Question

Find the values of x and y using the given chord, secant , and tangent lengths.x=y=

Answer 1

Let's find the values of x and y.

Take the following steps:

Step 1:

Apply the equation below to find x

`x^2=2(2+10)`

Let's solve for x.

Apply distributive property:

`\begin{gathered} x^2=2(2)+2(10) \\ \\ x^2=4+20 \\ \\ x^2=24 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{x^2}=\sqrt[]{24} \\ \\ x=4.9 \end{gathered}`

Step 2:

Apply the equation below to find the value of y

`x^2=4(4+y)`

Substitute 24 for x² and find the value y:

`\begin{gathered} 24=4(4+y)^{} \\ \\ 24=4(4)+4(y) \\ \\ 24=16+4y \\ \\ \text{Subtract 16 from both sides:} \\ 24-16=16-16+4y \\ \\ 8=4y \end{gathered}`

Divide both sides by 4:

`\begin{gathered} (8)/(4)=(4y)/(4) \\ \\ 2=y \\ \\ y=2 \end{gathered}`

Therefore, we have:

x = 4.9

y = 2

ANSWER:

x = 4.9