KöMaL 2019 B5008

A circle $k_A$ is centred at $A$, and a circle $k_B$ is centred at $B$. Line $l_1$ touches $k_A$ at $A_1$ and $k_B$ at $B_1$. Line $l_2$ touches $k_A$ at $A_2$ and $k_B$ at $B_2$. Prove that the orthogonal projections of the line segments $A_1A_2$ and $B_1B_2$ onto the line $AB$ are of equal length.