Answer:
The value of n is 4.
Step-by-step explanation:
Theorem of intersection of two cords : If two cords AB and CD intersecting at point P, then
[tex]|AP|\times |PB|=|CP|\times |PD|[/tex]
Using the theorem of intersection of two cords, we get
[tex](n-2)\times 16=8\times (n+8)[/tex]
Use distribution property,
[tex]16n+32=8n+64[/tex]
[tex]16n-8n=64-32[/tex]
[tex]8n=32[/tex]
Divide both sides by 8.
[tex]n=\frac{32}{8}[/tex]
[tex]n=4[/tex]
Therefore the value of n is 4.
