Answer: [tex]d=13.8[/tex]
Step-by-step explanation:
A line that cuts a circle at two points is called "secant".
There is a theorem known as "Intersecting Secant Theorem". This is the theorem you need to use to find the value of "d".
According the Intersecting Secant Theorem:
[tex](14)(14+20)=(16)(16+d)\\(14)(34)=(16)(16+d)[/tex]
Having this expression, the next step is to solve for "d":
Use Distributive property:
[tex]476=256+16d[/tex]
Subtract 256 from both sides:
[tex]476-256=-256+256+16d[/tex]
[tex]220=16d[/tex]
Divide both sides by 16:
[tex]\frac{220}{16}=\frac{16d}{16}\\\\13.75=d[/tex]
The value of "d" rounded to the nearest tenth is:
[tex]d=13.8[/tex]
