The figure shows a circle with a chord AB
perpendicular to chord a CD at E. F is the midpoint of AB and G is the
midpoint of CD. A1, A2, A3, and A4,
are the areas of curvilinear triangles CEB, AEC, AED, and BED,
respectively. If A5 is the area of triangle EFG, prove that A1+ A2 - A3 - A4 = 8.A5 .