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.