Maximum Distance of a Sliding Triangle's Vertex

In right triangle $ABC$, $\angle C = 90^\circ$, $AC = 4$, and $BC = 2$. Points $A$ and $C$ lie on the $x$-axis and $y$-axis respectively. As $A$ slides along the $x$-axis, $C$ moves correspondingly along the $y$-axis. During this motion, find the maximum distance from point $B$ to the origin.