Online Geometry Problem 809: Trisecting a Line Segment AB, Three Circles, Radius, Center. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows a line segment AB. Circles with radius AB and centers A and B cut at C and D. Circle with radius CA and center C cuts AC extended and BC extended at E and F, respectively. Prove that DE and DF trisect AB (i.e., AM = MN = NB).