3. 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
A. inside the segment $M N$
B. inside the segment $F_{1} M$ or inside the segment $N F_{2}$
C. point $M$ or point $N$
D. cannot be determined
When $P$ is on the right branch of the hyperbola, let the point where the incircle of $\triangle P F_{1} F_{2}$ touches the side $F_{1} F_{2}$ be $S$, then we have $\left|M F_{1}\right|-\left|M F_{2}\right|=\left|P F_{1}\right|-\left|P F_{2}\right|=2 a \Rightarrow S$ coincides with $N$; similarly, when $P$ is on the left branch of the hyperbola, the point where the incircle of $\triangle P F_{1} F_{2}$ touches the side $F_{1} F_{2}$, $T$, coincides with $M$. Therefore, the answer is $C$.