Go Geometry Problems

Problem 583: Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Areas. Level: Mathematics Education, High School, College

The figure shows a quadrilateral ABCD. Diagonals AC and BD meet at O. If E, F, G, and H are the circumcenters of triangles AOB, BOC, COD, and AOD, respectively, prove that (1) EFGH is a parallelogram, (2) Area of the octagon AEBFCGDH is double the area EFGH.
 

Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Area
 

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