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.