

Geometry Problem 1070: Circle,
Chord, Equilateral Triangle, Square, Rectangle, Area,
Diameter, Perpendicular. Level: High School, SAT Prep, College, Mathematics Education
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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 O_{1} is perpendicular to EE_{1}. AA_{1}A_{2}E, BB_{1}B_{2}E,
and EE_{1}E_{2}E_{3} are squares. If ODD_{1}D_{2} is a rectangle so that
DD_{1} =
3OD, prove that the yellow shaded area is equal to the blue
shaded area.







