Suppose that the question is instead 'Is LN tangent to circle M?' (since BC is not in the image).
If LN is tangent to circle M, the angle between LN and NM has to be equal to 90°.
In other words, LNM has to be a right triangle.
If LMN is a right triangle, it has to verify the Pythagoras theorem
[tex]\begin{gathered} LM^2=LN^2+NM^2 \\ \Rightarrow12^2=9^2+6^2 \\ \Rightarrow144=81+36 \\ \Rightarrow144=117!!! \end{gathered}[/tex]
Therefore, LMN is not a right triangle and The answer is No, because 6^2+9^2<12^2
