Question 38
As shown in Fig. 7.1, $\odot O_1$ and $\odot O_2$ are tangent externally at point $T$. The quadrilateral $ABCD$ is inscribed in $\odot O_1$. The lines $DA$ and $CB$ are tangent to $\odot O_2$ at points $E$ and $F$, respectively. $BN$, the bisector of $\angle ABF$, intersects the segment $EF$ at point $N$. Line $FT$ intersects the arc $AT$ (which does not contain $B$) at point $M$. Prove that $M$ is the excenter of $\triangle BCN$.
Fig. 7.1
Fig. 7.1