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It's a trapezoid

Source: Kyiv City MO 2024 Round 1, Problem 11.2

January 28, 2024
geometrytrapezoid

Problem Statement

ABCDABCD is a trapezoid with BC∥ADBC\parallel AD and BC=2ADBC = 2AD. Point MM is chosen on the side CDCD such that AB=AMAB = AM. Prove that BM⊥CDBM \perp CD.
Proposed by Bogdan Rublov
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