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Problem 586: Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency. Level: Mathematics Education, High School, College

The figure shows a cyclic quadrilateral ABCD with circumcenter O. Diagonals AC and BD meet at M. Let P be any point inside or outside the circle O. If E, F, G, and H are the circumcenters of triangles APB, BPC, CPD, and APD, respectively, prove that lines EG, FH, and MO are concurrent at the same point Q.
 

Cyclic Quadrilateral, Diagonals, Circumcenters, Any point, Concurrency
 

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