Problem 335. Cyclic Quadrilateral,
Perpendicular to sides, Concyclic points

The figure shows a cyclic
quadrilateral ABCD. AE and BF are perpendicular to CD. CG. and DH are
perpendicular to AB. Prove that (1) AE.BF = CG.DH, (2) Points E,
F, G, H are concyclic.