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. A_{1}, A_{2}, A_{3}, and A_{4},
are the areas of curvilinear triangles CEB, AEC, AED, and BED,
respectively. If A_{5} is the area of triangle EFG, prove that A_{1}+ A_{2}  A_{3}  A_{4} = 8.A_{5} .
