9. (HUN 3) The incenter of the triangle $A B C$ is $K$. The midpoint of $A B$ is $C_{1}$ and that of $A C$ is $B_{1}$. The lines $C_{1} K$ and $A C$ meet at $B_{2}$, the lines $B_{1} K$ and $A B$ at $C_{2}$. If the areas of the triangles $A B_{2} C_{2}$ and $A B C$ are equal, what is the measure of angle $\angle C A B$?