Online Geometry Problem 869: Triangle, Median, Three Equilateral
Triangles, Collinear Points, Midpoint. Level: High School,
College,
Mathematics Education

The figure below shows a triangle ABC with
the median BM. If triangles ABD, BME, and BCF are equilateral, prove
that (1) D,E, and F are collinear; (2) E is the midpoint of DF. This entry contributed by Ajit Athle.