Online Geometry Problem 811: Trisecting a Line Segment AB with four Circles and one Line, Radius, Center, Diameter, Chord. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows a line segment AB. Circle with center A and radius AB cuts BA extended at C. Circle with center B and radius BC cuts AB extended at D. Circle with center D and radius DA cuts circle A at E. Circle with center E and radius EA cuts AB at F. Prove that F trisects AB (i.e., AF = AB / 3).