Math: Geometry Problems 583. Activate Flash plug-in or JavaScript and reload to view the Math Geometry Problems, online geometry classes, Geometry help, College, Online Learning.  Site created and maintained by Antonio Gutierrez.

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
 

Home | Search | Geometry | Problems | All Problems | Visual Index | 581-590 | Areas | Octagon | Quadrilateral | Parallelogram | Area of a Parallelogram | Circumcenter | Common Chord | Email | Post a comment or solution