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OD _|_ AB - All-Russian MO 2000 Regional (R4) 9.7

Source:

September 26, 2024
geometryperpendicular

Problem Statement

On side ABAB of triangle ABCABC, point DD is selected. Circle circumscribed around triangle BCDBCD, intersects side ACAC at point MM, and the circumcircle of triangle ACDACD intersects the side BCBC at point N N (M,N≠CM,N \ne C). Let OO be the circumcenter of the triangle CMNCMN. Prove that line ODOD is perpendicular to side ABAB.
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