<s>[INST] In a given triangle $ABC$, the angle bisector theorem states that the angle bisector of $\angle A$ will divide the opposite side, $BC$, into segments of length $x$ and $y$, such that

$$\frac{x}{y}=\frac{AB}{AC}.$$

If $AB=10$, $AC=8$, and $BC=16$, what is $x$?[/INST]