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(con)cyclic wanted, other circumcircle related (2012 Kyiv City MO 9.5 10.4)

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August 1, 2020
geometryConcycliccyclic quadrilateralcircumcircle

Problem Statement

The triangle ABCABC with AB>ACAB> AC is inscribed in a circle, the angle bisector of ∠BAC\angle BAC intersects the side BCBC of the triangle at the point KK, and the circumscribed circle at the point MM. The midline of ΔABC\Delta ABC, which is parallel to the side ABAB, intersects AMAM at the point OO, the line COCO intersects the line ABAB at the point NN. Prove that a circle can be circumscribed around the quadrilateral BNKMBNKM.
(Nagel Igor)
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