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Rectangle, two circumcircles and centroid

Source: Problem 3 of Russian Regional Olympiad 2011, grade 11

September 1, 2011
geometryrectanglecircumcirclegeometry proposed

Problem Statement

Point KK lies on the circumcircle of a rectangle ABCDABCD. Line CKCK intersects line segment ADAD at point MM so that AM:MD=2AM:MD=2. OO is the center the rectangle. Prove that the centroid of triangle OKDOKD belongs to the circumcircle of triangle CODCOD. (Author: V. Shmarov)
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