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Problem 584: Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms. Level: Mathematics Education, High School, College

The figure shows a cyclic quadrilateral ABCD with circumcenter O. Diagonals AC and BD meet at M. If E, F, G, and H are the circumcenters of triangles AMB, BMC, CMD, and AMD, respectively, prove that the quadrilaterals EFGH, OEMG, and OFMH are parallelograms.
 

Cyclic quadrilateral, Circumcircles
 

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