Step-by-step explanation:
NM is tangent to the circle at M and NL & NK are are secants.
[tex] \therefore \: MN^2 = NA \times NK \\ = 6 \times (6 + 5) \\ = 6 \times 11 \\ \therefore \: MN^2 = 66 \\ \therefore \: MN = \sqrt{66} \\ \therefore \: MN = 8.124 \\ \huge \red{ \boxed{ \therefore \: MN = 8.12}} \\ \\ MN^2 = NQ \times NL\\
66= 5.7\times (5.7+x)\\
\therefore\: (5.7+x)= \frac{66}{5.7}\\\\
\therefore\: 5.7+x = 11.6\\
\therefore\: x = 11.6 - 5.7\\
\huge \purple { \boxed{ \therefore\:x = 5.9}}
[/tex]
