KöMaL 2008 K188

The base $AB$ of an isosceles triangle ABC is extended beyond vertex $B$ by the length of the leg. The endpoint obtained is $C_1$. A perpendicular is erected onto the base $AB$ at vertex $A$. $C_2$ is the point on the perpendicular that lies in the same half plane as vertex $C$, at a distance from $A$ that equals the length of the leg. Given that the points $C_1$, $C$ and $C_2$ are collinear, find the angles of triangle ABC .