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Trapezium and isosceles triangles

Source: Polish Junior Math Olympiad 2019 Finals

October 23, 2020
geometrytrapezoid

Problem Statement

Let ABCDABCD be the isosceles trapezium with bases ABAB and CDCD, such that AC=BCAC = BC. The point MM is the midpoint of side ADAD. Prove that ∢ACM=∢CBD\sphericalangle ACM = \sphericalangle CBD.
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