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OK// AB wanted in isosceles trapezoid (2021 Kyiv City MO Round2 10.4.1)

Source:

February 15, 2021
geometrytrapezoidisoscelesparallel

Problem Statement

Let ABCDABCD be an isosceles trapezoid, AD=BCAD=BC, AB∥CDAB \parallel CD. The diagonals of the trapezoid intersect at the point OO, and the point MM is the midpoint of the side ADAD. The circle circumscribed around the triangle BCMBCM intersects the side ADAD at the point KK. Prove that OK∥ABOK \parallel AB.
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