Answer:
[tex]x = 16.6\ cm[/tex]
Step-by-step explanation:
To answer this question use the secant line theorem.
If two secant segments are drawn towards a circle from an outer point, then the product of the length of the secant segment y and the length of its outer secant segment is equal to the product of the length of the other secant segment and its external secant segment.
This is:
[tex](12+6)*6 = (5+x)*5[/tex]
Now we solve the equation for the variable x
[tex]18*6 = 5*5+x*5[/tex]
[tex]108 = 25+5x[/tex]
[tex]5x = 108-25[/tex]
[tex]5x = 83[/tex]
[tex]x = \frac{83}{5}[/tex]
[tex]x = 16.6\ cm[/tex]
