Geometry Problem 1070: Circle, Chord, Equilateral Triangle, Square, Rectangle, Area, Diameter, Perpendicular. Level: High School, SAT Prep, College, Mathematics Education

The figure shows a circle O, chords AB and CD meet at E so that triangles AED and BEC are equilateral. The diameter AB of circle O₁ is perpendicular to EE₁. AA₁A₂E, BB₁B₂E, and EE₁E₂E₃ are squares. If ODD₁D₂ is a rectangle so that DD₁ = 3OD, prove that the yellow shaded area is equal to the blue shaded area.