Question 99
Suppose point $P$ is inside quadrilateral $A B C D$ such that
$$
\begin{aligned}
& \angle P A B = \angle P D A \\
& \angle P A D = \angle P D C, \\
& \angle P B A = \angle P C B, \text{ and } \\
& \angle P B C = \angle P C D
\end{aligned}
$$
If $P A = 4$, $P B = 5$, and $P C = 10$, compute the perimeter of $A B C D$.
$$
\begin{aligned}
& \angle P A B = \angle P D A \\
& \angle P A D = \angle P D C, \\
& \angle P B A = \angle P C B, \text{ and } \\
& \angle P B C = \angle P C D
\end{aligned}
$$
If $P A = 4$, $P B = 5$, and $P C = 10$, compute the perimeter of $A B C D$.