Go Geometry Problems

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


Home | SearchGeometry | Problems | All Problems | Visual Index | 581-590 | Quadrilateral | Cyclic Quadrilateral | Parallelogram | Circumcenter | Common Chord | Email | Post a comment or solution | By Antonio Gutierrez