We have been given diagram of a circle and its secants. We are asked to find the value of x.
We will use secant-secant theorem to solve our given problem.
When two secants share a common end-point outside circle, then the product of one secant segment and its external segment is equal to the product of other secant segment and its external segment.
Using secant-secant theorem, we will get an equation:
[tex]6\cdot(12+6)=5\cdot (5+x)[/tex]
Let us solve for x.
[tex]6\cdot(18)=25+5x[/tex]
[tex]108=25+5x[/tex]
[tex]25+5x=108[/tex]
[tex]25-25+5x=108-25[/tex]
[tex]5x=83[/tex]
[tex]\frac{5x}{5}=\frac{83}{5}[/tex]
[tex]x=16.6[/tex]
Therefore, the value of x is 16.6 cm.
