In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D,$ such that $AD = AB$. Line segment $\overline{AD}$ is extended to $E,$ such that $CD = CE$ and $\angle DBE = \angle BAD$. Show that triangle $ACE$ is isosceles. please answer soon
+1005 This is a writing problem from AoPS Intro to Geometry.
If you doubt me, please know that I solved this a few weeks ago.
Do not cheat, and actually use the office hours.
