KöMaL 2023 B5297

In a triangle $ABC$, $\angle BAC =2\angle CBA$. Let $A'$, $B'$, $C'$ denote interior points of sides $CA$, $AB$ and $BC$, respectively, such that triangle $A'B'C'$ is similar to triangle $ABC$. Show that the angle bisectors of angles $BAC$ and $B'A'C'$ intersect each other on the line segment $B'C'$.