Online Geometry
Problem 761: Scalene Triangle with an angle of 60
degrees, Euler Line, Equilateral Triangle. Level: High School, College,
Mathematics Education

The figure shows a scalene triangle ABC with
angle A = 60 degrees. If the Euler line intersects AB and AC at D and E,
respectively, prove that the triangle ADE is equilateral. This entry contributed by Ajit Athle.