Online Geometry Problem 755: Equilateral Triangle, Circumcircle, Chord, Arc, Midpoints, Perpendicular. Level: High School, College, Mathematics Education

The figure shows an equilateral triangle ABC with circumcircle O. E is the midpoint of a chord AD and F is the midpoint of arc BC. If FG is perpendicular to CD, prove that the triangle BEG is equilateral. This entry contributed by Ajit Athle.