4. $P$ is inside rectangle $A B C D$. $P A=2, P B=3$, and $P C=10$. Find $P D$.
Solution: $\square$
Draw perpendiculars from $P$ to $E$ on $A B, F$ on $B C, G$ on $C D$, and $H$ on $D A$, and let $A H=B F=w, H D=F C=x, A E=D G=y$, and $E B=G C=z$. Then $P A^{2}=w^{2}+y^{2}, P B^{2}=w^{2}+z^{2}, P C^{2}=x^{2}+z^{2}$, and $P D^{2}=x^{2}+y^{2}$. Adding and subtracting, we see that $P D^{2}=P A^{2}-P B^{2}+P C^{2}=95$, so $P D=\sqrt{95}$.