To prove this claim, let a, b, and c be the lengths of HG, EG
and EH, respectively. Given triangle GEH is a right triangle,
then by using the pythagorian theorem gives us or It can be
noted that length FG = BG = HG = a since all are radii of the
circle as shown above.Therefore length EF = FG - EG = a - b and
length BE = BG + GE = a + b. It follows that area of rectangle
BCDE = (base)*(height). area of rectangle BCDE = (BE)*(ED) area
of rectangle BCDE = (BE)*(EF) given length EF = ED area of
rectange BCDE = (a + b)(a - b) as noted above area of rectange
BCDE = area of rectangle BCDE == area of square HEKL as shown
above. Back to quadrature of rectange page