<s>[INST] In the given figure, it is given that $\triangle ABC$ is a right triangle with altitude $\overline {AD}$ and the perpendicular from $A$ to $BC$ cast a shadow $\overline {PX}$ which creates right triangles. In the figure, it is given that $\{AP\} = \{PB\}$ and $\triangle AXP$ is a 45-45-90 triangle. Let $AC=6$. How can we find the length of $AX$?[/INST]