KöMaL 2022 B5255

Vertex $A$ of a triangle $ABC$ is reflected about vertex $B$, $B$ is reflected about $C$, and $C$ is reflected about $A$. The reflections are points $C_1$, $A_1$ and $B_1$, respectively. Show that there exists a triangle with sides of lengths $AA_1$, $BB_1$ and $CC_1$.