Pr. 1027 Gogeometry, https://gogeometry.blogspot.com/2014/07/geometry-problem-1027-triangle-double.html

 Let D, E be points onto the sides BC, AB of triangle ABC so that <CAD=2<BAD=4x, AD=AC, DE=DC, find <ABC.

Proof:
If F is reflection of E about AD, then triangle CDF is equilateral, and easy angle calculation shows x=10, wherefrom <ABC=50.