12. Let the left and right foci of the hyperbola be $F_{1}, F_{2}$, and the left and right vertices be $M, N$. If the vertex $P$ of $\triangle P F_{1} F_{2}$ is on the hyperbola, then the point where the incircle of $\triangle P F_{1} F_{2}$ touches the side $F_{1} F_{2}$ is $\qquad$.
12. Point $M$ or $N$ Hint: If $P$ is a point on the right branch, $E$, $F$, and $G$ are the points where the incircle touches the sides $P F_{1}$, $P F_{2}$, and $F_{1} F_{2}$, respectively, then $\left|F_{1} G\right|-\left|F_{2} G\right|=\left|P F_{1}\right|-\left|P F_{2}\right|=2 a$, i.e., $G$ and $N$ coincide. When $P$ is a point on the left branch, similarly, $G$ and $M$ coincide.