Go Geometry Problem 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. 

Cyclic quadrilateral, perpendicular to sides

 

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