Question

What is the value of d to the nearest tenth?

Answer 1

Answer: $d=13.8$

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:

$(14)(14+20)=(16)(16+d)\\(14)(34)=(16)(16+d)$

Having this expression, the next step is to solve for "d":

Use Distributive property:

$476=256+16d$

Subtract 256 from both sides:

$476-256=-256+256+16d$

$220=16d$

Divide both sides by 16:

$\frac{220}{16}=\frac{16d}{16}\\\\13.75=d$

The value of "d" rounded to the nearest tenth is:

$d=13.8$