Go Geometry Problem Problem 464: Square, Center, Arc, Angle, 120 Degrees

Problem 464. The figure shows a square ABCD with center O. It contains arcs AEFC, BFD, and BED drawn with centers at D, A and C, respectively. Lines CE and FD meet at G. Prove that the measure of angle DOG is 120 degrees.
 

Square, Center, Arc, 120 degrees
 

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