IR-MO 2002 Problem 7

In triangle $ABC$ , $AD$ is angle bisector ( $D$ is on $BC$ ) if $AB+AD=CD$ and $AC+AD=BC$ , what are the angles of $ABC$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.