Problem 578: Circle, Perpendicular Chords, Midpoints, Curvilinear Triangle, Area, 90 Degrees. Level: Math Education, High School, SAT Prep, College

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 .