades 8-9 p1

September 8, 2019
geometrytrapezoidanglesequal segments

Problem Statement

In trapezoid ABCDABCD, the sides ADAD and BCBC are parallel, and AB=BC=BDAB = BC = BD. The height BKBK intersects the diagonal ACAC at MM. Find ∠CDM\angle CDM.
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