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Online Geometry Problem 711: Rectangle, Midpoint, Angle, Concyclic Points, Cyclic Quadrilateral. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a rectangle ABCD, E midpoint of BC and F midpoint of CD. AE and BF meet at G. DE meets AF, BF at H, N. Prove that (1) angle AED = 2 angle BAE; (2) angle AFB = 2 angle DAF; (3) angle EAF +  angle GNH = 180 degrees; (4) Points A,G,N,H are concyclic.
 

Rectangle, Midpoints, Concyclic Points, Cyclic Quadrilateral
 

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