KöMaL 2024 C1794

Circles $k_1$ and $k_2$ are externally tangent to each other at point $A$, circles $k_2$ and $k_3$ are externally tangent to each other at point $B$, and finally circles $k_1$ and $k_3$ are externally tangent to each other at point $C$. Line $AB$ intersect circle $k_3$ at point $D$ (different from $B$). Prove that line segments $AC$ and $CD$ are perpendicular to each other.